Strojni{ki vestnik 48(2002)3, Journal of Mechanical Engineering 48(2002)3, ISSN ISSN UDK :53.08 UDC

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1 Strojni{ki vestnik 48(2002)3, Journal of Mechanical Engineering 48(2002)3, ISSN ISSN UDK :53.08 UDC :53.08 Strokovni ~lanek (1.04) Jurkovi~ J., [ali S.: Identifikacija dinai~nih lastnosti - The Speciality Dynaic paper Properties (1.04) Identifikacija dinai~nih lastnosti sestavljenih nosilnih strojnih delov The Dynaic Properties of Coposite Supporting Parts for Machines Jo`e Jurkovi~ - Sao [ali Cilj raziskave je bila definicija etode za prierjalno erjenje dinaiènih lastnosti lepljenih stenskih eleentov (sestavljenih plošè), ki so naenjeni gradnji nosilnih delov strojev in naprav. Metoda oogoèa razeroa hitro in zanesljivo prierjanje dinaiènih lastnosti, toèneje aplitud, frekvenc in dušenja odalnih naèinov sestavljenih plošè. Vstopni signal pri doloèanju frekvenènega odziva sestavljenih plošè je poenil ehanski ipulz, erjen z erilniko pospeška, izstopni signal pa je bil rezultirajoèi zvoèni tlak na razdalji 1 od preizkušane plošèe. Uporabnost etode je ocena (i) izer ter ateriala sten, (ii) userjenosti jedra in (iii) vrste polnila pri izbiri optialne strukture sestavljene plošèe za dano situacijo Strojniški vestnik. Vse pravice pridržane. (Kljuène besede: plošèe sestavljene, lastnosti dinaiène, ugotavljanje lastnosti, etode erilne) Our ai was to define a ethod for coparing the easureents of the dynaic properties of glued wall eleents (coposite plates), intended for constructing the supporting parts of achine tools and devices. The ethod enables a relatively fast and reliable coparison of the dynaic properties: ore precisely of the aplitudes, the frequencies and the daping of the corresponding odes of the coposite plates. In the frequency response function (FRF) easureents the input signal was a echanical ipulse, easured by an acceleroeter, and the output signal was the resulting sound pressure at a distance of 1 fro the specien. The applicability of the ethod is an estiation of (i) the diensions and the aterial of the walls, (ii) the core orientation, and (iii) the type of filling used in the optiu construction of coposite plates for a given situation Journal of Mechanical Engineering. All rights reserved. (Keywords: coposite plates, dynaic properties, identification of properties, easureent ethods) 0 UVOD Poveèanje natanènosti izdelave in krajšanje izdelovalnih krogov narekujeta nenehen razvoj posaeznih sklopov obdelovalnih strojev in naprav ([1] in [2]). Izboljšani rezalni ateriali in spreenjeni pogonski sistei zagotavljajo vse veèje obdelovalne hitrosti. Tej useritvi orajo slediti tudi podajalne in strežne naprave ([3] in [4]). Vsi dinaièni sklopi strojev in naprav so vgrajeni v nosilnih delih, ki prevzeajo statiène in dinaiène obreenitve zaradi obdelovalnega postopka [5]. Obièajni ateriali s svojii priarnii lastnosti poenijo predvse na podroèju dinaiènega odziva doloèeno oejitev. Izhajajoè iz teh ugotovitev, se za najrazliènejše dele strojev in naprav vse veè uporabljajo razlièni drugaèni ateriali ([6] do [8]). Izboljšanje dinaiènih lastnosti poeni zagotavljanje dinaiène togosti in dušenja, ki v konèni fazi poenita pozitiven vpliv na natanènost obdelovanca. 0 INTRODUCTION Both an increase in the accuracy and a reduction in the ties needed for anufacturing processes dictate the developent of the individual parts of achine tools and devices ([1] and [2]). Iproveents on cutting tools and advances in achine-tool drives ean higher achining speeds. This is a trend that ust be followed by feeding and anipulating devices ([3] and [4]). All the dynaic joints of achine tools and devices are built into their supporting parts, which statically and dynaically sustain the resulting loading that results fro the achining process [5]. Due to their inherent properties any conventional aterials are liited in ters of their dynaic response. Therefore, a variety of alternative aterials for achine parts are taking their place ([6] to [8]). Iproving the dynaic properties eans ensuring the dynaic stiffness and daping, both of which can increase the accuracy of the workpiece. stran 143

2 Skladno s te so bili tudi na Fakulteti za strojništvo v Ljubljani opravljeni razvojnoraziskovalni koraki na podroèju sestavljenih aterialov in njihove uporabnosti za gradnjo nosilnih delov ([9] do [11]). Za identifikacijo dinaiènih lastnosti preskušancev so uporabili sestavljene plošèe [9] v razlièicah, katerih osnova je sheatsko prikazana na sliki 1, njihove znaèilnosti pa v preglednici 1. Sestavljene plošèe z debelino jedra 20 in ploskovno razsežnostjo 300 x 500 so bile izdelane iz jeklene in aluinijaste ploèevine z debelino 1 in 2. Jedro, ki predstavlja vesni del (zlepljen s stenaa), je trapezno strukturirana ploèevina, strina trapeznih stranic jedra pa je 60. Glede na najveèjo izero eleenta (500 ) je bilo jedro vzdolžno ali preèno userjeno (sl. 1). Spodnji del slike 1 prikazuje prier, ko je ed stenaa oziroa jedro sestavljene plošèe polnilo (poliestrski beton, poliuretansko polnilo). At the Faculty of Mechanical Engineering in Ljubljana we investigated soe coposite aterials for use as supporting parts [9] to [11]. For the identification of the dynaic properties we used coposite plates [9] of different shapes. These plates are shown scheatically in Figure 1, and their characteristics are presented in Table 1. The coposite plates, with a core thickness of 20 and surface diensions of 300 x 500, were ade of steel and aluiniu plates with thicknesses of 1 and 2 illietres. The core, which is glued to both flatsheets, is a etal plate with the profile of a trapezoid and 60 side angles. The longest diension of the eleent (500 ) was oriented longitudinally or transversally (see Figure 1). The lower part of Figure 1 shows the coposite with a filling (polyester concrete, polyurethane) between the flatsheets and the core. 300 v precno / transversally 20 t v vzdolzno / longitudinally p 500 t polnilo / filling Sl. 1. Analizirane sestavljene plošèe Fig. 1. Analyzed coposite plates Preglednica 1. Znaèilnosti analiziranih sestavljenih plošè Table 1. Characteristics of the analyzed coposite plates oznaka label t p useritev jedra core orientation polnilo filling JE1V 1 1 vzdolžna / longitudinal / JE1P 1 1 preèna / transversal / JE2V 2 2 vzdolžna / longitudinal / JE2P 2 2 preèna / transversal / JE1VBE 1 1 vzdolžna / longitudinal poliestrski beton polyester concrete JE1VPO 1 1 vzdolžna / longitudinal poliuretansko polnilo polyurethane stran 144

3 Eno od izhodišè gradnje sestavljenih plošè je bilo uporabiti èi anj ateriala in s prierno strukturo dobiti optialne nosilne lastnosti [12]. Pri te so uporabili osnovna pravila za t.i. lahko gradnjo nosilnih delov ([13] in [14]). Eleentarne dele so lepili v celoto, pri èeer so bili pri tehnologiji lepljenja upoštevani veljavni standardi [15]. Pred èaso opravljeno dinaièno testiranje lastnosti istih sestavljenih plošè [9] je bilo opravljeno z obièajno etodo, opisano v literaturi [16]. Na kratko, frekvenèni odziv lepljenih plošè je bil dobljen kot razerje ed rezultirajoèi pospeško (hitrostjo) in sinusno vzbujevalno silo na njihovi geoetrièni sredini. K eksperientalno dobljeni frekvenèni odzivo so bile sintetizirane ustrezne funkcije in iz njih ovrednotene dinaiène znaèilnosti posaeznih struktur [16]. Metoda je, tako glede potrebnih eksperientalnih naprav kakor tudi po sae izvajanju testiranj, zahtevna. Z naeno, da bi zagotovili preprostejšo, a še uporabno etodo, ki bi zagotovila vsaj prierjalno doloèanje dinaiènih lastnosti sestavljenih plošè, so tokrat uporabili eritve frekvenènega odziva z vstopni ehanski ipulzo, izstopni signal pa je bil zvoèni tlak na razdalji 1 od plošèe [17]. One of the construction targets for the coposite was to use the iniu aount of aterial in order to achieve the optiu support characteristics [12]. This was achieved with the use of the so-called light construction of supporting parts ([13] and [14]). The eleentary parts were glued into an assebly, where the basic rules of gluing technology were considered [15]. Recently perfored dynaic tests on the sae coposite plates [9] were perfored using a classical ethod described in the literature [16]. Briefly, a frequency response function (FRF) of the glued plates was obtained as a ratio of the resulting acceleration (velocity) to the sinusoidal input force at their geoetrical centre. The corresponding functions were synthesised to the easured FRFs and fro these functions the corresponding dynaic characteristics of the individual speciens were calculated [16]. In ters of experiental equipent and easureent procedure this ethod is coplex. In order to achieve a siple and useful ethod for coparative easureents of the dynaic characteristics we used FRF easureents with echanical excitation and the resulting sound pressure at 1 fro the specien [17]. zvoèno izolirana koora anechoic chaber penasta gua foa rubber elastièna vrvica nylonline preizkušanec specien ikrofon s predojaèevalniko icrophone with preaplifier vzbujevalna naprava excitation device pospeškoer acceleroeter penasta gua foa rubber napajalnik / power supply.. Bruel&Kjaer WB 1372 ojaèevalnik / aplifier MIKOJ PC: erilna kartica / acquisition board: nabojni ojaèevalnik / charge aplifier KISTLER 5001 National Instruents AT-A2150C (software LabWIEV).. ikrofon / icrophone: Bruel&Kjaer (tip / type 4188).. predojaèevalnik / preaplifier: Bruel&Kjaer.. (tip / type 2671) pospeškoer / acceleroeter: Bruel&Kjaer (tip / type 4374) Sl. 2. Merilna oprea Fig. 2. Measureent equipent PC stran 145

4 1 METODA IN REZULTATI 1.1 Merilna oprea in potek eritev Merilna oprea, ki je bila uporabljena pri doloèanju relativne dinaiène togosti preskušancev, je prikazana na sliki 2 [17]. Notranja stena koore je bila obložena s piraidno profilirano penasto guo, ki je prepreèevala odboje zvoka vzbujenega preskušanca. Preskušanci so bili ed eritvai vpeti na dveh elastiènih vrvicah, ki sta v danih razerah zagotavljali optialno vpetje pri erjenju njihovega frekvenènega odziva [16]. Mehansko vzbujanje preskušancev (sestavljenih plošè) je bilo izvedeno s tuljavo, podaljšani jedro in na njegove koncu pritrjeni erilniko pospeška, kakor je prikazano na sliki 3. Tu je prav tako prikazano esto vzbujanja na plošèah ter tipièna oblika ipulznega signala pri vzbujanju plošè, kar je bilo doseženo z ajhni koso penaste gue ed erilniko pospeška in preskušance. Mesto vzbujanja na geoetrièni sredini sestavljene plošèe je bilo izbrano na podlagi predhodnih testov odalnih oblik [9]. Zaradi sietriène oblike preskušancev je nareè to esto, vsaj za nekaj prvih odalnih naèinov, kraj relativno velikih aplitud, torej relativno velike zastopanosti odalnih naèinov. Po drugi strani pa kraj vzbujanja po naèrtih ni iel bistvenega vpliva na potek eritev, saj je bil njihov konèni rezultat razerje ed izstopni in vstopni signalo, ne pa absolutna vrednost enega ali drugega. V prieru vzbujanja na estu z relativno ajhno (veliko) zastopanostjo nekega odalnega naèina je bil logièno tudi odzivni zvoèni tlak za ta odalni naèin ajhen (velik). Med erjenje frekvenènega odziva (trajanje 1,024 s) preskušanec ni bil v stiku z 0,65-graski erilniko pospeška. Ta je bil uporabljen naesto erilnika sile, kar poeni, da so bile enote vstopnega signala /s 2. Zaradi stalne ase erilnika pospeška so seveda te enote sorazerne enota newton. Za vsak prekušanec je bilo opravljenih 20 posaeznih eritev frekvenènega odziva. Še pred analogno digitalno pretvorbo signala zvoènega tlaka so bile z nizkopasovni filtro na erilni kartici odstranjene vse frekvence, višje od 20 khz. Nastavljena frekvenca vzorèenja signalov f s je bila 16 khz, kar pa v praksi za dano erilno kartico poeni dejanskih 1,024 MHz [18]. Število digitalnih toèk N je bilo , kar pri nastavljeni frekvenci vzorèenja ustreza dolžini sneanja signalov T= 1,024 s [19]: 1 METHODS AND RESULTS 1.1 Measureent equipent and procedure Figure 2 shows the easureent arrangeent for deterining the relative dynaic stiffness of the speciens [17]. In order to prevent sound reflection due to the excited specien the inside of an anechoic chaber was lined with pyraid-shaped foa rubber. During the easureents of their FRF the speciens were suspended on two nylon lines, which provided optiu support under the experiental conditions [16]. As shown in Figure 3 the echanical excitation of the coposite plates was perfored with a coil, a long core and an acceleroeter fixed at the end of this core. Figure 3 also shows the position of the excitation and the shape of the ipulse input signal, which was achieved by inserting a sall piece of foa rubber between the acceleroeter and the specien. The position of excitation, at the geoetrical centre of the coposite plate, was selected on the basis of previous easureents of odal shapes [9]. Due to the syetrical shape of the speciens this position is a place of relatively high aplitudes, at least for the odes with low frequencies. In other words, these odes are well represented at the selected position of excitation. On the other hand, the position of excitation presuably did not significantly influence the easureents since the final result was a ratio of the output to the input signal and did not involve their absolute agnitudes. In the case of excitation at the position with a relatively low (high) proportion of soe ode, logically the response sound pressure for this ode is also low (high). During the FRF easureents with a duration of s the specien was not in contact with the 0.65-gra acceleroeter. This was used instead of a force transducer, which eans that the units of the input signal were /s 2. Because of the constant ass of the acceleroeter these units are proportional to Newtonian units. For each specien we perfored 20 individual FRF easureents. Using a low-pass filter as part of the data-acquisition board eant that frequencies higher than 20 khz were reoved fro the output signal (sound pressure) before the A/D conversion. The selected sapling frequency was 16 khz, which actually eans MHz for the data-acquisition board that we used [18]. The nuber of discrete saples N was , which resulted in a total length of the signal in the tie doain T= s [19]: T = N / f s (1). S tako izbranii paraetri sneanja signalov je bila zagotovjena kakovostna hitra Fourierjeva transforacija signalov. Pri tej ora nareè biti izpolnjen pogoj, da je število zajetih digitalnih toèk N enako 2 n, kjer je The selected conditions during the signal recording resulted in a qualitative fast Fourier transforation, where the nuber of discrete points N has to be 2 n, and n is a posi- stran 146

5 vzbujevalna naprava excitation device vzet spring esto vzbujanja place of excitation 500 tuljava coil pospeškoer acceleroeter jedro core 250 vzbujanje excitation 150 penasta gua foa rubber 300 /s 2 pospešek acceleration vstopni signal / vstopni signal input Input signal signal s èas tie Sl. 3. Vzbujevalna naprava, esto vzbujanja in oblika vstopnega signala Fig. 3. Excitation device, place of excitation and shape of input signal n celo pozitivno število (v naše prieru je n = 14) [19]. Vsak èasovni posnetek zvoènega tlaka je bil prograsko obdelan še z 80-odstotno t.i. okensko funkcijo ( Force window ), s katero dosežeo konèno vrednost aplitude signala enako niè [16]. Konèni rezultat eritve posaezne sestavljene plošèe je bil enostranski aplitudni frekvenèni spekter [19], torej povpreèje 20 posaeznih spektrov v enakih razerah erjenja. Aplitude izerjenega povpreènega frekvenènega odziva (t.j. frekvenènega odziva) so za vse eritve izražene v enotah Pa / (/s 2 ), in sicer v vrednostih srednjega kvadratnega pogreška. Za vsak izraziti resonanèni vrh v frekvenène odzivu je bila vrednost koherenène funkcije ed 0,95 in 1,0 za vse preskušance. tive integer (in our case n = 14) [19]. Each signal of sound pressure was processed by an 80%-Force window function in order to suppress the aplitudes of the signal at its end [16]. The final result of each easureent was a one-sided aplitude frequency spectru [19], an average of 20 individual spectra under the sae easureent conditions. For the average frequency spectru the aplitudes are expressed in units of Pa / (/s 2 ) in rs values. The value of the coherence function was between 0.95 and 1.0 for each resonant peak in the FRF for all speciens. 1.2 Analiza vpliva posaeznih lastnosti sestavljenih plošè na njihove dinaiène lastnosti Model 1.2. Analysis of the influence of particular properties of coposite plates on their dynaic characteristics Model Zvoèno polje okoli telesa, ki vibrira, lahko predstavio z vrsto krogelnih valov. Èe je telo v prierjavi z oddaljenostjo od esta opazovanja ajhnih izer, lahko zvoèni tlak na estu opazovanja zaradi teh valov opišeo z enaèbo [20]: Srcz pt () = sin zct ( -rp ) 4pr p The sound pressure around the vibrating body can be represented by a series of spherical waves. If the body is sall in coparison to the distance between it and the place of observation, then the sound pressure at the place of observation due to these waves is given by [20]: (2), stran 147

6 kjer so: S - najveèja eisija zraka v 3 /s, r - gostota zraka, c - hitrost zvoka, z=2p/l (l je valovna dolžina), r p - razdalja od izvora zvoènega tlaka, t - èas. Iz enaèbe (2) vidio, da se zvoèni tlak spreinja obratno sorazerno z oddaljenostjo od vira. Èe v enaèbi (2) p(t) nadoestio s p n (t), vstavio z=2p/l ter upoštevao, da je l=c/f (f poeni frekvenco zvoènega valovanja), dobio po okrajšavi za prier nedušenega nihanja: kjer p n (t) poeni nedušen zvoèni tlak p (t). Nedušen zvoèni tlak p n (t) je posledica ajhnega vira zvoka v obliki krogelnih valov, ed drugi pa je odvisen tudi od oddaljenosti od vira zvoka in od frekvence zvoènega valovanja. Reèeo lahko, da so izraziti frekvenèni vrhovi v frekvenène odzivu preskušancev posledica lastnih gibalnih oblik plošèe. Vsaki lastni gibalni obliki ustreza odalna aso, togost k, koeficient viskoznega dušenja b in površino sevanja A, kakor je prikazano na sliki 4. Tako je najveèja eisija zraka S v 3 /s glede na sliko 4 odvisna od ploskve s površino A in najveèje hitrosti nihanja te ploskve &X aks [20]: S r f f p'() n t = sin ( ct-r ) 2r p where S is the axiu rate of air eission of the sall source, r is the density of the air, c is the velocity of sound, z=2p/l (l is the wavelength), r p is the distance fro the sound source, and t is tie. We can see fro equation (2) that the sound pressure is inversely proportional to the distance fro the source. After replacing p(t) by p n (t) in equation (2) and taking into account that z=2p/l, and l=c/f (f is the frequency of sound waves), we obtain for the case of an undaped oscillation: 2 p p (3), c where p n (t) indicates the undaped sound pressure p (t). The undaped sound pressure p n (t) is a consequence of the sall sound source in the shape of spherical waves and it is also dependent on the distance fro the sound source and its frequency. We can say that the significant frequency peaks in the FRF of the speciens correspond to the noral odes of the coposite plates. Each noral ode has a odal ass, a stiffness k, a coefficient of viscous daping b, and a sound-radiating surface A, as shown in Figure 4. According to Figure 4, S in 3 /s depends on a ebrane with area A and the axiu velocity of the oscillation of this surface X & [20]: ax S = AX& aks (4). p ( t ) k I A b Xt ( ) A Sl. 4. Enoasni ehansko-akustièni siste z ebrano površine A Fig. 4. One-ass echanical-acoustical syste with ebrane of area A Ob upoštevanju enaèbe (4) v enaèbi (3), dobio Ploskev A niha v skladu z znaèilnosti ipulzno vzbujenega sistea asa - dušilka - vzet. Slika 4 kaže, da je brezasna ploskev A togo pripeta na aso. Torej je tlak p n (t) neposredno odvisen od, b in k, s katerii lahko opišeo lastno dušeno nihanje sisteov drugega reda. Èe je takšen siste vzbujen z ipulzo sile, je enaèba gibanja ploskve A [21]: AX& r f f p t f ct r aks '(, n = konst) = sin ( - ) 2rp Substituting Eq. (4) into Eq. (3), we obtain 2 p p (5). c Surface A vibrates according to the ipulsively excited syste consisting of a ass, daper and spring. Figure 4 shows that a assless ebrane with area A is rigidly connected to the ass. Thus, p n (t) is directly dependent on, b and k, which deterine the natural daped oscillation of second-order systes. If such a syste is excited by an ipulse then the equation of otion for surface A is [21]: stran 148

7 X&& () t + bx& () t + kx () t = 0 (6), kjer sta X && in X & pospešek in hitrost nihanja ploskve A. Rešitev enaèbe (6) je [21]: where X && and X & are the acceleration and velocity of surface A, respectively. The solution of equation (6) is [21]: d w0 t XZ dw0xz Xt () = e ( XZcos w0d t+ sin w0d t) w0d (7), kjer so: X where X Z and X & Z in X & Z zaèetna aplituda in zaèetna hitrost Z are the initial aplitude and the initial velocity of the oscillation at the oent the sa- nihanja ob prenehanju ipulzne otnje, w 0 = k/ lastna frekvenca nedušenega nihanja, ple disturbed: w 0 = k/ is the natural frequency of 2 2 w0d = 1 - d w0 frekvenca lastnega dušenega the undaped oscillation; w0d = 1 - d w0 is the nihanja in d = b/2 k brezdienzijski faktor natural frequency of the daped oscillation; and viskoznega dušenja [21]. V enaèbi (7) lahko zaèetno d = b/2 k is the diensionless viscous daping aplitudo štejeo za niè [21], zaèetno hitrost analiziranega sistea pa lahko izrazio z upoštevanje ipulznega stavka: factor [21]. In equation (7) the initial aplitude ay be considered as zero [21] and the initial velocity of the analysed syste can be expressed fro the condition of the conservation of oentu: I=G 2 -G 1 = ( X & -0) Z (8), kjer so I - ipulz sile, G 1 in G 2 pa gibalni kolièini na zaèetku in koncu delovanja ipulza. Hitrost gibanja ploskve A je pred delovanje ipulzne otnje niè, po prenehanju ipulza pa X & [21]. Torej je: Z where I is a echanical ipulse, and G 1 and G 2 are the oenta at the beginning and at the end of the echanical ipulse action, respectively. The velocity of surface A before the action of the echanical ipulse is zero, and after the action it is X & [21]. Thus: Z Enaèba (7) se tako poenostavi v: Iz enaèbe (5) vidio, da anjka èlen za opis dušenja zvoènega tlaka p (t) s slike 4, ki se je vsekakor pojavilo po ipulzne vzbujanju plošèe. Iz enaèbe (10) vidio, da je dušenje aplitude nihanja hibridnega sistea, ki seva zvoèni tlak p (t), 0 lahko opisano s èleno e - dw t. Èe upoštevao še, da frekvenca f poeni pravzaprav frekvenco lastnega dušenega nihanja, tj. w 0d /2p, lahko zapišeo: Equation (7) can be rewritten as: -d w0 t I X( t) = e ( sin w0dt) w (9). (10). We can see fro expression (5) that a description of the daping of the sound pressure p (t) fro Figure 4 is not included. The daping definitely occurred after the ipulse excitation of the coposite plates. Fro equation (10) it is evident that the daping of the oscillation of a hybrid syste, which radiates sound pressure p (t), 0 can be expressed by e - dw t. Considering also that the frequency f is actually a natural frequency of the daped oscillation (i.e., w 0d /2p), we can write: æ 0t AX& dw aks rw0d w ö - 0d p'( t, w (11). 0d = konst) = e sin ( ct-rp ) ç 4 rp c è p ø Iz enaèbe (10) lahko izpeljeo prvi odvod Fro equation (10) we can calculate the first derivative of the aplitude of oscillation, which eans the velocity aplitude nihanja in tako dobio izraz za hitrost nihanja dušenega ehanskega sistea: of the daped oscillation of the echanical syste: Najveèja hitrost nihanja ploskve A se pojavi na zaèetku nihanja dušenega hibridnega sistea: X& = I Z / 0t I 0 X& -dw d w () t = e ( cosw0dt- sin t) I w0d (12). w0d The axiu velocity of oscillation of surface A occurs at the beginning of oscillatory otion of the daped hybrid syste: ( 0) I X& aks t = = (13). Nazadnje lahko zvoèni tlak p (t) zapišeo kot: Finally, the sound pressure p (t) can be written as: 0d stran 149

8 æ dw0t AI rw0d w ö - 0d p'( t, w (14). 0d = konst) = p'( t) = e sin ( ct-rp ) ç 4 r p c è p ø Analiza eritev je pokazala, da je dušenje d za The analysis of the easureents showed that vse sestavljene plošèe nogo anjše od ena, torej the daping d is significantly saller than one for all lahko reèeo, da je w0d. Ob upoštevanju, da the coposite plates, thus, we can say that w0d. so I, r in r p enaki za vse eritve, iz enaèbe (14) Considering also that I, r and r p are the sae for all vidio, da je aplituda (P) posaeznega easureents, we can conclude fro equation (14) resonanènega vrha iz frekvenènega odziva ipulzno that the aplitude (P) of the individual resonant peak vzbujenih plošè: in the FRF of ipulsively excited plates is: A k P= K (15), kjer je K konstanta z vrednostjo (I r)/(4p r p ) in enotai kg 2 s/ 4. Absolutna vrednost konstante K je v nadaljnji analizi nepoebna, saj gre le za prierjavo posaeznih frekvenènih odzivov oziroa velièin, dobljenih iz teh odzivov. Pozitivna lastnost nosilnih gradnikov strojev in naprav je poleg velike statiène togosti tudi velika dinaièna togost ob èi anjši asi. To poeni veliko razerje k/ iz enaèbe (15). Seveda pa orajo biti aplitude nihanja takšnih strojnih delov èi anjše, kar poeni tudi èi anjše vrednosti za P, saj je oè zvoènega tlaka glede na jakost vzbujanja neposredno odvisna od oèi vibracij preskušanih plošè. Iz enaèbe (15) vidio, da bosta oba pogoja izpolnjena pri razeroa ajhne A/, velike k/ in njune relativno ajhne znožku. Skleneo lahko, da je prierjavo dinaiène togosti preskušanih plošè ogoèe opraviti s prierjavo pripadajoèih resonanènih vrhov v njihove frekvenène odzivu, kar kaže slika 5. Glede na izhodišèni resonanèni vrh poeni ožnost 1 najbolj neugodno kobinacijo odalne togosti in ase, ožnost 6 pa najugodnejšo. Možnosti 2 in 3 lahko štejeo za neugodni, ožnosti 4 in 5 pa za ugodni, kakor kaže slika 5. Dodati je treba, da je ožnost 4 bolj ugodna, èe poveèanje aplitude resonanènega vrha ni veèje od poveèanja njegovega položaja (frekvence), kar logièno izhaja iz enaèbe (15). where K is a constant with agnitude (I r)/(4p r p ) in units of kg 2 s/ 4. Because the following analysis was focused only on a coparison between different FRFs and their corresponding paraeters, the agnitude of the constant K is irrelevant. In addition to a high static stiffness the dynaic stiffness of the supporting parts of achine tools and devices is also a positive feature. This indicates a high ratio k/ fro equation (15). However, for such achine parts the aplitudes of oscillation should be relatively sall, which indicates relatively sall values for P. Naely, the intensity of the sound pressure with respect to the intensity of excitation depends directly on the intensity of the vibrations for the tested plates. We can see fro equation (15) that both conditions will be fulfilled when A/ is relatively sall, k/ is relatively high, and the product of both ratios is relatively sall. We can conclude that a coparison of FRFs and the corresponding resonant peaks allows us to copare the dynaic stiffness of the tested plates, as shown in Figure 5. With respect to the presented resonant peak alternative: 1 eans the least favourable cobination of odal stiffness and ass, whereas alternative 6 is the ost favourable. As indicated in Figure 5, alternatives 2 and 3 can be seen as unfavourable, whereas alternatives 4 and 5 are favourable. It should be noted that alternative 4 is ore favourable if the increase in the aplitude of the resonant peak is not higher than the increase in its position (frequency), which is logical according to equation (15). By anal- frekvenèni odziv frequency response frekvenca frequency Sl. 5. Relativni položaj in aplituda resonanènega vrha (1 do 3: neugodno, 4 do 6: ugodno, 6: najbolj ugodno) Fig. 5. Relative position and aplitude of resonant peak (1 to 3: unfavourable, 4 to 6: favourable, 6: ost favourable). stran 150

9 Analogno je ožnost 3 anj ugodna, èe je zanjšanje aplitude anjše od zanjšanja frekvence resonanènega vrha Vpliv debeline sten in useritve jedra Slika 6 prikazuje rezultate eritev za jeklene sestavljene plošèe v frekvenène obsegu 300 do 1300 Hz, kjer lahko analizirao vpliv debeline sten in useritve jedra. Že na prvi pogled je oèitno, da sta za vsako sestavljeno plošèo znaèilna vsaj dva izrazita frekvenèna vrhova, ki jia lahko doloèio frekvenco, aplitudo in dušenje. Vsi ti trije paraetri ter razerje A/ iz enaèbe (15) so za pripadajoèe preskušance za prva dva resonanèna vrha zbrani v preglednici 2. Z veliko zanesljivostjo lahko trdio, da je veliko razerje A/ pokazatelj slabih dinaiènih lastnosti nosilnih gradnikov obdelovalnih strojev. Ti bi za vsak odalni naèin orali izkazovati veliko aso () in logièno ajhne dinaièno aktivne površine (A), kar poeni ajhno razerje A/. Nadalje, v danih razerah eritev je prierno predpostaviti vsaj približno enakost površin A (0,5 0,3 = 0,15 2 ) za vse plošèe. Meritve oblik odalnih naèinov so nareè pokazale, da je vsaj pri odalnih naèinih z razeroa nizko frekvenco aktivna celotna površina za vse preskušance [9]. To poeni, da lahko za vsak resonanèni vrh izraèunao tudi relativne vrednosti ter k, ki so prav tako prikazane v preglednici 2. Medte ko sta bili aplituda P ter frekvenca f resonanènega vrha prebrani neposredno iz frekvenènega odziva, je bil v analizi faktor viskoznega dušenja d izraèunan kot [16]: ogy, alternative 3 is less favourable if the decrease in the aplitude is saller than the decrease in the frequency of the corresponding resonant peak The influence of the flatsheets thickness and the core orientation Figure 6 shows the results of easureents for steel coposite plates in the frequency range fro 300 to 1300 Hz, which allows us to analyse the influence of the flatsheets, thickness and the core orientation. At a first glance it is evident that at least two significant peaks with their corresponding frequencies, aplitudes and dapings are typical for each coposite plate. For the first two resonant peaks these three paraeters, and the A/ ratio fro equation (15), are presented in Table 2 for the corresponding speciens. With considerable certainty we can say that the high A/ ratio indicates bad dynaic properties for the supporting eleents of achine tools. These should have a large ass () and, logically, sall surfaces with dynaic activity (A) for each ode; this eans a sall A/ ratio. Next, under our experiental conditions, it is reasonable to assue that the surfaces A (0,5 0,3 = 0,15 2 ) are the sae for all the plates. Naely, the easureents of odal shapes showed that at least for low-order odes the whole surface of the speciens was active [9]. This eans that we can calculate relative values for and k for each resonant peak. These values are also presented in Table 2. Whereas aplitude P and frequency f of the resonant peak were read directly for the FRF plot, the viscous daping factor d was calculated as [16]: 1 2 kjer f 1 in f 2 poenita frekvenci nižje in višje od resonanène frekvence, kjer je aplituda resonanènega vrha enaka P/ 2 [16]. f - f (16), f where f 1 and f 2 indicate frequencies (lower and higher than the resonant frequency) where the aplitude of the resonant peak is P/ 2 [16] Vpliv polnila ed jedro in stenai sestavljene plošèe Slika 7 in preglednica 3 prikazujeta rezultate eritev za jekleno sestavljeno plošèo z debelino sten 1 in vzdolžno useritvijo jedra za tri razliène priere: (i) brez polnila, (ii) s poliesterski betono in (iii) s poliuretansko aso ed obea stenaa in jedro (sl. 1). 2 ANALIZA REZULTATOV IN RAZPRAVA S slike 6 in iz preglednice 2 vidio, da vzdolžna useritev jedra ne glede na debelino stene poeni bistveno veèjo togost prvega odalnega naèina v prierjavi s preèno useritvijo jedra. Toèneje, v prieru plošèe z debelino sten 1 je to razerje The influence of the filling between the core and the flatsheets of the coposite plates Figure 7 and Table 3 show the results on easureents for a steel coposite plate with a flatsheet thickness of 1 and longitudinal orientation of core for three different cases: (i) without filling, (ii) with polyester concrete and (iii) with polyurethane filling between the core and the flatsheets (see Figure 1). 2 ANALYSIS OF RESULTS AND DISCUSSION We can see fro Figure 6 and Table 2 that apart fro the flatsheet thickness the longitudinal core orientation results in a higher stiffness of the first ode in coparsion to the transversal orientation of the core. More precisely, in the case of a plate stran 151

10 Sl. 6. Frekvenèni odziv plošè kot funkcija debeline sten in useritve jedra Fig. 6. Frequency response as a function of flatsheet thickness and core orientation Preglednica 2. Prva dva resonanèna vrha analiza vpliva debeline sten in useritve jedra Table 2. The first two resonant peaks analysis of the influence of flatsheet thickness and core orientation 1. vrh / 1st peak P d f Pa//s 2 Hz k / A/ K -1 kg s/ 2 K 4 /kg s k* K 4 /kg s 3 rd/s JE1V 0, , ,0 4009,0 2,89E-7 518,4E3 8,33E12 JE1P 0, , ,2 2489,0 5,22E-7 287,2E3 1,78E12 JE2V 0, , ,4 4350,5 2,60E-7 577,5E3 10,9E12 JE2P 0, , ,9 3046,7 5,19E-7 289,2E3 2,68E12 2. vrh / 2nd peak P d f Pa//s 2 Hz k / A/ K -1 kg s/ 2 K 4 /kg s k* K 4 /kg s 3 rd/s JE1V 0, , ,6 4785,0 8,36E-7 179,4E3 4,11E12 JE1P 0, , ,5 5482,0 1,88E-7 798,3E3 24,0E12 JE2V 0, , ,4 5770,5 10,92E-7 137,4E3 4,57E12 JE2P 0, , ,9 6728,7 4,90E-7 305,9E3 13,8E12 *A=0,15 2 Sl. 7. Frekvenèni odziv plošè kot funkcija polnila ed stenaa in jedro Fig. 7. Frequency response as a function of the filling between the flatsheets and the core stran 152

11 Preglednica 3. Prva dva resonanèna vrha analiza vpliva polnila Table 3. The first two resonant peaks analysis of the influence of the filling 1. vrh / 1st peak P d f Pa//s 2 Hz 4,7:1, v prieru debeline sten 2 pa 4,1:1. To je v skladu s predhodnii preskusi, pri katerih je bilo naesto ipulznega vzbujanja plošè uporabljeno sinusno vzbujanje, frekvenèni odziv plošèe pa je bil definiran kot razerje ed odzivni pospeško (hitrostjo) plošèe in vzbujevalno silo na njeni geoetrièni sredini [9]. Prierjava ed plošèaa z debelino sten 2 in 1 pokaže, da je togost prvega odalnega naèina v razerju 1,5:1 za preèno useritev jedra in 1,3:1 za vzdolžno. Tudi to je v skladu s predhodnii eritvai [9], skleneo pa lahko, da za dano situacijo veèja debelina sten pripoore k veèanju togosti prvega odalnega naèina opazno anj kot useritev jedra. Uèinek userjenosti jedra je alenkostno veèji pri bolj debeli steni sestavljene plošèe. Faktor dušenja prvega odalnega naèina je v splošne veèji za preèno userjenost jedra in za anjšo debelino sten. To je sao delno v skladu s predhodnii eritvai [9], kjer se je izkazalo, da ia v prieru preène userjenosti jedra plošèa z 2- ilietrsko steno nekaj veèje dušenje od tiste z 1- ilietrsko steno. Dodati pa je treba, da so v splošne vrednosti faktorjev dušenja za vse plošèe (prejšnje in zdajšnje eritve) veliko anjše od ena, torej je neskladje s predhodnii eritvai praktièno neznaèilno. Za drugi odalni naèin situacija ni analogna tisti za prvega, saj razlièno debeli plošèi s preèno userjenostjo jedra izkazujeta neprierno veèjo togost od plošè z vzdolžno userjenostjo jedra. Takšni rezultati so v skladu s prejšnjii ugotovitvai [9] in so pojasnjeni z obliko drugega odalnega naèina, pri katere prihaja do upogibanja okoli preène osi plošèe. Nadalje, togost tega odalnega naèina je v prieru preène postavitve jedra skoraj dvakrat veèja za 1 debelo plošèo v prierjavi s plošèo z debelino sten 2. Kljub teu, da so se frekvence gibalnih oblik ujeale s prejšnjii raziskavai [9], pa je bila pri slednjih togost druge gibalne oblike (upogibanje okoli preène osi) veèja za veèjo debelino stene pri enaki userjenosti jedra. k / A/ K -1 kg s/ 2 K 4 /kg s k* K 4 /kg s 3 rd/s JE1V 0, , ,0 4009,0 2,89E-7 518,4E3 8,33E12 JE1VBE 0, , ,2 2853,8 5,67E-7 264,2E3 2,15E12 JE1VPO 0, , ,5 3930,1 1,98E-7 755,8E3 11,7E12 2. vrh / 2nd peak P d f Pa//s 2 Hz k / A/ K -1 kg s/ 2 K 4 /kg s k* K 4 /kg s 3 rd/s JE1V 0, , ,6 4785,0 8,36E-7 179,4E3 4,11E12 JE1VBE 0, , ,9 3857,2 5,05E-7 296,7E3 4,41E12 JE1VPO 0, , ,0 5233,9 7,54E-7 198,7E3 5,44E12 *A=0,15 2 with a flatsheet thickness of 1 this ratio is 4.7:1, and in the case of a flatsheet thickness of 2 the ratio is 4.1:1. This is in agreeent with previous experients where sinusoidal excitation was used instead ipulse the excitation, and FRF was defined as the ratio of the response acceleration (velocity) to excitation force at the geoetrical centre of the plate [9]. For plates with a flatsheet thickness of 2 and 1 the stiffness of the first ode is 1.5:1 for a transversal core orientation, and 1.3:1 for a longitudinal orientation. This is also in agreeent with previous easureents [9], thus we can conclude that for a given situation the flatsheet thickness is less significant for the first ode stiffness than core orientation. The effect of core orientation is slightly higher for the thicker flatsheet of the coposite plate. The daping factor of the first ode is higher for the transversal core orientation and for the thinner flatsheets. This is only partly in agreeent with previous easureents [9], where for a transversal core orientation the daping is slightly higher for the thicker (2 ) than for the thinner (1 ) coposite plate. However, the values for the daping factors are significantly saller than one for all plates, in general, as a result, this disagreeent is insignificant. Because both the 1-- and 2--thick plates with a transversal core orientation show a significantly higher stiffness in coparison to the plates with a longitudinal core orientation for the second ode, there is no analogy between the situation for the first and second ode. Such results are in agreeent with previous findings [9] and are explained by the second ode shape, which is bending along the transversal direction of the plate. Next, for a transversal core orientation in the case of a flatsheet thickness of 1 the stiffness of this ode is alost 100% higher in coparison to the plate with a flatsheet thickness of 2. In spite of the fact that the ode frequencies are in agreeent with the previous tests [9] the latter indicate higher stiffness of the second ode (bending along the transversal axis) for a thicker plate in coparison to the thinner one for the sae core orientation. stran 153

12 Velika asa poliestrskega betona je bistveno zanjšala razerje ed togostjo in aso (nezaželeno) za oba prva odalna naèina v prierjavi s plošèo brez polnila oziroa s poliuretano. Za prvo gibalno obliko je togost plošèe s poliestrski betono anjša od obeh drugih plošè, kar kaže relativno neuèinkovitost betona v strukturi sestavljene plošèe (predvidoa slaba oprijetost betona s stenai in jedro ali podobno). V skladu s prièakovanji je, da je v višje frekvenène podroèju (od 700 Hz navzgor) frekvenèni odziv plošèe s poliestrski betono bistveno ugodnejši, torej anj intenziven, v prierjavi z obea prierjania (sl. 7). Na dušenje prve gibalne oblike poliuretan praktièno ni iel vpliva v prierjavi s plošèo brez polnila, paè pa je vplival na veèje dušenje v prierjavi s plošèo s poliestrski betono. Enako kakor pri prierjavi plošè brez polnila, a z razlièno debelino sten in userjenostjo jedra, je treba na te estu poudariti, da so vse izerjene vrednosti faktorja dušenja veliko anjše od ena, zato orebitne razlike praktièno niso znaèilne. Izkazani vpliv betonskega polnila nareè ni v skladu s predhodnii eritvai [9], ki so pokazale alenkostno veèje dušenje plošèe z betono v prierjavi s plošèaa s poliuretanski polnilo in brez njega. Po drugi strani pa sta analizi drugega resonanènega vrha predhodnih [9] in zdajšnjih eritev v sozvoèju, saj obe izkazujeta razeroa veliko dušenje plošèe z betono v prierjavi s preostalia dvea plošèaa. Nadalje, togost plošèe z betonski polnilo je najveèja, togost plošèe brez polnila pa najanjša [9]. Za boljšo fizikalno razlago dobljenih frekvenènih odzivov je na sliki 8 prikazana njihova prierjava za sestavljene plošèe JE1V, JE1VBE ter AL1P In coparison to the plates without filling and with polyurethane filling a relatively large ass of the polyester concrete significantly reduced the ratio of stiffness to ass (which is undesired) for the first two odes. The relative inefficiency of the polyester concrete in the structure of the coposite plate (presuably bad adhesion between the core and the flatsheets, or soething siilar) is evident in the lower stiffness of the first ode for this plate in coparison to another two plates. As expected, in a higher frequency range fro 700 Hz up the FRF of the plate with polyester concrete is significantly ore favourable, thus less intensive in coparison to the copared FRFs (see Figure 7). The daping of the first ode was practically independent of the polyurethane filling in coparison to the plate without it. However, in coparison to the polyester concrete the polyurethane filling resulted in a higher daping of this ode. In a coparison between the plates without filling and the plates with different thicknesses of flatsheets and core orientations, it should be noted here that the values of the daping factor are uch less than one. Therefore, the easured differences are, in practise, not significant. Naely, the deonstrated effect of the polyester concrete is not in agreeent with the previous easureents [9], which showed slightly higher daping of the coposite plates with concrete in coparison to the plates without filling and with polyurethane filling. On the other hand, the analyses of the second resonant peak of the previous [9] and present easureents are in agreeent, because they both indicate a relatively high daping of the plate with polyester concrete in coparison to the other two plates. The stiffness of the plate with the concrete filling is the highest, whereas the stiffness of the the plate without the filling is the lowest [9]. For a better interpretation of the physical background of the easured FRFs Figure 8 shows a coparison of the coposite plates: JE1V, JE1VBE and Sl. 8. Prierjava s frekvenèni odzivo aluinijaste sestavljene plošèe Fig. 8. A coparison with the frequency response of the aluiniu coposite plate stran 154

13 za širše frekvenèno podroèje. Slednja sestavljena plošèa je geoetrijsko enaka JE1P, le da je aterial sten in jedra aluinij. Poleg oèitno neugodne lege prvega resonanènega vrha (razeroa nizka frekvenca in visoka aplituda) je za aluinijasto sestavljeno plošèo znaèilna razeroa velika površina pod frekvenèni odzivo. Za prierjavo, površine za plošèe JE1V, JE1VBE ter AL1P so v razerju 0,34 : 0,09 :1. To poeni relativno intenziven odziv (vibracije) aluinijaste plošèe in ajhen odziv sestavljene plošèe s poliestrski betono glede na JE1V. Glede na rezultate predstavljene v in 1.2.3, je logièno, da je aluinijasta sestavljena plošèa s preèno postavitvijo jedra od vseh preskušenih dinaièno najbolj neugodna. Torej sta za opis dinaiènih lastnosti poebna tako lega in aplituda prvega resonanènega vrha (zaželena ajhna aplituda in visoka frekvenca) kakor tudi površina pod grafo celotnega frekvenènega odziva (zaželena ajhna površina). Kljub opazno veèjeu dušenju (zaželeno) prvega resonanènega vrha za AL1P v prierjavi z drugia dvea sestavljenia plošèaa lahko skleneo, da je frekvenèni odziv aluinijastega preskušanca najslabši. Sestavljena plošèa s poliestrski betono, kljub nekoliko neugodnejšeu prveu (in drugeu) resonanèneu vrhu v prierjavi z JE1V, izkazuje skorajda nièen odziv v frekvenène podroèju, v katere je odziv za JE1V in AL1P še relativno oèan (nezaželeno). Kljub dejstvu, da v poglavju predstavljeni odel predvideva relativno veliko oddaljenost (r p ) od vira zvoka, v naše prieru to ni bilo najbolj idealno izpolnjeno. Oddaljenost ikrofona od preskušanca je bila nareè koaj dvakrat toliko, kolikor je njegova najveèja izera. To in pa razliènost etod pri doloèanju dinaiènih lastnosti je najverjetnejši razlog za nekatera razhajanja pri rezultatih eritev. 3 SKLEP Rezultati raziskave so v precejšnji eri v skladu s predhodnii eritvai [9], pri katerih je bilo uporabljeno sinusno vzbujanje plošè, frekvenèni odziv pa je bil definiran kot razerje ed izstopni pospeško (hitrostjo) plošèe in vstopno silo na njeni geoetrièni sredini. Kljub dejstvu, da v predstavljeni odel predvideva relativno veliko oddaljenost (r p ) od vira zvoka, v naše prieru to ni bilo najbolj idealno izpolnjeno. Oddaljenost ikrofona od preskušanca je bila nareè koaj dvakrat toliko, kolikor je njegova najveèja izera, predvidoa pa to na eritve faktorja dušenja in resonanènih frekvenc ne vpliva [16]. Doloèene razlike pri rezultatih obeh postopkov (glej poglavje 2) lahko razložio z razlièni naèino vzbujanja, od katerega je odziv realnih (nelinearnih) sisteov naèeloa oèno odvisen [16]. AL1P, for a wide frequency range. The last of these coposite plates is geoetrically the sae as JE1P; however, the aterial of the flatsheets and the core is aluiniu. In adition to an unfavourable position of the first resonant peak (relatively low frequency and high aplitude) the aluiniu plate indicates a relatively large area under its FRF. For coparison, the areas under the FRFs for plates JE1V, JE1VBE and AL1P are in the ratios: 0.34 : 0.09 :1. This eans a relatively intense response (vibrations) of the aluiniu plate and a weak response of the plate with the polyester concrete in coparison to JE1V. According to results fro sections and it is logical that the aluiniu coposite plate with a transversal core orientation is dynaically the worst. Therefore, not only the position, but also the aplitude (sall aplitude and high frequency are desired) in addition to the area under the FRF (sall area is desired), are iportant in defining the dynaic properties. Despite the higher daping (desired) of the first resonant peak for AL1P in coparison to the other two coposed plates it is reasonable to conclude that the FRF of the aluiniu specien is the worst. Regardless of the slightly ore unfavourable characteristics of the first (and also the second) resonant peak in coparison to JE1V, the plate with polyester concrete deonstrates an alost null response in the frequency range where this one is relatively strong for JE1V and AL1P (not desired). Despite the fact that in section the presented odel presues a relatively large distance (r p ) fro the sound source, this was not ideally fulfilled in our case. Naely, the distance between the icrophone and the specien was hardly twice its largest diension. In addition to the differences between the ethods for easuring the dynaic properties, this is the ost probable reason for soe dispersing conclusions. 3 CONCLUSION The results of our research are ostly in agreeent with previous easureents [9], where sinusoidal excitation of the plates was applied and the FRF was defined as a ratio of the output acceleration (velocity) to the input force plate at its geoetrical centre. Despite the fact that in section the presented odel asues a relatively large distance (r p ) fro the sound source, this was not ideally fulfilled in our case. Naely, the distance between the icrophone and specien was hardly twice its largest diension. Presuably, this does not affect the easureents of daping factor and resonant frequencies [16]. Definite differences in the results of both ethods (see section 3.) can be explained with the different types of excitation, which strongly affects the response of real (nonlinear) systes [16]. stran 155

14 Meritve frekvenènega odziva sestavljenih plošè za gradnjo nosilnih delov obdelovalnih strojev so v splošne pokazale znaèilen vpliv ateriala, debeline sten, useritve jedra ter polnila ed stenaa in jedro. Frekvenèni odziv je bil definiran kot razerje ed rezultirajoèi zvoèni tlako, erjeni 1 od prosto vpetih plošè, in vstopni ehanski ipulzo. Izraziti frekvenèni vrhovi v frekvenène odzivu so tako bili ponazorjeni z ipulzno vzbujeni enoasni ehansko-akustièni sisteo, sestavljeni iz ase (diskretna asa ), dušilke (koeficient viskoznega dušenja b), vzeti (togost k) in brezasne ebrane s površino A. Rezultati analize kažejo poebno vlogo vseh analiziranih vplivov na gibalno obliko oziroa dinaiène lastnosti sestavljenih plošè. Vzdolžna orientacija jedra na pravokotnih prekušancih se je izkazala za superiorno glede prve gibalne oblike, saj sta togost ter razerje ed togostjo in aso (frekvenca) te gibalne oblike veèja v prierjavi s plošèai s preèno useritvijo jedra. Nasprotno se je izkazalo pri drugi gibalni obliki, tj. upogibanje okoli preène osi plošèe, in zanj preèna useritev jedra poeni veèjo togost in razerje togosti proti asi v prierjavi z vzdolžno useritvijo jedra. Precej anjši vpliv od useritve jedra je na spreebo togosti prve gibalne oblike iela spreeba debeline sten sestavljenih plošè. V prierjavi z 1- ilietrsko steno ia plošèa z 2-ilietrsko steno približno 30 do 50% veèjo togost, edte ko za drugo gibalno obliko ni bilo opaziti zanesljive odvisnosti ed debelino stene in togostjo oblike. Sestavljena plošèa s poliestrski betono kot polnilo je pokazala znaèilno ajhno razerje ed togostjo in aso prvega (in drugega) odalnega naèina v prierjavi s plošèo brez polnila. Toda ugodnost njenega frekvenènega odziva v podroèju od 700 Hz navzgor, kjer izkazuje izrazito dinaièno nedejavnost (nizko razerje A/ za vse visoke odalne naèine), je v prierjavi z vsei drugii preskušanci oèitna. V splošne je bil faktor dušenja analiziranih gibalnih oblik veliko anjši od ena, zato izerjeni razlika ed nji pripadajoèi dušenje ni bila posveèena velika pozornost. Kljub teu je oè skleniti, da preèna useritev jedra ali anjša debelina sten poenita veèje dušenje za obe analizirani gibalni obliki. Dušenje prve gibalne oblike plošèe s poliestrski betono je bilo nekaj anjše od dušenja plošèe brez betona, edte ko je za drugo gibalno obliko plošèa z betono izkazala precej veèje dušenje. Plošèa s poliuretanski polnilo se je v vseh pogledih (dušenje, aplitude) obnesla bolje kakor plošèa brez polnila. Skleneo lahko, da predstavljena etoda kljub svoji poenostavitvi obièajne oblikovne analize oogoèa grobo identifikacijo dinaiènih lastnosti sestavljenih plošè. Kakor kaže, lahko z etodo bistveno poenostavio izbiro optialnih izer sten, FRF easureents of the coposite plates intended for supporting parts of achine tools and devices deonstrated a significant influence of the aterial, the flatsheets, thickness, the core orientation and the filling between the flatsheets and the core. The FRF was defined as the ratio of the resulting sound pressure easured at 1 fro the free-supported plates to the input echanical ipulse. The significant resonant peaks in the FRF were approxiated with an ipulsively excited one-ass syste (echanical-acoustical) which consists of ass (discrete ass ), daper (coefficient of viscous daping b), spring (stiffness k) and assless ebrane with area A. The results of the analysis point to an iportant role of all the analysed effects on the odal behaviour and on the dynaic properties of the coposite plates. In coparison to the transversal core orientation the longitudinal one deonstrated the superiority of the rectangular-shaped speciens for the first ode. The reason for this is that the ratio of stiffness to ass (frequency) for this ode was higher for the plates with a longitudinal core orientation. In contrast, for the second ode, which is bending along the transversal axis of the plate, the transversal core orientation eans both higher stiffness and ratio of stiffness to ass in coparison to the longitudinal core orientation. The effect of flatsheet thickness on the first ode stiffness was significantly lower than the effect of core orientation. In coparison to the flatsheet with a thickness of 1 the plate with a 2-illietre flatsheet has approxiately 30 50% higher stiffness, whereas for the second ode no significant correlation between flatsheet thickness and odal stiffness was easured. The coposite plate with polyester concrete deonstrated a significantly lower ratio of stiffness to ass of the first (and also the second) ode in coparison to the coposite plate without filling. However, the benefit of the plate with polyester concrete in the range fro 700 Hz in coparison to the other plates is evident in the significant dynaic non-activity (low A/ ratio for all higher odes). In general, the daping factor of the analysed odes was significantly less than one, therefore, the easured differences in odal daping were not significant. Despite this, we can conclude that transversal rather than longitudinal or thinner rather than thicker flatsheet thicknesses ean higher daping for both the analysed odes. The daping of the first ode for the plate with polyester concrete was slightly lower in coparison to the plate without the filling, whereas for the second ode the concrete plate deonstrated significantly higher daping. The plate with polyurethane filling showed better perforance in coparison to the plate without the filling in ters of daping and aplitudes. It is reasonable to conclude that despite soe siplifications of classical odal analysis, the presented ethod gives us a rough indication of the dynaic properties of coposite plates. It sees that this ethod can avoid a coplex odal analysis with stran 156