Influence of Large Amplitudes on Flexural Vibrations of Elastic Plates

Abstract

Fur die nichtlinearen Biegeechwdngungen dunner rechteckiger oder kreisf ormiger Platten werden Ndherungslosungen angqeben, wobei verschiedene Falle von Randbedingungen betrachtet werden. Dabei wird der Einfhp groper Amplituden auf freie und erzwungene Schwingungen klargeatellt.Approximate solutions for the nonlinear bending vibrations of thin plates are presented for the cages of rectangular and circular plate8 subjected to various boundary conditions, and the effects of large amplitudes on both the free and forced vibration8 are clarified. Haxonmcfi n p~6 n a m e~~o e pemewie HenHHeBHbur st16pa4nB TOHHHX npmoyronmmc H HpyrOBblX llnaCTElHOH C PaaHHMH HpaeBbIMH YCJIOBEIHIMH. BbIHCHfxeTCJi 3##eKT 6onbm~x am-nnHTyH HJIR CB060nHbIX H BbIHYH(JIC!HHbIX ~o n e 6 a~~B .

The Nonlinear Bending of Simply Supported Elastic Plate

“…The essential geometric boundary conditions used are (BC3 and BC5 in Table 1 simply supported (SS-3) square plate, under uniformly distributed load. Figure 11 shows similar results for clamped (CC-l) square plate under uniformly distributed loadThe results are compared with the Ritz solution of Way [5], double Fourier-series solution of Levy [6], the finite-difference solution of Wang [7], the Galerkin solution of Yamaki [8], and the displacement finite-element solution of Kawai and Yoshimura [9]. Finite-element solutions were computed for the five degrees of freedom (NDF = 5), and for three degrees of freedom (NDF = 3); in the latter case, the in-plane displacements were suppressed.…”

Large-Deflection and Large-Amplitude Free Vibrations of Laminated Composite-Material Plates

“…As pointed out in a recent study [15], the YNS theory can be derived from the corresponding classical thin-plate theory by treating the slope- [32], doutle Fourier-series soluCion of Levy [33], the finite-difference solution of Wang [34], the Galerkin solution of Yamaki [35], and the displacement finite-element solution of Kawai and Yoshimura [36]. Finiteelement solutions were computed for the five degrees of freedom (NDF = 5), and for three degrees of freedom (NDF = 3); in the latter case, the in- that of Chia and Prabhakara [28].…”

Large-deflection and large-amplitude free vibrations of laminated composite-material plates

“…The results are compared with the Ritz solution of Way [32], doutle Fourier-series soluCion of Levy [33], the finite-difference solution of Wang [34], the Galerkin solution of Yamaki [35], and the displacement finite-element solution of Kawai and Yoshimura [36]. that of Chia and Prabhakara [28].…”