Three-dimensional Vibration Analysis of Crystal Plates via Ritz Method [chapter]

Qian Li, VaiPan Iu
III European Conference on Computational Mechanics  
Three-dimensional vibration of rectangular Y-cut crystal plate has been investigated in this paper. The three displacements components of plate are expanded in three directions by series of Chebyshev polynomial multiplied by the boundary function R which makes expansions satisfy the essential boundary conditions along the edges. The eigenvalue matrix for natural vibration frequencies is obtained for rectangular crystal plate by Ritz method and then solved by computer program. The result of an
more » ... The result of an infinite plate excited by thickness-shear deformation parallel to one edge is proved by exact solutions. The natural free vibration frequencies of rectangular Y-cut crystal plate of are compared with those by finite element method. The agreements are close. Besides, convergence study demonstrates the high efficiency. Finally, the free vibration mode shapes of clamped square Y-cut crystal are plotted.
doi:10.1007/1-4020-5370-3_115 fatcat:zp4e5syeuzbmxmeke3xp3fporm