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An efficient numerical approach utilizing a variational weak form, grounded in 2D elastic theory and variational principles, is proposed for analyzing the in-plane vibrational behavior of rectangular plates resting on elastically restrained boundaries. The differential and integral operators can be discretized into matrix representations employing the differential quadrature method (DQM) and Taylor series expansion techniques. The discretization of dynamics equations stems directly from a weak formulation that circumvents the need for any transformation or discretization of higher-order derivatives encountered in the corresponding strong equations. Utilizing the matrix elementary transformation technique, the displacements of boundary and internal nodes are segregated, subsequently leading to the derivation of the generalized eigenvalue problem pertaining to the free vibration analysis of the Functionally Graded Material (FGM) rectangular plate. Furthermore, the study examines the impact of the gradient parameter, aspect ratio, and elastic constraints on the dimensionless frequency characteristics of the FGM rectangular plate. Ultimately, the modal properties of an in-plane FGM rectangular plate are investigated.
Details
Transformations (mathematics);
Series expansion;
Matrix representation;
Rectangular plates;
Operators (mathematics);
Quadratures;
Boundaries;
Functionally gradient materials;
Aspect ratio;
Porous materials;
Vibration analysis;
Taylor series;
Free vibration;
Deformation;
Boundary conditions;
Discretization;
Variational principles
; Sen, Li 4 1 School of Science, Jiangsu University of Science and Technology, Zhenjiang 212003, China; [email protected] (X.W.); [email protected] (S.Y.)
2 School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology, Zhenjiang 212003, China, Zhenjiang Jizhi Ship Technology Co., Ltd., Zhenjiang 212003, China
3 School of Science, Jiangsu University of Science and Technology, Zhenjiang 212003, China; [email protected] (X.W.); [email protected] (S.Y.), Zhenjiang Jizhi Ship Technology Co., Ltd., Zhenjiang 212003, China, Yangzijiang Shipbuilding Group, Taizhou 212299, China
4 School of Science, Changzhou Institute of Technology, Changzhou 213032, China; [email protected]