FREE AND FORCED VIBRATION OF REISSNER–MINDLIN PLATES WITH FREE EDGES RESTING ON ELASTIC FOUNDATIONS

2001 ◽  
Vol 244 (2) ◽  
pp. 299-320 ◽  
Author(s):  
H.-S. SHEN ◽  
J. YANG ◽  
L. ZHANG
Keyword(s):  
Forced Vibration ◽  
Elastic Foundations ◽  
Free Edges

Nonlinear Forced Vibration Analysis for Thin Rectangular Plate on Nonlinear Elastic Foundation

2012 ◽  
Vol 204-208 ◽  
pp. 4716-4721 ◽  
Author(s):  
Yong Gang Xiao ◽  
Cui Ping Yang ◽  
Hui Hu
Keyword(s):  
Rectangular Plate ◽  
Elastic Foundation ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Thin Rectangular Plate ◽  
Nonlinear Elastic Foundation ◽  
Nonlinear Forced Vibration ◽  
Forced Vibration Analysis ◽  
Nonlinear Elastic ◽  
Free Edges

In this paper, nonlinear forced vibration analysis for thin rectangular plate with four free edges on nonlinear elastic foundation is researched. Based on Hamilton variation principle, the equations of nonlinear vibration motion for the thin rectangular plate under period loads on nonlinear elastic foundation are established. In the case of four free edges, the suitable expressions of trial functions satisfied all boundary conditions for the problem are proposed. Then, we convert the equations to a system of nonlinear algebraic equations by using Galerkin method and they are solved by using harmonic balance method. In the analysis of numerical computations, the effect to the amplitude-frequency characteristic curve which due to change of the structural parameters of plate、the parameters of foundation and the parameters of excitation force are discussed.

scholarly journals New Finite Modeling of Free and Forced Vibration Responses of Piezoelectric FG Plates Resting on Elastic Foundations in Thermal Environments

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Pham Minh Phuc ◽  
Nguyen Thi Kim Khue
Keyword(s):  
Forced Vibration ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
The Finite Element Method ◽  
Third Order ◽  
Elastic Foundations ◽  
Thermal Environments ◽  
Fg Plates ◽  
Vibration Responses ◽  
Forced Vibration Analysis

This paper carries out free and forced vibration analysis of piezoelectric FGM plates resting on two-parameter elastic foundations placed in thermal environments. By employing the third-order shear deformation theory and the finite element method, this work establishes free and forced vibration equations of piezoelectric FGM plates, where the materials are assumed to be varied in the thickness directions, and the mechanical properties depend on the temperature. Then, comparative examples are conducted to verify the proposed theory and mathematical model, and the results of this study and other methods meet a very good agreement. Then, effects of geometrical and material properties such as the feedback coefficient, voltage, volume fraction index, temperature as well as the parameters of elastic foundations on free and forced vibration of the plates are investigated, and the conclusions are given out to provide the effective direction for the design and practical use of these structures.

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