scholarly journals Discussion: “Nonlinear Vibration of a Rectangular Plate Arbitrarily Laminated of Anisotropic Material” (Bert, C. W., 1973, ASME J. Appl. Mech., 40, pp. 452–458)

1973 ◽  
Vol 40 (4) ◽  
pp. 1148-1149 ◽  
Author(s):  
R. Schmidt
Keyword(s):  
Nonlinear Vibration ◽  
Rectangular Plate ◽  
Anisotropic Material

Nonlinear Vibration of a Rectangular Plate Arbitrarily Laminated of Anisotropic Material

1973 ◽  
Vol 40 (2) ◽  
pp. 452-458 ◽  
Author(s):  
C. W. Bert
Keyword(s):  
Composite Material ◽  
Nonlinear Vibration ◽  
Rectangular Plate ◽  
Anisotropic Material ◽  
Present Theory ◽  
Practical Case ◽  
Orthotropic Plates ◽  
Simplified Approach ◽  
Isotropic Plates ◽  
Special Cases

A new simplified approach is presented for calculating the flexural frequencies of a composite-material plate undergoing moderately large, normal deflections. The plate may be arbitrarily laminated with respect to the midplane, so that bending-stretching coupling is present. The approach used is a generalization of the work of Wah for homogeneous, isotropic plates. In the case of orthotropic plates, it differs from various orthotropic extensions of the popular Berger hypothesis. The present theory is applied to the practical case of a clamped rectangular plate with finite in-plane restraint. The results are compared satisfactorily with those of previous analyses for various special cases.

Nonlinear Vibration of a Cantilever FGM Rectangular Plate with Piezoelectric Layers Based on Third-Order Plate Theory

2011 ◽  
Vol 415-417 ◽  
pp. 2151-2155
Author(s):  
Ying Wang ◽  
Yu Xin Hao ◽  
Jian Hua Wang
Keyword(s):  
Differential Equations ◽  
Nonlinear Vibration ◽  
Rectangular Plate ◽  
Initial Conditions ◽  
Plate Theory ◽  
Nonlinear Differential Equations ◽  
Nonlinear Dynamic Analysis ◽  
Control Voltage ◽  
Third Order ◽  
Piezoelectric Layers

This paper deals with nonlinear dynamic analysis of a cantilever FGM rectangular plate with piezoelectric layers subjected to the transversal excitation in thermo-electro-mechanical environment. The material properties of plate and piezoelectric layers are assumed to be temperature-dependent. The governing equations of the functionally graded plate are based on the Reddy’s third-order shear deformation plate theory that includes thermo-piezoelectric effects and Hamilton’s principle. The governing nonlinear partial differential equations are transformed into ordinary nonlinear differential equations using the Galerkin method and the nonlinear and linear frequencies obtained using the Runge–Kutta method. The effects played by control voltage and system initial conditions on the nonlinear vibration of the plate are studied.

Scattering from a Thin Rectangular Plate at Glancing Incidence

2001 ◽  
Vol 21 (2) ◽  
pp. 147-163 ◽  
Author(s):  
Hirohide Serizawa ◽  
Kohei Hongo ◽  
Hirokazu Kobayashi
Keyword(s):  
Rectangular Plate ◽  
Thin Rectangular Plate

THE SCHEME OF BIORTHOGONALIZATION OF VECTORS IN SOLVING THE PROBLEM OF RECTANGULAR PLATE BENDING

2019 ◽  
Vol 50 (6) ◽  
pp. 673-678
Author(s):  
Vladimir Ivanovich Lysukhin ◽  
Julian Fedotovich Yaremchuk
Keyword(s):  
Rectangular Plate ◽  
Plate Bending
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