TRANSVERSE VIBRATIONS OF SIMPLY SUPPORTED ANISOTROPIC RECTANGULAR PLATES CARRYING AN ELASTICALLY MOUNTED CONCENTRATED MASS

Analysis and numerical results are presented for free transverse vibrations of isotropic rectangular plates having arbitrarily varying non-homogeneity with the in-plane coordinates along the two concurrent edges on the basis of Kirchhoff plate theory. For the non-homogeneity, a general type of variation for Young’s modulus and density of the plate material has been assumed. Generalized differential quadrature method has been used to obtain the eigenvalue problem for such model of plates for four different combinations of boundary conditions at the edges namely, (i) fully clamped, (ii) two opposite edges are clamped and other two are simply supported, (iii) two opposite edges are clamped and other two are free, and (iv) two opposite edges are simply supported and other two are free. By solving these eigenvalue problems using software MATLAB, the lowest three eigenvalues have been reported as the first three natural frequencies for the first three modes of vibration. The effect of various plate parameters on the vibration characteristics has been analysed. Three dimensional mode shapes have been plotted. A comparison of results with those available in literature has been presented.

Download Full-text

FORCE VIBRATIONS OF SIMPLY SUPPORTED ANISOTROPIC RECTANGULAR PLATES

Journal of Sound and Vibration ◽

10.1006/jsvi.1998.1910 ◽

1999 ◽

Vol 220 (1) ◽

pp. 178-185 ◽

Cited By ~ 7

Author(s):

P.A.A. Laura ◽

D.R. Avalos ◽

H.A. Larrondo

Keyword(s):

Rectangular Plates ◽

Simply Supported ◽

Anisotropic Rectangular Plates

Download Full-text

Postbuckling Behavior of Unsymmetrically Layered Anisotropic Rectangular Plates

Journal of Applied Mechanics ◽

10.1115/1.3423213 ◽

1974 ◽

Vol 41 (1) ◽

pp. 155-162 ◽

Cited By ~ 55

Author(s):

C. Y. Chia ◽

M. K. Prabhakara

Keyword(s):

Nonlinear Differential Equations ◽

Fourier Method ◽

Rectangular Plates ◽

Postbuckling Behavior ◽

Anisotropic Plates ◽

Simply Supported ◽

Aspect Ratios ◽

Special Cases ◽

Present Solution ◽

Anisotropic Rectangular Plates

An analysis for the postbuckling behavior of unsymmetrically layered rectangular anisotropic plates is presented. Each layer is assumed to have arbitrary thickness, elastic properties, and orientation of orthotropic axes with respect to the plate axes. The governing nonlinear differential equations in the sense of von Karman are solved in conjunction with boundary conditions for clamped edges by use of the multiple Fourier method. In the case of simply supported edges, a solution based on the method is also obtained for unsymmetrical angle-ply plates. In the examples, a nine-term approximation to each series is used and load-deflection relations, bending moments, membrane forces are presented for clamped cross-ply and angle-ply and simply supported angle-ply plates with various aspect ratios. Numerical results obtained from the present solution are, in special cases, compared with available data.

Download Full-text