Vibrations Of Nonhomogeneous Rectangular Plates Research Articles

Buckling and vibration analysis of non-homogeneous rectangular Kirchhoff plates resting on two-parameter foundation

Effect of two parameter foundation has been analyzed on the transverse vibrations of non-homogeneous rectangular plates of uniform thickness when the two opposite edges are simply supported and these are subjected to linearly varying in-plane forces on the basis of Kirchhoff plate theory. The non-homogeneity of the plate material is assumed to arise due to the exponential variation in young’s modulus and density of the plate material along one direction. Using Levy approach, the partial differential equation governing the motion of such plates has been reduced to an ordinary differential equation. Differential quadrature method has been used to obtain the frequency equations for two different combinations of clamped and simply supported boundary conditions at the other two edges. These frequency equations have been solved numerically using MATLAB. The lowest three roots of these equations have been reported as first three natural frequencies corresponding to the first three modes of vibration. The effect of various parameters such as foundation parameters, non-homogeneity parameter, density parameter, aspect ratio, in-plane force parameter and loading parameter has been investigated on the frequencies. By allowing the frequency to approach zero, the critical buckling loads for various value of different parameters have been computed. Three dimensional mode shapes for a specified plate for both the boundary conditions have been plotted. A comparison of results with those available in literature has been presented.

Transverse Vibrations of Nonhomogeneous Rectangular Plates with Variable Thickness

The effect of nonhomogeneity on the free transverse vibration of thin rectangular plates of linearly varying thickness along one direction has been studied using two-dimensional boundary characteristic orthogonal polynomials in the Rayleigh-Ritz method. The nonhomogeneity of the plate is assumed to arise due to linear variations in Young's modulus and density of the plate material with the in-plane coordinates. The first three frequencies have been computed for four different combinations of clamped, simply supported, and free edges. The effect of thickness variation together with varying values of aspect ratio and nonhomogeneity on frequencies is illustrated. Mode shapes for specified plates are given.

Boundary Characteristic Orthogonal Polynomials in the Study of Transverse Vibrations of Nonhomogeneous Rectangular Plates with Bilinear Thickness Variation

The free transverse vibrations of thin nonhomogeneous rectangular plates of variable thickness have been studied using boundary characteristic orthogonal polynomials in the Rayleigh-Ritz method. Gram-Schmidt process has been used to generate these orthogonal polynomials in two variables. The thickness variation is bidirectional and is the cartesian product of linear variations along two concurrent edges of the plate. The nonhomogeneity of the plate is assumed to arise due to linear variations in Young's modulus and density of the plate material with the in-plane coordinates. Numerical results have been computed for four different combinations of clamped, simply supported and free edges. Effect of the nonhomogeneity and thickness variation with varying values of aspect ratio on the natural frequencies of vibration is illustrated for the first three modes of vibration. Three dimensional mode shapes for all the four boundary conditions have been presented. A comparison of results with those available in the literature has been made.

Boundary Characteristic Orthogonal Polynomials in the Study of Transverse Vibrations of Nonhomogeneous Rectangular Plates with Bilinear Thickness Variation

The free transverse vibrations of thin nonhomogeneous rectangular plates of variable thickness have been studied using boundary characteristic orthogonal polynomials in the Rayleigh-Ritz method. Gram-Schmidt process has been used to generate these orthogonal polynomials in two variables. The thickness variation is bidirectional and is the cartesian product of linear variations along two concurrent edges of the plate. The nonhomogeneity of the plate is assumed to arise due to linear variations in Young's modulus and density of the plate material with the in-plane coordinates. Numerical results have been computed for four different combinations of clamped, simply supported and free edges. Effect of the nonhomogeneity and thickness variation with varying values of aspect ratio on the natural frequencies of vibration is illustrated for the first three modes of vibration. Three dimensional mode shapes for all the four boundary conditions have been presented. A comparison of results with those available in the literature has been made.