Effect of non-homogeneity on natural frequencies of vibration of elliptic plates

Abstract This paper presents the effect of non-homogeneity of the material of plate structures on the vibration frequencies. The non-homogeneity of the plate is characterized by taking a variety of combinations of linear as well as quadratic variations in the Young’s modulus and density of the material. Boundary characteristic orthogonal polynomials using Gram-Schmidt procedure have been employed in the Rayleigh Ritz method. The results have been included for the first few frequencies of the plate element for all the boundary conditions viz. clamped, simply supported and free. Related Tables and graphs are incorporated to show the effect of the non-homogeneity parameter on the frequencies of the vibration of elliptic and circular plates.

[1]  R. H. Gutierrez,et al.  Transverse vibrations of orthotropic, non-homogeneous rectangular plates , 1984 .

[2]  S. Chakraverty,et al.  On the use of orthogonal polynomials in the rayleigh-ritz method for the study of transverse vibration of elliptic plates , 1992 .

[3]  J. Awrejcewicz,et al.  Complex Parametric Vibrations of Flexible Rectangular Plates , 2004 .

[4]  R. Bhat.  Natural frequencies of rectangular plates using characteristic orthogonal polynomials in rayleigh-ritz method , 1986 .

[5]  Snehashish Chakraverty,et al.  Transverse vibration of simply supported elliptical and circular plates using boundary characteristic orthogonal polynomials in two variables , 1992 .

[6]  The Equations of Motion of a Plate with Residual Stress , 2006 .

[7]  S. Chakraverty,et al.  Transverse vibration of completely-free elliptic and circular plates using orthogonal polynomials in the Rayleigh-Ritz method , 1991 .

[8]  Arthur W. Leissa,et al.  Vibration of Plates , 2021, Solid Acoustic Waves and Vibration.

[9]  M. Petyt,et al.  Natural frequencies for free vibration of nonhomogeneous elliptic and circular plates using two-dimensional orthogonal polynomials , 1997 .

[10]  P. Ribeiro.  A Hierarchical Finite Element for Geometrically Non-linear Vibration of Thick Plates , 2003 .

[11]  A. W. Leissa,et al.  Literature Review : Plate Vibration Research, 1976 - 1980: Complicating Effects , 1981 .

[12]  J. S. Tomar,et al.  Transverse vibrations of nonuniform rectangular orthotropic plates , 1983 .

[13]  Vibrations of nonhomogeneous plates of variable thickness , 1982 .

[14]  Axisymmetric vibrations of an isotropic elastic non-homogeneous circular plate of linearly varying thickness , 1982 .

[15]  Rama B. Bhat,et al.  Flexural vibration of polygonal plates using characteristic orthogonal polynomials in two variables , 1987 .

[16]  A. W. Leissa,et al.  Literature Review: survey and analysis of the Shock and Vibration literature : Recent Studies in Plate Vibrations: 1981-85 Part II. Complicating Effects , 1987 .

[17]  A. W. Leissa,et al.  Recent Research in Plate Vibrations. 1973 - 1976: Complicating Effects , 1978 .

[18]  S. Chakraverty,et al.  Boundary characteristic orthogonal polynomials in numerical approximation , 1994 .