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

被引：0
作者：
S. Chakraverty
Ragini Jindal
V. K. Agarwal
机构：
[1] Central Building Research Institute,BPPP Divn.
[2] Bhaskaracharya College of Applied Sciences (University of Delhi),Dept. of Mathematics
[3] ex Principal,undefined
[4] D.N. College,undefined
来源：
Meccanica | 2007年 / 42卷
关键词：
Non-homogeneity; Elliptic plate; Orthogonal polynomials; Gram Schmidt process; Mechanics of vibration;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
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.
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页码：585 / 599
页数：14
相关论文
共 37 条
  • [11] Jain NC(1976)Note on the transverse vibrations of an isotropic circular plate with density varying parabolically Indian J Theor Phys 24 179-182
  • [12] Laura PAA(1971)Free vibrations of an isotropic nonhomogeneous circular plate AIAA J 9 963-964
  • [13] Gutierrez RH(1985)Natural frequencies of rectangular plates using characteristic orthogonal polynomials in Rayleigh-Ritz method J Sound Vib 102 493-499
  • [14] Tomar JS(1987)Flexural vibration of polygonal plates using characteristic orthogonal polynomials in two variables J Sound Vib 114 65-71
  • [15] Sharma RK(1994)Boundary characteristic orthogonal polynomials in numerical approximation Commun Numer Methods Eng 10 1027-1043
  • [16] Gupta DC(1998)Reccurence scheme for the generation of two-dimensional boundary characteristic orthogonal polynomials to study vibration of plates J Sound Vib 216 321-327
  • [17] Tomar JS(1992)On the use of orthogonal polynomials in Rayleigh–Ritz method for the study of transverse vibration of elliptic plates J Comput Struct 43 439-443
  • [18] Gupta DC(1992)Transverse vibrations of simply supported elliptic and circular plates using boundary characteristic orthogonal polynomials in two variables J Sound Vib 152 149-155
  • [19] Jain NC(1991)Transverse vibrations of completely free elliptic and circular plates using orthogonal polynomials in Rayleigh Ritz method Int J Mech Sci 33 741-751
  • [20] Pan M(1997)Natural frequencies for free vibration of nonhomogeneous elliptic and circular plates using two-dimensional orthogonal polynomials Appl Math Model 21 399-417
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