RAYLEIGH-RITZ METHOD IN THE STUDY OF TRANSVERSE VIBRATION OF NONHOMOGENEOUS ORTHOTROPIC RECTANGULAR PLATES OF UNIFORM THICKNESS RESTING ON WINKLER FOUNDATION
In this paper, Rayleigh-Ritz method has been used to study the effect of nonhomogeneity together with the Winkler foundation on the vibrational characteristics of orthotropic rectangular plates of uniform thickness on the basis of classical plate theory. Nonhomogeneity of the plate material is assumed to arise due to the linear variations in Young’s moduli and density along both the directions of the orthotropy. The energy functional for such plates has been minimized using boundary characteristic orthogonal polynomials in two directions. These polynomials satisfying geometric boundary conditions are generated using the Gram-Schmidt process. Frequencies of the plates for varying values of nonhomogeneity parameters, density parameters, foundation parameter and aspect ratio for four different combinations of clamped, simply supported and free edges have been computed using Jacobi method. Three dimensional mode shapes for first three modes for all the boundary conditions considered here have been presented. A comparison of frequencies for homogeneous isotropic uniform square plates as a special case has been presented.
nonhomogeneous orthotropic rectangular uniform thickness winkler foundation
R.Lal Yajuvindra Kumar
Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee-247 667, India
国际会议
The Fifth International Conference on VETOMAC-V(第五届振动工程及机械技术国际会议)
武汉
英文
63-68
2009-08-27（万方平台首次上网日期，不代表论文的发表时间）