Characteristic orthogonal polynomials in the study of transverse vibrations of nonhomogeneous rectangular orthotropic plates of bilinearly varying thickness |
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Authors: | R Lal Kumar Yajuvindra |
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Institution: | (1) 184, South Soti Gunj, Opposite Bhopal Nursing Home, Begum Bridge Road, Meerut, 250001, Uttar Pradesh, India;(2) Department of Applied Sciences and Humanities, Institute of Technology and Management, Huda-Sector 23-A, Gurgaon, 122 017, Haryana, India;(3) School of Civil Enginnering, Universiti Sains Malaysia, Engineering Campus, 14300 Nobong Tebal, Seberang Perai Selatan, P. Pinang, Malaysia |
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Abstract: | Effect of nonhomogeneity on the vibrational characteristics of thin orthotropic rectangular plates of bilinearly varying thickness
has been studied using boundary characteristic orthogonal polynomials in the Rayleigh-Ritz method. The thickness variation
is taken as the Cartesian product of linear variations along two concurrent edges of the plate. The orthogonal polynomials
in two variables are generated using the Gram-Schmidt process. The nonhomogeneity of the plate material is assumed to arise
due to linear variations in Young’s moduli, shear modulus and density of the plate with the in-plane coordinates. Numerical
results have been computed for four different combinations of clamped, simply supported and free edges. Effect of thickness
variation together with varying values of aspect ratio and nonhomogeneity on the natural frequencies is illustrated for the
first three modes of vibration. Three dimensional mode shapes have been presented. Comparison has been made with the known
results. |
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