### A Numerical Approach to Study the Effects of Foundation and Non-Homogeneity on the Vibrations of Orthotropic Circular Plates of Varying Thickness

The effect of Pasternak foundation and non-homogenity on the axisymmetric vibrations of polar orthotropic

parabolically varying tapered circular plates has been analyzed on the basis of classical plate theory. Ritz

method has been used to find the numerical solution of the specified problem. The efficiency of the Ritz method

depends on the choice of basis function based upon deflection of polar orthotropic plates. The effects of

different plate parameters viz. elastic foundation, non-homogeneity, taper parameter and that of orthotropy on

fundamental, second and third mode of vibration has been studied for clamped and simply-supported boundary

conditions. Mode shapes for specified plates have been drawn for both the boundary conditions. Convergence

and comparison studies have been carried out for specified plates.

**Author(s) Details**

Dr. Shivani Srivastava

Freelancing Consultant and Researcher, Kolkata, India.

**Dr. Seema Sharma**

Department of Mathematics, Gurukul Kangri University, Haridwar, India.

**Dr. Roshan Lal**

Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India.

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