Shivani Srivastava¹, Seema Sharma², Roshan Lal³

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¹ Department of Mechanical Engineering, Indian Institute of Technology Madras, Chennai, India.
² Department of Mathematics, Gurukul Kangri University, Haridwar, India.
³ Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, India.
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Abstract: 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 have 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.

Keywords: Pasternak Foundation, Parabolically Varying Thickness, Circular Plate, Polar Orthotropy, Non-Homogenity

Cite this paper: Srivastava, S. , Sharma, S. and Lal, R. (2015) Effect of Foundation and Non-Homogeneity on the Vibrations of Polar Orthotropic Parabolically Tapered Circular Plates. Applied Mathematics, 6, 1563-1573. doi: 10.4236/am.2015.69139.

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