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In industrial machinery and automobiles the critical damping plates are used as shock absorbers to dampen system and return rest position, in the shortest period of time. The paper is focused on the effects of various parameters on critical damping of a complicated system including a tapered bidirectional graded circular plate subjected to radially variable in-plane pre-load and rested on visco-Hetenyi elastic medium with semi-rigid restraint. By employing a Chebyshev-Ritz method, dependency of critical damping is investigated for the first time on various parameters including bidirectional arbitrary material gradation, variable in-plane pre-load, Hetenyi elastic medium parameters, tapering, semi-rigid restraint and Poisson’s ratio. For the Chebyshev-Ritz method developed here, the proper scale factor and orthogonal shifted Chebyshev polynomials of the first kind without auxiliary function requirement are used. The conventional rule of mixture and Mori-Tanaka homogenization scheme are used to model transverse gradation. The characteristic equation is calculated by vanishing determinant of the total potential energy Hessian. An equivalent ABAQUS model is introduced to eliminate necessity of complicated modeling of original structure.

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