The shell is resting on elastic foundations, in thermal environments.
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Used Hamilton's principle, the Galerkin method and Runge – Kutta method.
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Used the analytical approach.
Abstract
The novelty of this study is using the analytical approach to investigate the nonlinear dynamic response and vibration of shear deformable functionally graded truncated conical panel with piezoelectric actuators, resting on Pasternak type elastic foundations in thermal environments. Material properties are graded in the thickness direction according to a simple power law distribution in terms of the fractions of constituents. The governing equations are derived based on the first order shear deformation shell theory with a von Karman – Donnell type of kinematic nonlinearity in which the Hamilton's principle is used to derive the equations of motion of piezoelectric functionally graded truncated conical panel. The those equations are solved by the Galerkin method and Runge – Kutta method to determine the nonlinear deflection amplitude – time curves and natural frequency of the functionally graded panel. In numerical results, the effects of applied actuator voltage, temperature increment, dimensional parameters, semi – vertex angle, material properties and elastic foundations on the nonlinear dynamic response and vibration of the piezoelectric functionally graded truncated conical panel are discussed in details. The approach are verified with the known results in the literature.
