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Abstract: Free vibration of functionally graded material rectangular plates with simply supported and clamped edges in the thermal environment is studied based on the three-dimensional linear theory of elasticity. Simply supported and clamped FGM plates with temperature-dependent material properties subjected to uniform temperature rise, linear temperature rise and nonlinear temperature rise are considered. The three displacements of the plates are expanded by a series of Chebyshev polynomials multiplied by appropriate functions to satisfy the essential boundary conditions. The natural frequencies are obtained by Ritz method. The numerical results of the present approach are compared with the results of other researchers for the validation. Parametric study is performed for supported conditions, temperature fields, volume fraction indices of FGM plates. [Copyright &y& Elsevier]

Abstract: Free vibration of functionally graded material sandwich rectangular plates with simply supported and clamped edges is studied based on the three-dimensional linear theory of elasticity. Two common types of FGM sandwich plates, namely, the sandwich with FGM facesheet and homogeneous core and the sandwich with homogeneous facesheet and FGM core, are considered. The three displacements of the plates are expanded by a series of Chebyshev polynomials multiplied by appropriate functions to satisfy the essential boundary conditions. The natural frequencies are obtained by Ritz method. Rapid convergence is observed in this study. The natural frequencies of simply supported power-law FGM sandwich plates are compared with results from different two-dimensional plate theories. Parametric study is performed for varying volume fraction, layer thickness ratios, thickness–length ratios and aspect ratios of the sandwich plates. [Copyright &y& Elsevier]

Abstract: The stationary probability density function (PDF) solution of the stochastic response of nonlinear oscillators is investigated in this paper. The external excitation is assumed to be a combination of Gaussian and Poisson white noises. The PDF solution is governed by the generalized Kolmogorov equation which is solved by the exponential-polynomial closure (EPC) method. In order to evaluate the effectiveness of the EPC method, different nonlinear oscillators are considered in numerical analysis. Nonlinearity exists either in displacement or in velocity for these nonlinear oscillators. The impulse arrival rate, mono-modal PDF and bi-modal PDF are also considered in this study. Compared to the PDF given by Monte Carlo simulation, the EPC method presents good agreement with the simulated result, which can also be observed in the tail region of the PDF solution. [Copyright &y& Elsevier]