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Nonlinear Free Vibration of Functionally Graded Nanobeams on Nonlinear Elastic Foundation
Abstract Nonlinear free vibration of functionally graded (FG) nanobeams on nonlinear elastic foundation is studied. The elastic foundation with cubic nonlinearity and a shearing layer is considered. The governing equations are derived based on the first-order shear deformation theory in conjunction with the von Kármán’s assumption and the Eringen’s nonlocal elasticity theory. Differential quadrature method as an efficient numerical tool is adopted to discretize the governing equations and the related boundary conditions. The discretized equations are transformed from time domain to frequency domain. The direct displacement control iterative method is used to solve the nonlinear system of algebraic equations, and the nonlinear frequency is obtained. Some examples are solved to show the applicability, rapid rate of convergence and accuracy of the method by comparing the results with those available in the literature. The effects of nonlocal parameter, boundary conditions, length-to-thickness ratios and the foundation parameters on the nonlinear free vibration of the FG nanobeams are studied.
Nonlinear Free Vibration of Functionally Graded Nanobeams on Nonlinear Elastic Foundation
Abstract Nonlinear free vibration of functionally graded (FG) nanobeams on nonlinear elastic foundation is studied. The elastic foundation with cubic nonlinearity and a shearing layer is considered. The governing equations are derived based on the first-order shear deformation theory in conjunction with the von Kármán’s assumption and the Eringen’s nonlocal elasticity theory. Differential quadrature method as an efficient numerical tool is adopted to discretize the governing equations and the related boundary conditions. The discretized equations are transformed from time domain to frequency domain. The direct displacement control iterative method is used to solve the nonlinear system of algebraic equations, and the nonlinear frequency is obtained. Some examples are solved to show the applicability, rapid rate of convergence and accuracy of the method by comparing the results with those available in the literature. The effects of nonlocal parameter, boundary conditions, length-to-thickness ratios and the foundation parameters on the nonlinear free vibration of the FG nanobeams are studied.
Nonlinear Free Vibration of Functionally Graded Nanobeams on Nonlinear Elastic Foundation
Vosoughi, A. R. (author)
2016-03-01
10 pages
Article (Journal)
Electronic Resource
English
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