A new Chebyshev spectral approach for vibration of in-plane functionally graded Mindlin plates with variable thickness
2019
Abstract This paper presents a new and simple approach for vibration analysis of in-plane functionally graded (IPFG) plates with variable thickness based on the Chebyshev
spectral method. Both the
material propertiesand the thickness which vary in the plane of the plate are approximated by high-order Chebyshev expansions. Gauss-Lobatto sampling is adopted for spatial discretization. A consistent governing equation in discrete form is derived by utilizing Lagrange’s equation for all kinds of IPFG plates whose
material propertyfunctions and thickness function are square-integrable and infinitely differentiable in the domain. Its
mass matrixis diagonal and
stiffness matrixis symmetric. Classical and point-supported boundary conditions are incorporated through projection matrices. This approach is independent of the type of material
gradation, meshfree, and flexible to adjust the computation cost and precision according to needs. A series of numerical examples involving different kinds of material
gradations, thickness variations, and boundary conditions are carried out to demonstrate the validity of the proposed method. The results obtained from the present method show a good convergence and agree with those in literature very well.
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