Nonlinear Free Vibrations of Functionally Graded Microplates Based on the Modified Couple Stress Theory

Abstract

AbstractIn this study, axisymmetric nonlinear natural frequencies of simply supported functionally graded (FG) annular microplate are investigated. In the formulation, it is considered that the mechanical properties such as modulus of elasticity, shear modulus of elasticity, and material properties such as density of the FG microplate change in the thickness direction. The size effect is taken into account by using the modified couple stress theory (MCST). Formulation is based on the Mindlin plate theory, and the nonlinearity in the formulation is due to von Karman’s large deformation assumption. The governing nonlinear partial differential equations of motion and boundary conditions for the FG microplate are derived by using the variational approach and Hamilton’s principle. The harmonic balance method is utilized in order to obtain a nonlinear eigenvalue problem. An iterative eigenvalue solver is used to determine the nonlinear natural frequencies of the FG microplate as a function of vibration amplitude.KeywordsFunctionally graded microplateNonlinear vibrationModified couple stress theory