Stability and nonlinear dynamical analysis of functionally graded microplates

This paper conducts an investigation into the nonlinear dynamical analysis of a functionally graded microplate resting on an elastic foundation. The first part of the paper is devoted to formulate the forced nonlinear mathematical model of the functionally graded microsystem in the Hamiltonian framework. To this end, the von Karman plate theory together with the modified couple stress theory is used to obtain the in-plane and transverse motions of the microplate; the Mori-Tanaka homogenisation scheme is employed to take into account the variable material properties of the microplate through its thickness. A Winkler-type elastic foundation is considered as the bed of the microplate; a series of linear and nonlinear springs are attached to the microplate so as to approximate the elastic characteristics of the foundation. In the second part of this study, the resonant behaviour of the functionally graded microplate is obtained by numerical simulations via use of a parameter-continuation technique together with direct time-integration scheme. Moreover, the influences of the key parameters of the system (such as the material index and foundation's linear and nonlinear coefficients) affecting the bifurcations on the forced resonant behaviour of the functionally graded microplate are explored through extensive numerical simulations. The outcome of this paper, which is the size-dependent nonlinear resonant oscillations, can readily be used in MEMS industry, where functionally graded microplates are used as deformable electrodes.