Size-dependent forced vibration of an imperfect functionally graded (FG) microplate with porosities subjected to a moving load using the modified couple stress theory

In the present paper, static bending and forced vibration of an imperfect FG microplate carrying a moving load are dealt with based on Mindlin plate theory (MPT) and the modified couple stress theory (MCST). The material properties of FG microplate change continuously along thickness direction according to simple power law. The concept of neutral surface is used to eliminate stretching-bending coupling. The imperfection of the microplate is caused by the porosities that may occur inside FG material during the fabrication. The energy approach basis on the Lagrange equations is used to obtain the response of FG microplate. The trial functions denoting the transverse deflection and the rotations about x and y coordinates are expanded into the series using the two dimensional polynomials to acquire the approximate solution. An efficient and simple method is presented to satisfy the various boundary conditions with the help of some auxiliary functions in the trial functions. The equations of motion of FG microplate are solved in time domain by means of Newmark's method. The effects of the material variation, porosity volume fraction and porosity scheme, length scale parameter and the velocity of the moving load on the dynamic responses are investigated. Besides, the reliability of the present formulation and the computer codes developed by the authors is established by using the static responses of FG microplate.