Static/dynamic analyses of sandwich micro-plate based on modified strain gradient theory

Abstract

In this work, bending and dynamic analyses of a three-layered functionally graded micro annular plate whit piezomagnetic layers are investigated based on FSD circular plate theory. The micro plate is subjected to magnetic field. It is assumed that the micro annular plate is resting on an orthotropic elastic medium. The stress relations which cooperate both mechanical and magnetic interactions are calculated based on MSGT and the governing equations are extracted through Hamilton’s principles. In order to solve the governing equations of micro annular plate, the numerical Ritz method is applied. After convergence of Ritz solving domain the obtained results are compared and adapted with the output results of the previous studies. Effects of magnetic field, thickness of metal-to-ceramic ratio, length-to-width ratio of micro annular plate, small scale parameter and thickness of piezomagnetic layers ratio are studied on the frequencies and deflection of micro annular FGM plate. The results show that applying the magnetic field lead to increase of micro structure stiffness and enhances the natural frequencies, while the maximum deflection of micro structure decreases with increasing micro annular plate stiffness. Also, it is concluded that that due to the high ceramic stiffness, the natural frequencies and the deflection of the micro annular plate reduces and increases with increasing of the thickness of the metal to the ceramic ratio, respectively.