Vibration and dynamic analysis of a cantilever sandwich microbeam integrated with piezoelectric layers based on strain gradient theory and surface effects

Abstract

In this paper, size-dependent vibration and dynamic analysis of an advanced sandwich composite microbeam including piezoelectric layers based on higher-order strain gradient and surface effects theories are investigated. To evaluate and analyze the effect of surface energy, length scale parameters and dynamic response on the transverse vibration and stability of sandwich smart composite microbeam with piezoelectric layers, the partial differential equation of motion is obtained using Hamilton's principle. Subsequently, this equation is transformed into a set of ordinary differential equations according to the generalized differential quadrature method. The influences of various material length scale associated with strain gradient theory, geometry and surface parameters such as thickness to material length scale parameter, surface residual stress, Young's modulus of surface layer, surface mass density and surface piezoelectric constant on structural dynamic deflection behavior and natural frequency have been investigated. In addition, the vibration and dynamic responses of the model were compared with those micro sandwich beams based on modified couple stress and classical theories. The obtained results are compared with the results available in the literature to validate the correctness of the present solution method. The results indicated that strain gradient theory with considering the surface effects increases the model stiffness and shifts the amplitudes to lower magnitude faster in comparison to other theories. Moreover, the influences of material length related to dilatation gradient on vibrational frequency are significant among the other parameters. Also, the free vibrational frequency increases with decreasing the length to thickness ratio.