Influence of micro-length-scale parameters and inhomogeneities on the bending, free vibration and wave propagation analyses of a FG Timoshenko's sandwich piezoelectric microbeam

In this study, the strain gradient theory is employed to derive governing equations of motion of a functionally graded Timoshenko's sandwich microbeam resting on Pasternak's foundation. The microbeam is including a micro-core and two piezoelectric face-sheets on top and bottom. The plate is actuated with applied electric potential at top of piezoelectric face-sheets. The governing equations of motion are derived using Hamilton's principle and strain gradient theory. After derivation of governing equations of motion, the problem is solved for three classes of analysis including wave propagation, free vibration and bending analysis. The numerical results are presented to reflect the effect of important parameters such as wave number, applied voltage, inhomogeneous index, parameters of foundation and material length-scale parameters on the different responses. The obtained results indicated that changing material length-scale parameters leads to a stiffer structure that increase natural frequencies and decreases transverse deflection and maximum electric potential.