Free vibration, wave propagation and tension analyses of a sandwich micro/nano rod subjected to electric potential using strain gradient theory

Strain gradient theory is used to study free vibration, wave propagation and tension analyses of a sandwich micro/nano rod made of piezoelectric materials under electric potential. The structure is resting on a Pasternak's foundation medium. Love's rod model is used for derivation of displacement field. The piezoelectric face sheets are subjected to two-dimensional electric potential including an applied voltage at top of plate and a cosine term along the thickness direction. Hamilton's principle is used to derive governing equations of motion in terms of axial displacement and electric potential. Three distinct behaviors of the present problem including free vibration, wave propagation and tension analyses are performed. Some important numerical results are presented in detail to capture the effect of materials length scales and applied voltage on the different behaviors of microrod.