Nonlinear free vibration analysis of simply supported piezo-laminated plates with random actuation electric potential difference and material properties

Studies are made on nonlinear free vibrations of simply supported piezo-laminated rectangular plates with immovable edges utilizing Kirchoff’s hypothesis and von Kármán strain–displacement relations. The effect of random material properties of the base structure and actuation electric potential difference on the nonlinear free vibration of the plate is examined. The study is confined to linear-induced strain in the piezoelectric layer applicable to low electric fields. The von Kármán’s large deflection equations for generally laminated elastic plates are derived in terms of stress function and transverse deflection function. A deflection function satisfying the simply supported boundary conditions is assumed and a stress function is then obtained after solving the compatibility equation. Applying the modified Galerkin’s method to the governing nonlinear partial differential equations, a modal equation of Duffing’s type is obtained. It is solved by exact integration. Monte Carlo simulation has been carried out to examine the response statistics considering the material properties and actuation electric potential difference of the piezoelectric layer as random variables. The extremal values of response are also evaluated utilizing the Convex model as well as the Multivariate method. Results obtained through the different statistical approaches are found to be in good agreement with each other.