Nonlinear free vibration analysisof a piezo-laminated viscoelastic platesubjected to follower force

The geometrically nonlinear vibrations and stability of piezo-laminated viscoelastic plate subjected to uniformly distributed tangential follower force are investigated utilizing Kirchoff´s hypothesis and the two-dimensional viscoelastic differential constitutive relation. The von Ka´rman´s large deflection equations for generally laminated viscoelastic plates subjected to uniformly distributed tangential follower force are derived in terms of stress function and transverse deflection function. The force excited by the piezoelectric layer due to external voltage is modeled as the follower tensile force, the differential equation in the Laplace domain is deduced. Then, the differential equation of motion of the viscoelastic plate constituted by elastic behavior in dilatation and the Kelvin-Voigt model for distortion in time domain is derived. A deflection function satisfying the simply supported boundary conditions is assumed, and a stress function is obtained by solving the compatibility equation. A governing equation is obtained by applying the Galerkin´s method to the nonlinear partial differential equations.