Nonlinear vibrations of a pre-stressed laminated thin plate

In this communication, we present the numerical analysis of nonlinear vibrations of a pre-stressed, laminated, thin, square plate. The laminate is modeled as an isotropic nonlinear plate with effective elastic properties and the model is validated experimentally. The geometrically nonlinear vibrations are analyzed using the finite difference method, and the time integration technique based on the Newmark method combined with the fixed-point iterations to satisfy compatibility. The system exhibits behavior similar, but not identical, to the standard Duffing oscillator. Superharmonics are examined using phase space representation, Fourier transforms, deflection history, and centerline deflection shapes. The deflection shapes show significant presence of higher order spatial harmonics.