Frequency analysis of the nonlinear viscoelastic plates subjected to subsonic flow and external loads

• Nonlinear frequency response of the plates subjected to subsonic air flow are predicted.
• Frequency responses of the plate system is remarkably influenced by the aspect ratio.
• Primary, super-harmonic and sub-harmonic resonance conditions are taken into account.
• Both types of hardening and softening behavior are identified dependent on the aspect ratio.
• Closed-form frequency–amplitude solutions are obtained in different resonance conditions.

Frequency analysis of the nonlinear viscoelastic plates subjected to the subsonic fluid flow and external loads is presented in this paper. Von-Kàrmàn plate assumptions have been applied and the governing equation of motion of the plate has been derived considering Kelvin׳s structural damping model. Nono-dimensional forms of the governing equations are derived and the Galerkin׳s approach is employed to discretize the continuous system. Using Bernoulli׳s principal, the pressure distribution formula is obtained to model the fluid flow affecting the plate. Multiple Scales method has been used to solve the nonlinear equation of motion. Frequency response curves, time history responses and state space graphs have been obtained for the non-resonance, primary resonance, super-harmonic resonance and sub-harmonic resonance cases. Stability of the solutions has been analyzed and in a parametric study, effects of different parameters on the frequency responses have been studied.