Viscoelastic effects on nonlinear dynamics of microplates with fluid interaction based on consistent couple stress theory

In this study, the vibrations of a viscoelastic microplate in incompressible still fluid are investigated. The microplate is supposed simply supported in stationary fluid and made of viscoelastic material that follow the Leaderman viscoelastic model The fluid inertial effects as well as fluid damping on microplate vibration are also studied by applying three dimensional aerodynamic theory. The added mass values are obtained for various aspect ratios of the microplate and compared with available models. The non-classic stress and couple-stress tensors are calculated based on consistent couple stress theory and Leaderman integral. The resultant virtual works inserted in Hamilton’s principle and the governing equations of motion are derived. These coupled equation are simplified by Galerkin method and solved using harmonic balance analytical method. The results show that considering the added mass effects reduces the microsystem nonlinearity.

Keywords:

microplate , fluid effects , added mass , consistent couple stress , Viscoelastic