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

In this study, for the first time the forced vibration of a viscoelastic microplate in incompressible still fluid is investigated, simultaneously. The consistent couple stress theory which newly developed on the basis of the original couple stress theory is used in this study. 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 theories. 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. The results show that considering the added mass effects reduces the microsystem nonlinearity.