Resonant responses of three-layered shear-deformable microbeams

This paper analyses the coupled resonant motion of three-layered shear-deformable microbeams. On the basis of the modified couple stress theory, while both the rotational and translational motions are considered, the size-dependent potential energy of the three-layered microsystems is developed based on a continuous variation of the displacement field through the thickness and constitutive relations. The kinetic energy is also developed in terms of the continuous displacement field. The works done by the external dynamic load and the viscous damping are obtained in terms of the displacement field and microsystem parameters. A dynamic balance is applied to the works of external force and damping of the three-layered microbeam and its kinetic energy and size-dependent potential energy. The nonlinear continuous models for the longitudinal, transverse, and rotational motions are then reduced via use of a weighted-residual method. Numerical simulations upon the reduced-order models for the translational and rotational motions are performed for the three-layered microbeam via use of Houbolt's finite difference scheme together with Newton-Raphson method. The size-dependent nonlinear coupled resonant responses of the three-layered microsystem are obtained and presented in the form of frequency-responses and force-responses. The effects of three-layered microsystem parameters such as the thickness and material percentage of each layer on the microsystem motion are examined.