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This article deals with the vibrational characteristics of a laminated composite annular microplate using a non-classical continuum theory called modified couple stress theory (MCST). Also, the structure is patched with the piezoelectric layer and covered with a viscoelastic foundation that simulated via the Kelvin-Voight model. The non-classical governing equations and boundary conditions of the size-dependent annular microplate are derived by adding the symmetric rotation gradient and higher-order stress tensors to the strain energy. The current non-classical model is capable of capturing the size-dependency in the annular microplate by using only one material length scale parameter. Moreover, the mathematical formulation of annular microplate based on the classical model can be recovered from the present model by neglecting the material length scale parameter. Finally, the non-classical governing equations are solved using the generalized differential quadrature method (GDQM) for various boundary conditions. Afterward, a parametric study is carried out to investigate the effects of the length scale parameter, piezoelectric layer, radius ratio, circumferential and radial mode number, geometry of laminated layer, and boundary conditions on the frequency responses of the annular microplate by considering MCST. The results show that in the grater elastic properties ratio () factor, increasing the damping parameter () cannot make any changes in the frequency of the disk.

On the dynamics of a laminated annular piezoelectric microsystem on a viscoelastic substrate within modified couple stress elasticity