The size-dependent vibration analysis of micro-plates based on a modified couple stress theory

A microscale vibration analysis of micro-plates is developed based on a modified couple stress theory. The presence of the length scale parameter in this theory enables us to describe the size effect in micro-structures. A variational approach based on Hamilton’s principle is employed to obtain the governing equations of motion. To illustrate the new model, the free vibration analysis of a rectangular micro plate with two opposite edges simply supported and arbitrary boundary conditions along the other edges and a circular micro-plate are considered. The natural frequencies of micro-plates are presented for over a wide range of length scale parameters, different aspect ratios and various boundary conditions for both rectangular and circular micro-plates. The effect of length scale parameter on natural frequencies of micro-plates are discussed in details and the numerical results reveal that the intrinsic size dependence of material leads to increase the natural frequency.

Research highlights
► A new model is presented for vibration analysis of micro-plates using a modified couple stress theory.
► The model contains an internal material length scale parameter and can predict the size effect in micro-scale plates.
► The natural frequencies are presented for both rectangular and circular micro-plates.