Vibration analysis of multiple-layer microbeams based on the modified couple stress theory: analytical approach

The modified couple stress theory (MCST) is used to capture size effect on dynamic response in multiple-layer microbeams in the present article. Governing equations of the system are obtained based on the MCST and using Hamilton’s principle. The natural frequencies of the multiple-layer microbeam are calculated using the analytical method. Then, the results of the natural frequencies are presented with respect to different values of the system parameters such as the geometric layers and also the dimensionless material length-scale parameter. The results show that the material length-scale parameter values and also the length, width, and thickness of each layer are extremely effective on the vibration characteristic of the multiple-layer microbeams.