Analytical Approach for Vibration Analysis of a Microsensor with Two layers of Silicon and Piezoelectric based on MCST

Document Type: Original Research Paper


Faculty of Mechanical and Energy Engineering, Shahid Beheshti University, Tehran, Iran



The vibration analysis is an important step in the design and optimization of microsensors. In most of the cases, COMSOL software is employed to consider the size-dependency on the dynamic behavior in the MEMS sensors. In this paper, the Modified Couple Stress Theory (MCST) is used to capture the size effect on dynamic behavior in a microsensor with two layers of the silicon and piezoelectric. The governing equations of the system and also associated boundary conditions are derived based on the MCST and using Hamilton’s principle by obtaining the total kinetic and potential energies of the system. Then, the obtained governing equations are solved using an analytical approach to determine the natural frequencies of the system. The first, second and third natural frequencies of the microsensor are determined using an analytical approach. Finally, the natural frequency variations of the system are presented with respect to different values of the system parameters such as dimensionless parameters of the sensor geometric, the thickness of the silicon and piezoelectric layers and also the dimensionless material length scale parameter. The obtained results show that the material length scale parameter values and also the length, width, and thickness of each layer of the sensor are extremely effective on the vibration characteristics of the piezoelectric cantilever-based Micro Electro Mechanical System (MEMS) sensors. Also, the results show that the first natural frequency of the microsensor will decrease with either increasing dimensionless material length scale parameter or decreasing the thickness of silicon and piezoelectric. This analytical approach presents an efficient method to predict the dynamic behavior of microsensors and consequent optimization in their design procedure.