Bimodular Microbeams Based on the Elastic Foundation: Free Vibration

Abstract

The paper uses the modified couple stress theory to study the free vibration model of bimodular microbeams with an elastic foundation. Microbeams behave differently in the tension and compression zones due to the bimodular property, and the neutral layer depends on the sign of the bending moment. By figuring out the effective strain formula and applying Hamilton’s principle, the governing equation for free vibration can then be derived. The equation takes into account the size effect, the foundation parameters, and the bimodular property’s effects. Using the differential quadrature method, it is examined how the foundation parameters and the material length scale parameters affect free vibration. The findings indicate that frequency increases as parameter size increases.