Vibration Analysis of Magneto-Electro-Elastic Timoshenko Micro Beam Using Surface Stress Effect and Modified Strain Gradient Theory under Moving Nano-Particle

In this article, the free vibration analysis of magneto-electro-elastic (MEE) Timoshenko micro beam model based on surface stress effect and modified strain gradient theory (MSGT) under moving nano-particle is presented. The governing equations of motion using Hamilton’s principle are derived and these equations are solved using differential quadrature method (DQM). The effects of dimensionless electric potential, dimensionless magnetic parameter, material length scale parameter, external electric voltage, external magnetic parameter, slenderness ratio, temperature change, surface stress effect, two parameters of elastic foundation on the dimensionless natural frequency are investigated. It is shown that the effect of electric potential and magnetic parameter simultaneously increases the dimensionless natural frequency. On the other hands, with considering two parameters, the stiffness of MEE Timoshenko micro beam model increases. It can be seen that the dimensionless natural frequency of micro structure increases by MSGT more than modified couple stress theory (MCST) and classical theory (CT). It is found that by increasing the mass of nano-particle, the dimensionless natural frequency of system decreases. The results of this study can be employed to design and manufacture micro-devices to prevent resonance phenomenon or as a sensor to control the dynamic stability of micro structures.