Free vibration analysis of magneto-electro-elastic microbeams subjected to magneto-electric loads

Highlights: • Free vibration of a MEE microbeam is investigated. • The governing equations and boundary conditions are derived. • Natural frequencies of the microbeam under electric and magnetic potentials are obtained. • Critical values of electric and magnetic potentials that lead to buckling are obtained. Different types of actuating and sensing mechanisms are used in new micro and nanoscale devices. Therefore, a new challenge is modeling electromechanical systems that use these mechanisms. In this paper, free vibration of a magnetoelectroelastic (MEE) microbeam is investigated in order to obtain its natural frequencies and buckling loads. The beam is simply supported at both ends. External electric and magnetic potentials are applied to the beam. By using the Hamilton's principle, the governing equations and boundary conditions are derived based on the Euler–Bernoulli beam theory. The equations are solved, analytically to obtain the natural frequencies of the MEE microbeam. Furthermore, the effects of external electric and magnetic potentials on the buckling of the beam are analyzed and the critical values of the potentials are obtained. Finally, a numerical study is conducted. It is found that the natural frequency can be tuned directly by changing the magnetic and electric potentials. Additionally, a closed form solution for the normalized natural frequency is derived, and buckling loads are calculated in a numerical example.