Nonlinear Vibration of Microbeams under Magnetic Field Using the Modified Couple Stress Theory

In this work, nonlinear vibration of microbeams under magnetic field is studied. The equation governing motion of microbeam resting on a linear elastic layer and under magnetic field is derived by using the modified couple stress theory and Hamilton’s principle. Amplitude–frequency relationships of microbeams with pinned–pinned and clamped–clamped end conditions are obtained in closed-forms by using the equivalent linearization method with a weighted averaging. Accuracy of the present solution is verified by comparising the obtained solution with previous solutions. Efects of the material length scale parameter, the stiffness coefficient of the linear foundation and the magnetic field on the frequency ratios of microbeams are investigated in this paper.