Non-Linear Vibrations of a Microbeam Resting on an Elastic Foundation

In this study, response of a microbeam bonded to a non-linear elastic foundation is investigated. The model accounts for mid-plane stretching, an applied axial load, and an AC harmonic force. The microbeam is resting on a non-linear elastic foundation which introduces a cubic non-linear term to the equations of motion. Immovable end conditions introduce integral type nonlinearity. The integro-differential equations of motion are solved analytically by means of direct application of the method of multiple scales (a perturbation method). The amplitude and phase modulation equations are derived for the case of primary resonances. Frequency-response curves and non-linear frequencies are analyzed with respect to the effective physical parameters. Influence of elastic foundation coefficients, coefficients related to dielectric constants, and mid-plane stretching on the vibrations of the microbeam are investigated.