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Microbeams are widely used in micro-electro-mechanical systems (MEMS). These systems are alternatives to piezo-resistive sensors because of their high sensitivity and low power consumption. Unlike with the classical theory of continuous media, in order to see the effects of the system being micro-sized, the effect of micro-structure was added to the system based on the modified couple stress theory (MCST) for fluid conveying microbeam. By using Hamilton’s principle, the nonlinear equations of motion for the fluid conveying micro beam were obtained. Microbeam was investigated under electrical field and resting on an elastic foundation. It is assumed that the fluid velocity changes harmonically around a constant velocity and that the electrical field force changes harmonically with time. Approximate solutions of the system were achieved by using the multiple time scale method. 3:1 and 2:1 internal resonance cases were investigated. Detuning parameter-amplitude variation graphs were obtained, and stability areas were shown.

Investigation of 3:1 and 2:1 internal resonances in fluid conveying microbeam