Vibrations of fluid conveying micro-beam

In this study fluid carrying continuous media was considered as micro beam. To see the effects of the system being micro-sized, unlike the classical theory of continuous media, the effects of micro-structure added to the system with ?Modified Couple Stress Theory? (MCST). By using Hamilton?s principle, the nonlinear equations of motion for the fluid carrying micro beam was obtained. Micro beam considered under electrical field and resting on an elastic foundation. By considering extension of beam, elastic foundation, damping effect and electrical field strength the equations of motion gained extra nonlinear terms. The obtained equations of motion become independence from material and geometric structure by nondimensionalization. Flow velocity assumed as harmonically varying about a mean velocity. Still, the force of the electric field changes over time considered as harmonic. Approximate solutions of the system achieved by using the Multiple Time Scales Method (A perturbation method). The effect of micro-structure, the nonlinear terms from extension, linear and nonlinear spring constants, the occupancy rate of the beam, the fluid velocity, the force of the electric field on natural frequency and solutions were researched. Basic parametric resonance condition (fluid velocity change frequency is about twice of natural frequency), primary resonance condition (electrical field strength change frequency is about natural frequency) and special resonance condition that contains both critical condition for fluid carrying micro beam were studied. The stability analysis performed for the solutions. MCST compared with classical beam theory and showed that we should consider the effects of micro-structure during analysis. Keywords: Fluid carrying micro beam, perturbation analysis, nonlinear vibration, stability analysis