Dynamic Study of a Microbeam Conveying Fluid Flow on a Viscoelastic-Pasternak Foundation and Subjected to an Axial Load using Modified Couple Stress Theory

In this paper, dynamic analysis of a microbeam conveying incompressible fluid flow and resting on a nonlinear viscoelastic-Pasternak foundation under the action of an axial load is investigated using the modified couple stress theory. Two boundary conditions including cantilever and clamped-clamped are considered for the microbeam with rectangular and circular hollow cross sections. The effect of changes of different parameters such as fluid flow velocity, the length scale parameter (size effect), linear and nonlinear stiffneses of foundation, foundation’s damping coefficient, shear layer stiffness of foundation and the value of axial force on the linear and nonlinear natural frequency of microbeam have been investigated. Increasing the axial force leading to tangible decreases of the natural frequencies for the microbeam. Moreover, the stability range of a cantilever microbeam is lesser than the one for microbeam with clamped-clamped boundary condition. Also, using the modified couple stress theory, the frequency and critical fluid velocity stability range for the microtube is greater than the one obtained using classical beam’s theory.