Stability of fluid conveying nanobeam considering nonlocal elasticity

Abstract

In this study, the nonlocal Euler–Bernoulli beam theory is employed in the vibration and stability analysis of a nanobeam conveying fluid. The nanobeam is assumed to be traveling with a constant mean velocity along with a small harmonic fluctuation. In the considered analysis, the effects of the small-scale of the nanobeam are incorporated into the equations. By utilizing Hamilton’s principle, the nonlinear equations of motion including stretching of the neutral axis are derived. Damping effect is considered in the analysis. The closed form approximate solution of nonlinear equations is solved by using the multiple scale method, a perturbation technique. The effects of the different value of the nonlocal parameters, mean speed value and ratios of fluid mass to the total mass as well as effects of the simple–simple and clamped–clamped boundary conditions on the linear and nonlinear frequencies, stability, frequency–response curves and bifurcation point are presented numerically and graphically. The solvability conditions are obtained for the three distinct cases of velocity fluctuation frequency. For all cases, the stability areas of system are constructed analytically.