Size dependent nonlinear vibration of the tensioned nanobeam based on the modified couple stress theory

Abstract

Abstract This paper presents a nonlinear vibration analysis of the tensioned nanobeams with simple–simple and clamped–clamped boundary conditions. The size dependent Euler–Bernoulli beam model is applied to tensioned nanobeam. Governing differential equation of motion of the system is obtain by using modified couple stress theory and Hamilton's principle. The small size effect can be obtained by a material length scale parameter. The nonlinear equations of motion including stretching of the neutral axis are derived. Damping and forcing effects are considered in the analysis. The closed form approximate solution of nonlinear equations is solved by using the multiple scale method, a perturbation technique. The frequency-response curves of the system are constructed. Moreover, the effect of different system parameters on the vibration of the system are determined and presented numerically and graphically. The size effect is significant for very thin beams whose height is at the nanoscale. The vibration frequency predicted by the modified couple stress theory is larger than that by the classical beam theory. Comparison studies are also performed to verify the present formulation and solutions.