Forced axial vibration of micro and nanobeam under axial harmonic moving and constant distributed forces via nonlocal strain gradient theory

Abstract

In this paper the forced axial vibration of a nanobeam by deploying the nonlocal strain gradient theory exposed to a distributed moving force, is investigated. The assumed nanobeam in this paper is under the axial constant distributed load. The governing equations of the vibration of the nanobeam are obtained via the classic beam theory and the Hamilton principle. The determined partial differential equations are converted to differential equations by applying the assumed modes method. The dynamic axial displacement of the nanobeam along its length, is obtained by solving the differential equations via the convolution integral. The effect of length scale parameter, nonlocal parameter, velocity parameter, the constant distributed load and the excitation frequency on the maximum nondimensional dynamic axial displacement of the nanobeam are analyzed. Accordingly, the effect of these two parameters on the maximum nondimensional axial displacement of the nanobeam under the harmonic moving load is of significance importance.

Keywords:

• Axial response
• convolution integral
• maximum nondimensional axial displacement
• moving force
• nonlocal strain gradient