Size-dependent nonlinear vibration analysis of Euler–Bernoulli nanobeams acted upon by moving loads with variable speeds

Abstract

The size-dependent nonlinear vibration of Euler–Bernoulli nanobeams acted upon by moving harmonic loads traveling with variable velocities has been examined within the scope of the nonlocal strain gradient elasticity theory. Equations of motion have been derived by employing the extended Hamilton principle. For simply supported edges, the Galerkin discretizing method has been utilized to reduce the nonlinear partial differential equation of motion to a Duffing type equation. A multistage-linearization technique is employed to solve the Duffing equation approximately. The effects of the nonlocal and material length scale parameters, and the velocity, acceleration and the excitation frequency of the moving harmonic load on the nonlinear dynamic behavior of nanobeams are discussed in some detail.