Nonlinear harmonic vibration and stability analysis of a cantilever beam carrying an intermediate lumped mass

Nonlinear forced vibration of a cantilever beam with an intermediate lumped mass is studied, and the nonlinear governing equation of the vibrating beam using Euler–Lagrange method is derived. Two types of nonlinearities, including the inertial term and the elastic part, are included in the nonlinear differential equation of motion. The multiple scales method is adopted as the solution procedure for this problem and the conditions of the primary...