Parametric instability of a beam due to axial excitations and to boundary conditions

In this paper the stability of the lateral dynamic behavior of a pinned-pinned, clamped-pinned and clamped-clamped beam under axial periodic force or torque is studied. The time-varying parameter equations are derived using the Rayleigh-Ritz method. The stability analysis of the solution is based on Floquet's theory and investigated in detail. The Rayleigh-Ritz results are compared to those of a finite element modal reduction. It is shown that the lateral instabilities of the beam depend on the forcing frequency, the type of excitation and the boundary conditions. Several experimental tests enable the validation of the numerical results.