Dynamic Stability of a Base-Excited Thin Beam with Top Mass

This paper deals with a base-excited clamped-clamped vertical thin beam carrying a top mass. The thin beam is considered to be inextensible and initially not perfectly straight. Based on Taylor series expansions of the inextensibility constraint and the exact curvature, and by using one or more basis functions, a semi-analytical model is derived. This model is numerically validated through a comparison with quasi-static and modal analysis results obtained using finite element modelling. The steadystate nonlinear dynamics of the base-excited beam are investigated using numerical continuation of periodic solutions and bifurcations. Using these numerical tools, the dynamic stability of the beam is investigated for various parameter settings, including the effect of nonlinear damping. The continuation of bifurcations appears to be very suitable to determine whether or not parametric resonance occurs for certain parameter settings