A numerical analysis of large amplitude beam vibration under different boundary conditions and excitation patterns

Abstract

Large amplitude forced vibration behavior of thin beams under harmonic excitation is studied, incorporating the effect of geometric nonlinearity. Large amplitude free vibration analysis of the same system is also carried out to obtain the backbone curves. When a very small loading is considered, the system response becomes almost identical to the backbone curve, which confirms the validity of the large amplitude study. The sets of governing equations for both forced and free vibration problems are obtained using Hamilton’s principle, whereas the same for the static problem are obtained by applying the variational form of the energy principle. The solution of the static problem provides system stiffness as a function of deflection and it becomes an input to the corresponding free vibration problem. The results are presented in the nondimensional frequency–amplitude plane in the form of response curves, and the related backbone curves are shown to represent the complete system behavior. Results for different combinations of classical flexural boundary conditions and loading patterns are reported.