Analysis of buckled and pre-bent fixed-end columns used as vibration isolators

The use of a buckled or pre-bent column with fixed ends as a vibration isolator is analyzed. The column is designed to have a high axial stiffness under the weight that it supports, so that the static displacement of the weight is not excessive, and then to have a low stiffness during excitation. The base of the column is assumed to have an axial motion which is simple harmonic or a linear combination of two simple harmonic functions. The column is modeled as an elastica. First the equilibrium shape under the supported weight is determined. Then small steady-state vibrations about the equilibrium configuration are obtained numerically using a shooting method. The inertia of the supported weight and the transverse and axial inertias of the column are included. The axial displacement transmissibility is computed, and the effects of external and internal damping, column stiffness, supported weight, and initial curvature are investigated. For the two-frequency excitation, the effects of the relative amplitudes and frequencies of the excitation components are considered.