Vibration isolation using buckled or pre-bent columns—Part 1: Two-dimensional motions of horizontal rigid bar

The use of buckled columns, or pairs of pre-bent columns bonded with a viscoelastic filler, as vibration isolators is analyzed. They support a horizontal rigid bar at its ends, and harmonic vertical motion is applied at the base of the isolators. The displacement transmissibility is analyzed for both symmetric and asymmetric bars. In the latter case, the bar exhibits rotational as well as translational motion. Each column is modeled as an elastica, allowing for large deflections. Small steady-state vibrations about the equilibrium configuration of the system are analyzed. After formulation of the governing equations, a shooting method is utilized to obtain numerical solutions in Mathematica. The transmissibility is plotted as a function of the excitation frequency, and vibration shapes associated with peaks in the transmissibility plots are shown. For the buckled single-column isolators, the effect of the amount of asymmetry of the bar is examined. For the bonded two-column pre-bent isolators, the effects of the filler stiffness, amount of initial curvature, and supported weight are determined. The isolators can be effective for a large range of excitation frequencies.