Vibration isolation using buckled or pre-bent columns—Part 2: Three-dimensional motions of horizontal rigid plate

This is a continuation of previous work to investigate the use of pairs of pre-bent columns, bonded with a viscoelastic filler, as vibration isolators. In this paper, four of these devices support the corners of a square, rigid plate. When the system is in equilibrium, small harmonic vibrations are applied vertically to the base of the isolators, and the steady-state response of the system is determined. First, the system is analyzed for the fully symmetric case, i.e., the center of mass of the plate coincides with the geometric center. Then, the system is analyzed for various cases in which the center of mass has some eccentricity. The eccentric weight introduces rotational motions of the plate. The governing equations are formulated and then numerically solved in Mathematica using a shooting method. The displacement transmissibility is plotted over a range of excitation frequencies, and the mode shapes are shown for the first few resonant frequencies. Free vibration of the system is also considered. For this three-dimensional system, the pre-bent columns can be effective at isolating vibrations for a wide range of excitation frequencies.