Passive vibration isolation is important in the automotive industry where the undesirable effects of powerplant vibrational excitation need to be isolated from the occupants and the automobile interior. Recently, hydraulic engine mounts have proven to be effective in this capacity and have replaced traditional elastomeric mounts in many automobiles. While the characteristics of the mount itself are well-established, no systematic investigations have been conducted that consider the nonlinear response of the total system consisting of an engine on mounts.; Therefore, to better understand this type of vibration system, the harmonic response and vibration isolation performance of a planar, three degree of freedom rigid body on resilient linear supports is investigated. The nonlinear differential equations of motion for the system are derived using Lagrange's equations. Approximate solutions of these equations for four different forcing cases are formulated using the method of multiple scales. The frequency response of each degree of freedom for these four cases is obtained from these approximate solutions. Specifically, the response for this system where 1:1 and 2:1 internal resonances exist between the system linear natural frequencies is found. The analysis identifies regions where multiple steady-state solutions exist, and other regions where no constant amplitude steady-state solutions exist. The and related to a novel type of vibration isolator.; This thesis also includes a review of the four common metrics used to assess the performance of isolation systems. These metrics are: transmissibility, effectiveness, transmitted power, and the forces transmitted to the support structure. The assumptions made in the formulation of these metrics are presented, and the measure of the transmitted forces is modified and applied to the planar problem presented in the thesis.
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