Analysis of a vibration isolation table comprising post-buckled Γ-shaped beam isolators

In this paper, the static and dynamic characteristics of a nonlinear passive vibration isolation table is investigated through finite element analysis. The intended application is specifically isolation in the vertical direction where the isolator is required to be sufficiently stiff statically to bear the weight of the isolated object and soft dynamically for small oscillations about its equilibrium position. The modelled configuration consists of a rigid isolation table mounted on two Γ-shaped beam isolators which are loaded to their post-buckled state in their unstable buckling mode by the weight of the isolated mass. A nonlinear static analysis is presented to establish the negative stiffness provided by the buckled beams, and two linear springs are then added in parallel which are chosen to have just sufficient stiffness to restore stability. Modal analysis of the linearized system about its statically deformed position (1mm) gives a natural frequency of just 1Hz which is considerably lower than is achievable by a linear isolator. Motion transmissibility of the linearized system shows a non-resonant isolation region spanning two decades when the system is perfectly symmetric but additional resonance peaks appear when asymmetries are included in either the mass or stiffness distribution. Several strategies are explored for reducing the prominence of these resonances.