Dynamic Stiffness of Dielectric Elastomer Isolators

Abstract This work calculates the quasi-static and dynamic stiffnesses of dielectric elastomer isolators that are mechanically loaded by nominal (constant) compressive forces with sinusoidal fluctuations and have constant voltages applied through their thickness. Quasi-static membrane stretches due to nominal compressive loads are determined numerically for a wide range of voltages, and quasi-static compressive stiffnesses are calculated from the corresponding through-thickness displacements. Two calculations of quasi-static stiffness are presented, with each intended to be used for a different analysis relevant to isolator system design. The first determines the stiffness by finding the average slope of the force-displacement curve, where the nominal compressive load of interest is divided by the corresponding nominal compressive deflection. This is called the average slope stiffness, and it should be used for static calculations that determine nominal load sharing in vibration isolation systems. The second approach calculates the local slope of the force-displacement curve numerically at a particular nominal compressive load. This is called the local slope stiffness. It is intended for vibration isolation analyses. The two notions of stiffness introduced from quasi-static loading are then used to calculate dynamic stiffnesses from the time-dependent stretches induced by sinusoidal load fluctuations. For the average slope calculation, the stiffness is determined by dividing the nominal compressive load by the average dynamic stretch of the isolator. The local slope stiffness is calculated by dividing the fluctuating component of the compressive load by the first harmonic of the dynamic stretch. Comparisons of the stiffness calculations are presented for a wide range of excitation frequencies that include the resonances of the isolator. The resulting stiffnesses are shown to be controllable by varying the though-thickness voltage. The frequency dependence of the isolator’s stiffness is determined numerically. At excitation frequencies near resonance, the dynamic stiffness of the isolator changes substantially, and multi-valued stiffnesses are possible. The stiffnesses determined in this work could be used in component or system-level lumped-parameter models used in the design of vibration control systems. Dielectric elastomer isolators could be used as variable stiffness devices with semi-active, open-loop control of their properties.