On the dynamic stiffness of preloaded vibration isolators in the audible frequency range: modeling and experiments.

Abstract

The nonlinear, preload-dependent dynamic stiffness of a cylindrical vibration isolator is examined via measurements and modeling within an audible frequency range covering 50 to 1000 Hz at various preloads. The stiffness is found to depend strongly on frequency-resulting in peaks and troughs, and on preload-particularly above 500 Hz. The problems of simultaneously modeling the rubber prestrain dependence and its audible short-term response are removed by adopting a nearly incompressible material model, being elastic in dilatation while displaying viscoelasticity in deviation. The latter exhibits a time strain separable relaxation tensor with a single function embodying its time dependence. This function is based on a continuous fractional order derivative model, the main advantage being the minimum number of parameters required to successfully model the rubber properties over a broad structure-borne sound frequency domain, while embodying a continuous distribution of relaxation time. The weak formulations corresponding to the stiffness problem are solved by an updated Lagrangian nonlinear finite-element procedure. The model and measurement results agree strikingly well with static and dynamic measurements throughout the whole frequency domain for the examined preloads.