Response of non-linear dissipative shock isolators

In this paper, a simple technique combining the straightforward perturbation method with Laplace transform has been developed to determine the transient response of a single degree-of-freedom system in the presence of non-linear, dissipative shock isolators. Analytical results are compared with those obtained by numerical integration using the classical Runge-Kutta method. Three types of input base excitations, namely, the rounded step, the rounded pulse and the oscillatory step are considered. The effects of nonlinear damping on the response are discussed in detail. Both the positive and negative coefficients of the nonlinear damping term have been considered. It has been shown that a critical value of the positive coefficient maximizes the peak values of relative and absolute displacements. This is true for any power-law damping force with an index greater than 1. On the other hand, the overall performance of a shock isolator improves if the nonlinear damping term is symmetric and quadratic with a negative coefficient