Response of Shock Isolators with Piecewise Linear Asymmetric Damping

Abstract

The output of a single-degree-of-freedom (SDOF) piecewise linear system with asymmetric damping and linear stiffness excited by Dirac impulse excitation is studied. Analytical solutions of the response for piecewise linear systems are obtained by replacing the equation of motion with Dirac excitation by a homogeneous differential system with zero initial displacement and a given initial velocity. A significant improvement of the response consisting in a substantial reduction in the after-shock vibrations was obtained. The obtained results are applied to the damping optimization of a shock isolation system for forging hammers.