Numerical Simulation of Impact Responses for an Elastic Structure with a Viscoelastic Spring Including Nonlinear Hysteresis Damping

Abstract

To compute dynamic characteristics of nonlinear viscoelastic springs with elastic structures having huge degree-of-freedom, Yamaguchi proposed a new fast numerical method using finite element method. In this method, restoring forces of the springs are expressed using power series of their elongation. In the expression, nonlinear hysterisis damping is introduced. Finite element for the nonlinear spring having complex coefficients is expressed and is connected to the elastic structures modeled by linear solid finite element. Further, to save computational time, the discrete equations in physical coordinate are transformed into the nonlinear ordinary coupled equations using normal coordinate corresponding to linear natural modes. In this report, the proposed method is applied to simulation for impact responses of a silicone block with an elastic structure (a S-shaped structure) by colliding with a concentrated mass. The concentrated mass has initial velocities and collides with the silicon block. Accelerations of the elastic structure and the concentrated mass are measured using Levitation Mass Method proposed by Fujii. The calculated accelerations from the proposed FEM, corresponds to the experimental ones.