Damping response analysis for a structure connected with a nonlinear complex spring and application for a finger protected by absorbers under impact forces

• We analyze impact responses of a pair of viscoelastic shock absorbers with and without a human finger.
• We propose a new numerical method using complex nonlinear concentrated springs with FEM.
• We introduce complex values for the nonlinear spring constants to represent nonlinear hysteresis.
• To reduce DOF, we introduce normal coordinates corresponding to linear vibration modes.

This paper describes the dynamic response of a finger protected by a pair of viscoelastic absorbers under impact forces. The restoring forces of the finger and the absorbers are measured using the levitation mass method proposed by Fujii. In this study, we carry out numerical analysis of the dynamic response of a finger protected by absorbers under the same conditions as in the experiment. The absorbers and the finger are modeled by nonlinear concentrated springs using the power series of the elongations. Nonlinear complex spring constants are used to represent the changes in hysteresis as elongation progresses. This nonlinear spring is connected to a levitated block, which is modeled by three-dimensional finite elements. The experimental data are compared with the data calculated using our proposed finite element method.