Prediction of foam impulse response through combination of hereditary and fractional derivative approaches

Abstract

Purpose

The purpose of this paper is to cover an experimental investigation of the impulse response of the foam-mass system (FMS) to unveil some of the foam dynamic behavior features needed to optimize the impact comfort of seat-occupant system. The equation of motion of the studied system is modeled as a sum of a linear elastic, pneumatic damping and viscoelastic residual forces. An identification methodology based on two separated calibration processes of the viscoelastic parameters was developed.

Design/methodology/approach

The viscoelastic damping force representing the foam short memory effects was modeled through the hereditary formulation. Its parameters were predicted from the free vibrational response of the FMS using iterative Prony method for autoregressive–moving–average model. However, the viscoelastic residual force resulting in the long memory effects of the material was modeled with fractional derivative term and its derivative order was predicted from previous cyclic compression standards.

Findings

The coefficients of the motion law were determined using closed form solution approach. The predictions obtained from the simulations of the impulse and cyclic tests are reasonably accurate. The physical interpretations as well as the mathematical correlations between the system parameters were discussed in details.

Originality/value

The prediction model combines hereditary and fractional derivative formulations resulting in short and long physical memory effects, respectively. Simulation of impulse and cyclic behavior yields good correlation with experimental findings.

Citation

Elfarhani, M., Mkaddem, A., Rubaiee, S., Jarraya, A. and Haddar, M. (2019), "Prediction of foam impulse response through combination of hereditary and fractional derivative approaches", Multidiscipline Modeling in Materials and Structures, Vol. 15 No. 4, pp. 800-817. https://doi.org/10.1108/MMMS-10-2018-0164