Suggestion of a polynomial model with a convolution integral term for a vibration isolation element with hysteresis and non-linearity for force estimation

Abstract

Modelling of the force transmitted through vibration isolation elements in terms of the displacement and the velocity is very useful in transfer path or vibration power analysis of dynamic systems. Modelling using the complex stiffness in the frequency domain can be a good solution for linear elements, and force-state mapping can be a good solution for non-linear elements. In this study, it is noted that conventional force-state mapping with a linear part simply consisting of a linear spring and a viscous damper does not work sufficiently well for vibration isolation elements typically made of rubber materials; therefore, modelling of the linear part using the complex stiffness is proposed. The non-linear force-state model with the complex stiffness model for the linear part is applied to a set of simulation data for validation of the proposed approach and to another set of data measured from a cabin mount of an excavator for illustration. A form of the fractional polynomial function of the frequency is utilized for curve fitting of the linear complex stiffness in the frequency domain. The constraints for stability and causality on the coefficients and the order of this form are discussed. Procedures for the construction of the whole model are presented. Based on the modelling of the simulated and measured data, it is claimed that the suggested modelling is promising as a representation of the frequency- and amplitude-dependent complex stiffness of vibration isolation elements.