Steady-state harmonic response analysis of a stranded wire helical spring-mass system using an iterative harmonic balance method

Abstract

As a cylindrical spring wound by a wire strand, the stranded wire helical spring has been widely used as key repositioning components for high-end devices. Most of these devices can be simplified as single degree-of-freedom (DOF) stranded wire helical spring-mass systems. The steady-state harmonic response analysis method is an important tool for designing a system with the nonlinear spring. The present work proposes an iterative harmonic balance method to solve for the steady-state harmonic response of the single DOF stranded wire helical spring-mass system. Taking into account the nonlinearity of the stranded wire helical spring, a nonlinear model comprising a modified Bouc-Wen equation was proposed for describing the dynamic nature of the spring-mass system. Based on the harmonic balance method and nonlinear iterative methods, the seeking for the response solution was transformed into a nonlinear optimization issue for the nonlinear spring-mass system. The present method was examined using both simulations and experiments. The results show that the proposed approach is simple yet accurate, and thus being very practical for engineering applications.