Nonlinear Analysis of a Tapered Impact Damper Using the Method of Harmonic Balance

Abstract

Significant vibration amplitudes and cycles can be produced when structures with low inherent damping, including traffic signal structures, are excited near one of their natural frequencies. Measures implemented for the attenuation of these vibration amplitudes must be considered to prevent failure due to fatigue cracking. For the mitigation of these wind-induced vibrations, dynamic vibration absorbers or tuned mass dampers coupled to the structure are often used. This research will investigate the performance of a novel tapered impact damper, consisting of a hanging spring-mass oscillator inside a housing capable of reducing vibration amplitude over a broader frequency range than the conventional tuned mass damper. The overall two degree of freedom system, consisting of the structure and tapered impact damper is nonlinear. Many methods to analyze vibrations are based on linear theory and produce errors in the presence of nonlinearities. Other methods that address nonlinearities have high computational time and effort. This research focuses on an alternative analysis using the method of harmonic balance, capable of approximating periodic solutions of nonlinear systems using Fourier series, to model the damped traffic signal structure. The method of harmonic balance is applied to the traffic signal structure and impact damper system in the form of an analytical model, and the simulated response solutions were validated against experimental frequency and damping data.