STEADY-STATE ANALYSIS OF NONLINEAR SYSTEMS BY THE RECEPTANCE HARMONIC BALANCE METHOD

Abstract

If a system is comprised of linear and nonlinear elements then the receptance and harmonic balance methods may be combined to analyse the steady-state forced vibration of the system. This has huge advantages in that the linear parts of the system can be analysed quickly and efficiently using conventional tools, and they can then be connected to the nonlinear parts to determine the dynamic behavior of the complete system. Unlike previous work on this topic, the methodology is formulated using complex notation, which makes the algorithm derivation simple and compact. Numerical examples are presented to illustrate the method, including a Duffing oscillator and a two-degree-of-freedom system with hardening nonlinearity.