Chapter 2: Analytical Methods in Nonlinear Dynamics

Abstract

This chapter provides an overview of the various nonlinear dynamic behaviors intrinsic to engineered structures and systems during their operating conditions. Analytical methods for solving nonlinear ordinary differential equations are provided. The chapter begins with the Harmonic Balance and Variation of Parameters for relatively their relative simplicity and efficiency. The harmonic balance and variation of parameters methods are harmonic probing algorithms, which make them attractive tools in the field of nonlinear system identification (NSI), structural health monitoring (SHM), and nondestructive Inspection/Evaluation (NDI/E). Key parameters such as structural stiffness, damping, and inertia can be extracted via harmonic probing.