A Python Implementation of a Robust Multi-Harmonic Balance With Numerical Continuation and Automatic Differentiation for Structural Dynamics

Abstract

Abstract This work presents a tool that performs simulations in nonlinear vibration analysis. It can be used to appraise the structure's functionality and to determine the loading effects. Oscillations are fundamental in nature, appearing in practical engineering applications. General nonlinear problems hardly have analytical solutions, requiring sophisticated techniques to reach approximate solutions. This toolbox is an open-source Python implementation of a robust multiharmonic balance with predictor–corrector numerical continuation, Newton–Raphson root-solver, and forward automatic differentiation with dual numbers, which is a novelty. It shows promising converging robustness, especially in the construction of frequency response curves, when dealing with polynomial as well as sharp nonlinearities, such as dry-friction.