Work

Enriching harmonic balance with non‐smooth Bernoulli bases for accelerated convergence of non‐smooth periodic systems

Year: 2024

Type: article

Abstract: The harmonic balance method (HBM) has been widely applied to get the periodic solution of nonlinear systems, however, its convergence rate as well as computation efficiency is dramatically degraded when the system is highly non-smooth, e.g., discontinuous. In order to accelerate the convergence, an enriched HBM is developed in this paper where the non-smooth Bernoulli bases are additionally introduced to enrich the conventional Fourier bases. The basic idea behind is that the convergence rate of the HB solution, as a truncated Fourier series, can be improved if the smoothness of the solution becomes finer. Along this line, using non-smooth Bernoulli bases can compensate the highly non-smooth part of the solution and then, the smoothness of the residual part for Fourier approximation is improved so as to achieve accelerated convergence. Numerical examples are conducted on systems with non-smooth restoring and/or external forces. The results confirm that the proposed enriched HBM indeed increases the convergence rate and the increase becomes more significant if more non-smooth bases are used.

Source: Theoretical and Applied Mechanics Letters

DOI: 10.1016/j.taml.2024.100562

Authors: Yu Zhou, Jianliang Huang, Li Wang

Institution: Sun Yat-sen University

Language: English

Topic: Vibration and Dynamic Analysis

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,200

Funders: National Natural Science Foundation of China, Key Technologies Research and Development Program, National Key Research and Development Program of China, Basic and Applied Basic Research Foundation of Guangdong Province