TWO GENERALIZED INCREMENTAL HARMONIC BALANCE METHODS WITH OPTIMIZATION FOR ITERATION STEP

Huang Jianliang; Zhang Bingxu; Chen Shuhui

doi:10.6052/0459-1879-22-042

Volume 54 Issue 5

May 2022

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Huang Jianliang, Zhang Bingxu, Chen Shuhui. Two generalized incremental harmonic balance methods with optimization for iteration step. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(5): 1353-1363 doi: 10.6052/0459-1879-22-042

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Huang Jianliang, Zhang Bingxu, Chen Shuhui. Two generalized incremental harmonic balance methods with optimization for iteration step. Chinese Journal of Theoretical and Applied Mechanics, 2022, 54(5): 1353-1363 doi: 10.6052/0459-1879-22-042

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TWO GENERALIZED INCREMENTAL HARMONIC BALANCE METHODS WITH OPTIMIZATION FOR ITERATION STEP

doi: 10.6052/0459-1879-22-042

Department of Applied Mechanics and Engineering, Sun Yat-sen University, Guangzhou 510275, China

Received Date: 2022-01-21
Accepted Date: 2022-03-02

Available Online: 2022-03-03

Publish Date: 2022-05-01

Abstract

Abstract

As a semi-analytial and semi-numerical method, the incremental harmonic balance (IHB) method is capable of dealing with strongly nonlinear systems to any desired accuracy. However, as it is often in case numerical method, there exists initial value problem that can cause divergence with using the IHB method. To solve the initial value problem, two generalized IHB method are presented in this work. The first one (GIHB1) is combined with backtracking line search (BLS) optimization algorithm, which adjust the iteration step to decrease for the convergence of the solutions. The second one (GIHB2) is combined with BLS optimization algorithm and the dogleg method, which is an iterative optimization algorithm for the solution of non-linear least squares problems. The GIHB2 method is adopted for the Newton-Raphson iteration with gradient descent such that the convergence of the solutions increases monotonically along the path with gradient descent way with two parameters. At the end, two examples are presented to show the efficiency and the advantages of the two GIHB methods for initial value problem.
- nonlinear vibration,
- incremental harmonic balance method,
- initial value problem,
- backtracking line search,
- dogleg method

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References(38)

References

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