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On-line Access: 2019-04-02

Received: 2019-01-22

Revision Accepted: 2019-03-06

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Yiu-yin Lee


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Journal of Zhejiang University SCIENCE A 2019 Vol.20 No.4 P.300-304


Modified residue harmonic balance solution for coupled integrable dispersionless equations with disturbance terms

Author(s):  Yiu-yin Lee

Affiliation(s):  Department of Architecture and Civil Engineering, City University of Hong Kong, Kowloon Tong, Kowloon, Hong Kong, China

Corresponding email(s):   bcraylee@cityu.edu.hk

Key Words:  Coupled integrable dispersionless equations, Residue harmonic balance, Periodic solution

Yiu-yin Lee. Modified residue harmonic balance solution for coupled integrable dispersionless equations with disturbance terms[J]. Journal of Zhejiang University Science A, 2019, 20(4): 300-304.

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author="Yiu-yin Lee",
journal="Journal of Zhejiang University Science A",
publisher="Zhejiang University Press & Springer",

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%T Modified residue harmonic balance solution for coupled integrable dispersionless equations with disturbance terms
%A Yiu-yin Lee
%J Journal of Zhejiang University SCIENCE A
%V 20
%N 4
%P 300-304
%@ 1673-565X
%D 2019
%I Zhejiang University Press & Springer
%DOI 10.1631/jzus.A1900023

T1 - Modified residue harmonic balance solution for coupled integrable dispersionless equations with disturbance terms
A1 - Yiu-yin Lee
J0 - Journal of Zhejiang University Science A
VL - 20
IS - 4
SP - 300
EP - 304
%@ 1673-565X
Y1 - 2019
PB - Zhejiang University Press & Springer
ER -
DOI - 10.1631/jzus.A1900023

This is a supplementary study of the solution method previously proposed by the author. The proposed method is used for solving three-coupled integrable dispersionless equations with disturbance terms. It has only been adopted for solving (1) a nonlinear beam problem, and (2) a nonlinear vibro-acoustic problem. In the solution process, the three-coupled nonlinear equations can be transformed into only one Duffing equation. The higher-level nonlinear solutions, which were ignored in the previous method, can be generated using the proposed approach. Hence, in each step in the solution, only one independent nonlinear algebraic equation need be solved. As in the previous method, the proposed method has the advantage that the periodic solutions are represented by Fourier functions rather than the tedious implicit functions. The solutions from the proposed method agree reasonably well with those obtained from the classical harmonic balance method.

This is a continuation of the author's study on the solutions of nonlinear coupled integrable dispersionless equations. The effect of disturbance terms is taken into consideration. Also, the proposed method can lead to higher-order nonlinear solution that is ignored in the old method.


创新点:1. 在取得每一阶段破解方案的过程中, 只需处理一条非线性代数方程式及一组线性代数方程式; 2. 能找出旧方法不能找出的非线性答案.
方法:1. 使用理论推导、方程式替换及残余谐波平衡方法; 2. 通过仿真模拟,推导震动位移与频率之间的关系(图1)以及位移与速度之间的关系 (图2).
结论:1. 成功将改进残余谐波平衡方法应用于有扰动项的耦合可积非色散方程; 2. 通过与其他方法产生的数据进行比较,验证了所提方法的可行性和有效性(表1-3).

关键词:大幅自主震动; 残余谐波平衡; 有扰动项的耦合可积非色散方程

Darkslateblue:Affiliate; Royal Blue:Author; Turquoise:Article


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