Solution of the relativistic (an)harmonic oscillator using the harmonic balance method

被引：16

作者：

Belendez, A. ^{[1
]}

Pascual, C. ^{[1
]}

Mendez, D. I. ^{[1
]}

Neipp, C. ^{[1
]}

机构：

[1] Univ Alicante, Dept Fis, E-03080 Alicante, Spain

来源：

JOURNAL OF SOUND AND VIBRATION | 2008年 / 311卷 / 3-5期

关键词：

D O I：

10.1016/j.jsv.2007.10.010

中图分类号：

O42 [声学];

学科分类号：

070206 ; 082403 ;

摘要：

The harmonic balance method is used to construct approximate frequency-amplitude relations and periodic solutions to the relativistic oscillator. By combining linearization of the governing equation with the harmonic balance method, we construct analytical approximations to the oscillation frequencies and periodic solutions for the oscillator. To solve the nonlinear differential equation, firstly we make a change of variable and secondly the differential equation is rewritten in a form that does not contain the square-root expression. The approximate frequencies obtained are valid for the complete range of oscillation amplitudes, A, while the discrepancy between the second approximate frequency and the exact one never exceeds 0.82% and tends to 0.52% when A tends to infinity. Excellent agreement of the approximate frequencies and periodic solutions-with the exact ones are demonstrated and discussed. (c) 2007 Elsevier Ltd. All rights reserved.

引用

页码：1447 / 1456

页数：10

共 18 条

[1] Application of he's homotopy perturbation method to the relativistic (An)harmonic oscillator.: I:: Comparison between approximate and exact frequencies [J].