Study on High Performance Averaging Method for Strongly Nonlinear Oscillator.

强非线性振荡器的高性能平均方法研究。

• 批准号: 15560202
• 负责人: OKABE Tadashi
• 金额: $ 0.51万
• 依托单位: University of Miyazaki
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2004
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15560202/
• 关键词: Nonlinear Vibration; Averaging Method; Jacobian Elliptic Function; Stability Criterion; Duffing Equation; Quadratic Oscillator; Higher Harmonic Vibration; Sub-Harmonic Vibration

Averaging methods using the Jacobian elliptic function are developed in order to improve performances of the averaging method. In this research, the following results were achieved.(1)Elliptic Averaging Method Using Only One Term of the Jacobian Elliptic Function : Elliptic averaging methods are developed in order to calculate periodic solution of Duffing oscillator with perturbed term which is composed of a periodic external force, nonlinear damping and nonlinear restoring force. In these methods, only one term of the Jacobian elliptic cosine, sine or delta function is incorporated as generating solution. Highly accurate approximate solution for the systems based on Duffing oscillators with hardening, softening and snap-through spring are obtained by using elliptic averaging method of cn, sn or dn type properly.(2)Elliptic Averaging Method for Systems Based on Quadratic Oscillator : In order to calculate highly accurate approximate solution for systems based on quadratic oscillator, a … More n elliptic averaging method, which has been improved through the use of squared Jacobian elliptic sine function (sn^2), is developed.(3)Elliptic Averaging Method Using Combined Function of Two Jacobian Elliptic Functions : In order to improve the accuracy and to expand applicability of elliptic averaging method, Elliptic averaging method of sn+cn type, which use the combined function of Jacobian elliptic cosine and sine function as generation solution, are developed. This method can calculate more highly accurate approximation solution than elliptic averaging method of cn or sn type. Furthermore, approximate solution of higher harmonic and sub-harmonic vibration can be calculated by using elliptic averaging method of sn+cn type.(4)Stability Criterion : Most suitable stability criterion for elliptic averaging method is proposed.(5)Confirmation of Validity of Elliptic Averaging Method : The efficiency of the developed methods is demonstrated by comparing the computational results with those obtained by the shooting method. It is confirmed that the developed elliptic averaging methods can calculate the periodic solution with high accuracy of strongly nonlinear oscillator and have a wide range of applicability. Less

为了提高平均方法的性能，提出了基于雅可比椭圆函数的平均方法。在本研究中，取得了以下成果：(1)仅利用雅可比椭圆函数的一项的椭圆平均法：为了计算由周期外力、非线性阻尼和非线性恢复力组成的扰动项Duffing振子的周期解，提出了椭圆平均法。在这些方法中，只包含雅可比椭圆余弦、正弦或δ函数的一项作为生成解。适当地采用cn、sn或dn型椭圆平均法，得到了具有硬化、软化和卡通弹簧的Duffing振子系统的高精度近似解。(2)基于二次振子系统的椭圆平均法：为了计算基于二次振子系统的高精度近似解，提出了一种利用平方雅可比椭圆正弦函数（sn^2）改进的椭圆平均法。(3)利用两个雅可比椭圆函数的组合函数的椭圆平均法：为了提高椭圆平均法的精度，扩大椭圆平均法的适用性，提出了以雅可比椭圆余弦函数和正弦函数的组合函数作为生成解的sn+cn型椭圆平均法。与cn型或sn型椭圆平均法相比，该方法可以计算出精度更高的近似解。此外，采用sn+cn型椭圆平均法可以计算出高次谐波振动的近似解。(4)稳定性判据：提出了椭圆平均法最合适的稳定性判据。(5)椭圆平均法的有效性验证：将椭圆平均法的计算结果与射击法的计算结果进行比较，验证了椭圆平均法的有效性。结果表明，所建立的椭圆平均方法能够高精度地计算强非线性振子的周期解，具有广泛的适用性。少

项目成果

An Elliptic Averaging Method for Systems Based on Duffing Snap-Through Spring System.

基于 Duffing 弹通弹簧系统的系统椭圆平均方法。

• 发表时间: 2004
• 期刊: Proceedings of VETMAC-3 and ACSIM-2004 Vol.2
• 作者: 岡部 匡;Tadashi OKABE;岡部 匡;Tadashi OKABE;Tadashi OKABE;Tadashi OKABE
• 通讯作者: Tadashi OKABE

強非線形2次ばね系を基盤とする系に対する平均法の高性能化に関する研究

基于强非线性二次弹簧系统的系统平均法性能改进研究

• 发表时间: 2005
• 期刊: 日本機械学会論文集(C編) 701・71
• 作者: 岡部 匡

High Performance Averaging Method for Systems Based on Strongly Quadratic Nonlinear Oscillator

基于强二次非线性振荡器的系统高性能平均方法

• 发表时间: 2003
• 期刊: Proceedings of the 10th Asia-Pacific Vibration Conference 2003 Vol.2
• 作者: 岡部 匡;Tadashi OKABE;岡部 匡;Tadashi OKABE;Tadashi OKABE;Tadashi OKABE;岡部 匡;Tadashi OKABE
• 通讯作者: Tadashi OKABE

High Performance Averaging Method for Systems Based on Strongly Quadratic Nonlinear Oscillator.

基于强二次非线性振荡器的系统的高性能平均方法。

• 发表时间: 2003
• 期刊: Proceedings of the 10th Asia-Pacific Vibration Conference 2003 Vol.2
• 作者: 岡部 匡;Tadashi OKABE;岡部 匡;Tadashi OKABE;Tadashi OKABE;Tadashi OKABE;岡部 匡;Tadashi OKABE;Tadashi OKABE
• 通讯作者: Tadashi OKABE

Study on High Performance Averaging Method for Systems Based on Quadratic Strong System with Strong Nonlinearity.

基于强非线性二次强系统的系统高性能平均方法研究。

• 发表时间: 2005
• 期刊: Transactions of the Japan Society of Mechanical Engineers (Series C) Vol.71, No.701
• 作者: 岡部 匡;Tadashi OKABE
• 通讯作者: Tadashi OKABE