EXACT-SOLUTIONS FOR FREE-VIBRATION IN AN ASYMMETRICAL DUFFING EQUATION

被引：3

作者：

TAMURA, H ^{[1
]}

OKABE, T ^{[1
]}

SUEOKA, A ^{[1
]}

机构：

[1] KYUSHU UNIV,FAC ENGN,DEPT MECH ENGN,HIGASHI KU,FUKUOKA 812,JAPAN

来源：

JSME INTERNATIONAL JOURNAL SERIES C-DYNAMICS CONTROL ROBOTICS DESIGN AND MANUFACTURING | 1994年 / 37卷 / 02期

关键词：

NONLINEAR VIBRATION; FREE VIBRATION; EXACT SOLUTION; ASYMMETRICAL DUFFING SYSTEM; BILINEAR TRANSFORMATION;

D O I：

10.1299/jsmec1993.37.260

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

An algorithm is proposed for determining the exact solutions for free vibration in an asymmetrical Duffing oscillator. The system is composed of a spring function of the Duffing type (with linear and cubic terms with respect to displacement) accompanied by a constant force. It is reduced from the most comprehensive 3rd-order polynomial having arbitrary terms from a constant to the 3rd power. By employing a bilinear transformation, the system is successfully converted into a regular Duffing equation whose exact solutions already exist and are abstracted here. The whole procedure of obtaining the present solution is summarized in a flow chart. Numerical values of conversion constants, skeleton curves and waveforms are computed and illustrated for the typical cases of asymmetrical (hard, soft and snap-through) spring systems. It is demonstrated that the skeleton curves and waveforms are asymmetrical and that some of them exhibit multivalued responses for a given frequency.

引用

页码：260 / 268

页数：9

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