Equivalent Linearization Method Based on Energy-to-<em>c</em>th-Power Difference Criterion in Nonlinear Stochastic Vibration Analysis of Multi-Degree-of-Freedom Systems

WANG Guo-yan; DAI Min

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2001 > 22(8): 845-852

WANG Guo-yan, DAI Min. Equivalent Linearization Method Based on Energy-to-cth-Power Difference Criterion in Nonlinear Stochastic Vibration Analysis of Multi-Degree-of-Freedom Systems[J]. Applied Mathematics and Mechanics, 2001, 22(8): 845-852.

Citation:

PDF( 320 KB)

Equivalent Linearization Method Based on Energy-to-cth-Power Difference Criterion in Nonlinear Stochastic Vibration Analysis of Multi-Degree-of-Freedom Systems

WANG Guo-yan¹,
DAI Min²

1.
Key Laboratory of Solid Mechanics of MOE, Department of Engineering Mechanics and Technology, Tongji University, Shanghai 200092, P R China;
2.
Institute of Mathematics and Department of Financial Mathematics, School of Mathematical Sciences, Peking University, Beijing 100871, P R China

Received Date: 1999-11-23
Rev Recd Date: 2001-04-02
Publish Date: 2001-08-15

Abstract

Abstract

Basic equations of energy-tocth-power difference criterion were derived for multi-degreeof-freedom(MDOF) systems subjected to stationary Gaussian excitations with non-zero mean.Modal transform technique was used in order to reduce unknowns.Main computational formulae were presented and suggested values of c were given.Numerical results show that the method of this paper prevails over equation difference criterion both in accuracy and in simplicity.
- nonlinear,
- stochastic vibration,
- energy,
- equivalent linearization

FullText(HTML)

References(7)

References

[1]	王国砚,张相庭.非线性随机振动中基于能量c次方的等效线性化方法[J].振动与冲击,1998,17(3):6-9.
[2]	Iwan W D,Yang I M.Application of statistical linearization techniques to nonlinear multidegree-of-freedom system[J].Journal of Applied Mechanics,Transactions of the ASME,1972,39(2):545-550.
[3]	Atalik T S,Utku S.Stochastic linearization of multi-degree-of-freedom nonlinear systems[J].Earthquake Engineering and Structural Dynamics,1976,4(4):411-420.
[4]	Socha L,Soong T T.Linearization in analysis of nonlinear stochastic systems[J].Applied Mechanics Review,1991,44(10):399-422.
[5]	Caughey T K.Equivalent linearization techniques[J].The Journal of the Acoustical Society of America,1963,35(11):1706-1711.
[6]	Caughey T K.Derivation and application of the Kokker-Planck-equation to discrete nonlinear dynamicsystems subjected to white random excitation[J].The Journal of the Acoustical Society of America,1963,35(11):1683-1692.
[7]	张相庭.非线性随机振动理论研究进展及在工程上应用[A].见:黄文虎主编.一般力学(动力学、振动与控制)最新进展[C].北京:科学出版社,1994,132-139.