Pseudo analytical solution to time periodic stiffness systems

doi:10.1088/1674-1056/20/4/040501

中国物理B ›› 2011, Vol. 20 ›› Issue (4): 40501-040501.doi: 10.1088/1674-1056/20/4/040501

Pseudo analytical solution to time periodic stiffness systems

王延忠, 周元子

School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China

收稿日期:2010-06-12 修回日期:2010-12-30 出版日期:2011-04-15 发布日期:2011-04-15
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 50875009), the Defense Industrial Technology Development Program of China (Grant No. B0620060424) and the Aviation Science Foundation of China (Grant No. 20090451009).

Pseudo analytical solution to time periodic stiffness systems

Wang Yan-Zhong(王延忠) and Zhou Yuan-Zi(周元子)^†

School of Mechanical Engineering and Automation, Beihang University, Beijing 100191, China

Received:2010-06-12 Revised:2010-12-30 Online:2011-04-15 Published:2011-04-15
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 50875009), the Defense Industrial Technology Development Program of China (Grant No. B0620060424) and the Aviation Science Foundation of China (Grant No. 20090451009).

摘要/Abstract

摘要： An analytical form of state transition matrix for a system of equations with time periodic stiffness is derived in order to solve the free response and also allow for the determination of system stability and bifurcation. A pseudo-closed form complete solution for parametrically excited systems subjected to inhomogeneous generalized forcing is developed, based on the Fourier expansion of periodic matrices and the substitution of matrix exponential terms via Lagrange-Sylvester theorem. A Mathieu type of equation with large amplitude is presented to demonstrate the method of formulating state transition matrix and Floquet multipliers. A two-degree-of-freedom system with irregular time periodic stiffness characterized by spiral bevel gear mesh vibration is presented to find forced response in stability and instability. The obtained results are presented and discussed.

关键词: parametric excitation, time periodic stiffness, stability, response

Abstract: An analytical form of state transition matrix for a system of equations with time periodic stiffness is derived in order to solve the free response and also allow for the determination of system stability and bifurcation. A pseudo-closed form complete solution for parametrically excited systems subjected to inhomogeneous generalized forcing is developed, based on the Fourier expansion of periodic matrices and the substitution of matrix exponential terms via Lagrange-Sylvester theorem. A Mathieu type of equation with large amplitude is presented to demonstrate the method of formulating state transition matrix and Floquet multipliers. A two-degree-of-freedom system with irregular time periodic stiffness characterized by spiral bevel gear mesh vibration is presented to find forced response in stability and instability. The obtained results are presented and discussed.

Key words: parametric excitation, time periodic stiffness, stability, response

中图分类号: (Computational methods in statistical physics and nonlinear dynamics)

05.10.-a

45.20.dc (Rotational dynamics)

王延忠, 周元子. Pseudo analytical solution to time periodic stiffness systems[J]. 中国物理B, 2011, 20(4): 40501-040501.

Wang Yan-Zhong(王延忠) and Zhou Yuan-Zi(周元子) . Pseudo analytical solution to time periodic stiffness systems[J]. Chin. Phys. B, 2011, 20(4): 40501-040501.

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Pseudo analytical solution to time periodic stiffness systems

Pseudo analytical solution to time periodic stiffness systems

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