A new approach on vibration analysis of locally nonlinear stiffness and damping system
- PDF / 244,373 Bytes
- 6 Pages / 547.087 x 737.008 pts Page_size
- 5 Downloads / 193 Views
A new approach on vibration analysis of locally nonlinear stiffness and damping system Wang Yong Æ Huang Qibai Æ Zhou Minggang Æ Zhang Yongbo
Received: 26 June 2006 / Accepted: 4 September 2006 / Published online: 31 October 2006 Springer Science+Business Media B.V. 2006
Abstract The nonlinear force induced by spring and damping of 2-degree-of-freedom locally nonlinear vibrating system is regarded as applied force, and its mathematical model is established in this paper. Then impulse response temporal method of linear vibrating system is applied in the system, the response of locally nonlinear vibrating system is obtained by convolution integration between unit impulse response of corresponding linear system and equivalent nonlinear force, and numerical simulation of the model is attained. Finally, the feasibility of the new method on the domain of locally nonlinear vibrating system is verified by comparing the results, which supplies a new method to solve approximately vibration response of locally nonlinear vibrating systems. Keywords Locally nonlinear vibrating system Æ Impulse response temporal method Æ Vibration response Æ Nonlinear stiffness and Damping
W. Yong (&) Æ H. Qibai Æ Z. Minggang Æ Z. Yongbo School of Mechanical Science & Engineering, Huazhong University of Science & Technology, Wuhan, Hubei 430074, P.R. China e-mail: [email protected]
1 Introduction The vibration phenomena can be seen everywhere in the real life, and nearly all the vibrating systems are nonlinear. So, it is very significant to study nonlinear vibration. The nonlinear vibration theory has been developed rapidly since the 1920s. However, in contrast with linear systems, only a few vibration responses in nonlinear systems with multiple degrees of freedom can be solved accurately. There is no general accurate analytical solution which fits all kinds of nonlinear equations. Therefore, some approximate methods, such as the perturbation method, the multiscale method and the harmonic balance method, have been used to solve such equations and to study the laws of motion and the characteristic of vibration (Li and Wang 1996; Nayfeh and Mook 1979; Chen and Wu 2002). With the rapid development of computer technology, it is of great importance for the complicated systems, such as aviation, navigation and automobile, to simulate numerically the dynamical characteristic of vibrating systems. Generally, only a few components are nonlinear, and the majorities of vibration systems are linear. It is one of the keypoints in studying the nonlinear characteristic to solve the dynamical response of these systems. A 2-DOF locally nonlinear vibration model of the system is proposed in this paper. Considering the
123
2
Int J Mech Mater Des (2006) 3:1–6
inevitable influence of nonlinear stiffness and damping on the vibration response of an actual complicated system such as a motor, the nonlinear force induced by spring and damping of the vibrating system is regarded as outside force, and its mathematical model is established in this paper. Then
Data Loading...
