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《Journal of Vibration and Shock》 2015-04
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Modal approach for vibration of a structure with local constraints

LI Jin-lu;DING Qian;Department of Mechanics,Tianjin University;Tianjin Key Laboratory of Nonlinear Dynamics and Chaos Control;  
Braking process of a brake disc is a vibration problem with local contacting,local contact has an influence on the modes and natural frequencies of the disc system. The method of local discontinuous basis function can be used to estimate the modes of the system accurately. Here,a brake disc contacted by a brake boot or a friction block was simplified as a one-dimensional beam with loop structures. Its equation of motion was established. Firstly,the free vibration modes of the beam without contact defined as the reference modes were calculated. Then the contact of the friction block was simplified as several linear springs. Using the continuous conditions,the system's modes were calculated and orthogonalized with the reference modes,they were taken as the supplements of the reference modes and named the local discontinuoas basis functions. They were used to calculate the system response. Based on the discontinuous mode analysis,vibration of the brake disk under action of external excitation is calculated. The results showed that the local discontinuous basis function method is more accurate than the traditional modal method; the local contact of the friction piece can restrain the vibration symmetry of the brake disc to lead to disappearance of sine or cosine modes; nonlinear stiffness and friction make the vibration be wave type. This study laid a foundation for studying unstable vibration mechanism of structures with friction using the local discontinuous basis function method.
【Fund】: 国家自然科学基金资助项目(11272228);; 高等学校博士学科点专项科研基金资助项目(20120032110011)
【CateGory Index】: TB53
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