局部约束结构振动的模态研究

制动盘/摩擦块系统的制动过程属于局部接触振动问题。摩擦块局部接触(约束)会对系统模态及固有频率造成影响,进而影响制动噪声的产生。将刹车盘简化为一维循环梁结构,并建立了在摩擦块作用下的运动方程。首先计算无接触时梁自由振动的模态(参考模态)。然后用线性弹簧代替局部接触,列写出连续条件并计算模态,得到所谓局部非连续基函数。将局部非连续基函数与参考模态进行正交化处理后,作为参考模态的补充,用于计算系统响应。与差分法结果比较表明,与传统模态方法相比,局部非连续基函数法更为准确。研究发现局部接触会抑制循环结构振动的对称性,导致正弦或余弦模态消失,以及刚度非线性和摩擦作用,会使振动是波动型的。该工作为基于局部非连续基函数法研究摩擦结构不稳定振动机理打下了基础。

Modal approach for vibration of a structure with local constraints

Braking action of a brake disc is a local contacting problem, which brings influence to the modes and inherent frequencies of the system. The method of local discontinuous basis function can be used to estimate the modes of system accurately. In this paper, a brake disc, contacted by a brake boot or friction block, is simplified as a one-dimensional beam model with loop structure. The equation of motion is established. Firstly, the modes of the free vibration beam with no contact, defined as reference system, are calculated. Then the contact of the friction block is simplified as several linear springs. Considering the continuous conditions, the discontinuous modes are calculated and orthogonalized with the reference modes.,as the supplement of reference mode, used to calculate the system response. Compared with the finite difference method, Local discontinuous basis function method is more accurate than the traditional modal method.Analyses show that the local contact by the friction piece can restrain the symmetry of vibration of the brake plate, which leads to disappearance of sine or cosine modes. Based on the discontinuous mode analysis, vibration of the brake disk under action of external excitation is calculated. And the function of the nonlinear stiffness and friction, can make the vibration to be wave type.Further researches on structure unstable vibration mechanism of the brake noise can be carried out based on the above result.