摘要
考查地震或水下非接触爆炸冲击下旋转机械的动态响应特性,一般从研究转子系统基础冲击响应出发。由于陀螺效应和转子-轴承的交互效应,转子系统运动方程系数矩阵呈非对称性,不能在模态坐标下解耦,无法利用常规模态叠加法求解,所以以往的研究一般采用数值积分如Newmark法等进行迭代求解,但数值积分法相对模态叠加法要耗费较多的计算资源。提出了一种复数域内转子系统冲击响应计算方法,无需坐标解耦但仍可以利用线性叠加法进行响应求解。首先将激励和响应傅里叶展开成复数形式,包括正向旋转项和反向旋转项,根据方程左右两边相同频率前系数相等的事实得到特征方程,将特征方程写成简单矩阵束的本征方程形式,求得矩阵束的本征值和本征向量,将本征向量正规化,进一步得到矩阵束的逆阵,将逆阵元素取名为"频响因子",将逆阵与激励相乘即可得到频率响应幅值,将所有频率响应成分叠加即可得到系统响应。通过一个工程实例,比较了所提方法与数值积分方法的结果,比较分析表明,所提方法满足工程要求,可以作为转子系统基础冲击响应和瞬态响应计算的一种普适方法。
A mode-superposition method in complex domain to calculate shock responses of a rotor-bearing system was proposed.With no need to decouple equations,linear superposition computation of responses can still be performed just like in the conventional mode-superposition method.Shock excitation and response were both expanded into complex forms of Fourier series,including forward and backward rotating items.Characteristic equations were obtained by equating the coefficient matrixes with the same rotating frequency at both sides of the equation and were then rewritten in the form of latent value equations of simple matrix pencil.The inverse matrix with its elements called ＂frequency response coefficient＂ of the matrix pencil was calculated by using its right and left normalized latent vectors.Responses at each frequency were obtained by the product of the inverse matrix and shock excitation,and then synthesized into overall responses of the system.An engineering example was presented to compare the results of proposed method and numerical integration methods.Comparative analysis shows that the proposed method can meet the engineering requirements,and can be used as a universal method for shock response and transient response computation of rotor systems.
出处
《振动与冲击》
EI
CSCD
北大核心
2011年第9期221-226,共6页
Journal of Vibration and Shock
基金
国防"十一五"预研项目(4010106010303)
关键词
冲击瞬态响应
转子系统
复模态分析
矩阵束
左右本征向量
响应合成
频响因子
shock transient response
rotor system
complex modal analysis
pencil of matrix
left and right latent vector
response synthesizing
frequency response coefficient
