摘要
针对传统精细积分法系统状态方程中的非齐次项求解涉及到等效激励矩阵求逆问题,同时计算精度取决于该非齐次项拟合程度问题,提出将高斯-勒让德积分法与样条插值函数结合起来求解状态方程非齐次项,方法中运用指数矩阵运算精确求解高斯积分系数,并采用分段样条插值函数确定每一时间步长内高斯积分点处离散载荷。分别采用Newmark-β法、传统精细积分法以及样条插值高斯精细积分法计算瑞利阻尼模型悬臂梁振动系统所受外载荷的时程响应,并与振型叠加法的计算结果比较。结果表明,样条插值高斯精细积分法具有高精度、高效率以及不受积分时间步长严格限制的优点。
About system state equation solution of the non-homogeneous term of the precise integration method which involves the matrix inversion and calculation accuracy depending on the non-homogeneous term fitting precision,an improved gaussian precise integration method,by combining the Gaussian-Legendre integration with the piecewise spline interpolation method,is proposed.In the new method,using the precise integration exponential matrix to solve the coefficient of the Gaussian integral precisely,and using the spline interpolation function to determine gauss integral points of discrete load within each time step length.Newmark-βmethod,the traditional precise integration method and the improved gaussian precise integration method of this artical were used respectively to calculate time response of the Rayleigh damping models cantilever beam system by external load,and compared with the calculation result of modal superposition method.The result demonstrates that the improved Gaussian precise integration method has high precision,high efficiency and is not limited strictly by the integral time step.
出处
《国外电子测量技术》
2016年第2期49-54,共6页
Foreign Electronic Measurement Technology
关键词
动力响应
精细积分
高斯-勒让德积分
分段样条插值函数
dynamic response
precise integration
Gaussian-Legendre integration
piecewise spline interpolation function
