任意载荷振动问题分析的切比雪夫谱元法

Chebyshevspectral element method for solving vibration problems under arbitrary load

研究了用Chebyshev时间谱元法求解任意载荷作用下的振动问题,从Bubnov-Galerkin方法出发,深入分析了在第二类Chebyshev正交多项式极点处重心Lagrange插值来构造节点基函数及其特性,推导了任意载荷作用下振动问题的伽辽金谱元离散方案,利用最小二乘法求解线性方程组。以线性载荷、三角载荷、半正弦波载荷作用下的振动问题及正弦载荷作用下的悬臂梁的振动问题为例,验证了文中方法的可行性,并与配点法进行比较,进一步说明了文中方法的高精度性和可靠性。

The vibration problems under arbitrarily load are solved by Chebychev spectral elements method. The node basis functions are constructed by barycenter Lagrange interpolation at the extreme points of 2nd Chebyshev orthogonal polynomials, which characteristics are analyzed with Bubnov-Galerkin method. Galerkin discretization scheme of vibration problems under arbitrary load is derived, and the linear equations are solved by least squares method. Numerical results for some vibration problems under line load, triangular impulsive load, half sine-wave impulsive load and vibration of cantilever under sine-wave load illustrate the feasibility of the approximation scheme. The accuracy and reliability of the method are further illustrated bycomparing with the method of point collocation.