单向纤维复合材料弹簧固有频率计算

Computational Analysis for Natural Frequencies of Uniaxial Composite Cylindrical Helical Spring

为探究多种伪谱法在单向复合材料弹簧固有频率计算的准确性和效率问题,对约束形式为固支-固支的单向纤维复合材料圆柱螺旋弹簧动力学控制方程进行分析;基于勒让德伪谱法和第二类切比雪夫伪谱法对各向同性弹簧自由振动固有频率进行计算,与文献中的结果进行对比,验证勒让德伪谱法和第二类切比雪夫伪谱法计算各向同性材料弹簧固有频率的准确性;对一种结构参数和材料参数的单向纤维复合材料弹簧自由振动固有频率进行计算,三类伪谱法的计算结果与文献中结果基本一致,进一步证明三类伪谱法计算单向纤维复合材料弹簧固有频率的准确性;确定每类伪谱法Gauss-Lobatto最优配点个数,对比得出第二类切比雪夫伪谱法在此类问题中拥有较高的计算效率。

The focus of this paper is the analysis of the computational efficiency of pseudo-spectral methods in calculating the natural frequencies of uniaxial composite cylindrical helical springs.The dynamic control equations of uniaxial composite cylindrical helical springs with fixed-fixed constraints were analyzed.Based on the Legendre pseudo-spectral method and the second class Chebyshev pseudo-spectral method,the natural frequencies of springs of isotropic material were solved.Compared with the results in literatures,the accuracy of these two methods was verified.According to structural and material parameters,the natural frequencies of a uniaxial composite spring were calculated based on Legendre,the first and second class Chebyshev pseudo-spectral methods,and the calculation results were basically consistent with those in the literature.It could be further proved that the three kinds of pseudo-spectral methods can accurately calculate the natural frequencies of uniaxial composite springs.Moreover,the number of Gauss-Lobatto optimal collocation points of each pseudo-spectral method was determined,and it was concluded that the second class Chebyshev pseudo-spectral method possessed a higher solving efficiency in this problem.