自然弯扭梁动力分析的精细积分法

Precise integration method of dynamic analysis for naturally curved and twisted beams

摘要:

以自然弯扭梁理论为基础对一般横截面形状空间曲梁的振动特性进行了研究，分析中包括了横向剪切变形、转动惯量以及和扭转有关的翘曲的影响。应用差分法对空间坐标进行离散可以把控制方程化为关于时间的常微分方程组，通过求解可以得到该梁的固有频率。在分析简谐激励作用下结构的动力响应时，对精细时程积分法中的向量积分采用了Newton-Cotes公式，避免了矩阵求逆的困难。把上述方法用于求解两端固支曲梁的固有频率以及强迫振动时的位移时程曲线。计算表明，用本文方法得到的数值解和有限元结果非常接近。另一个算例涉及到两端固支圆截面螺旋形弹簧固有频率的计算，其数值结果和相关文献的结果吻合得很好。

关键词:自然弯扭梁; 精细时程积分法; Newton-Cotes积分; 固有频率; 弹簧

Abstract:

Vibrational behavior for spatial curved beams with general cross-sectional shapes, based on naturally curved and twisted beam theory, is theoretically investigated. The effects of transverse shear deformations, rotary inertia and torsion-related warping are included in the present formulations. The governing equations can be transformed to a set of ordinary differential equations with respect to time by utilizing a finite difference discretization in the spatial domain. Natural frequencies of the beams can be determined by solving these equations. In analyzing the dynamic response of the structures under harmonic excitation, Newton-Cotes formula, which avoids the trouble of the inverse matrix calculation, is used to evaluate vector integration in precise time-integration method. The present analysis will be used to solve the natural frequencies and the response curve of displacement of forced vibration of the beams fixed at both ends. Calculations show that the numerical results obtained are very close to the FE-results. Another example is related to the natural frequencies of cylindrical helical springs of circular cross-sections with both ends fixed. Results are in good agreement with other published data. Key words: naturally curved and twisted beam; precise time-integration method; Newton-Cotes integration; natural frequency; helical spring

Key words:naturally curved and twisted beam; precise time-integration method; Newton-Cotes integration; natural frequency; helical spring