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:

以空间曲梁理论为基础,对一般横截面形状自然弯扭梁的振动特性进行了研究，包括横向剪切变形、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，把控制方程化为关于时间的常微分方程组，通过求解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NewtonCotes公式，避免了矩阵求逆的困难.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的计算结果表明，数值解和有限元结果非常接近；两端固支圆截面螺旋弹簧固有频率的计算结果同样表明，数值解和相关文献的结果吻合得很好.

Abstract:

Based on spatial curved beam theory,vibrational behavior for naturally curved and twisted beams with general crosssectional shapes 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.