Precise Integration Method of Dynamic Analysis for Naturally Curved and Twisted Beams

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.