Vibration Analysis Of Spatial Curved Beam Based On Dynamic Stiffness Method

With the advantages of streamlined shape and good force characteristics,the curved beam structure plays an important role in aerospace,mechanical and civil engineering fields.At present,the research on the dynamics of spatial curved beams mainly focuses on equal crosssection,and the research on the variable cross-section spatial curved beams is still relatively weak.Therefore,the vibration problem of variable curvature variable deflection variable section spatially curved beams is studied in detail in this paper,and the main research contents are as follows:(1)To establish the differential equations of motion and control equations for the vibration of a spatially curved beam of variable curvature and deflection with variable cross-section subjected to load in any direction by associating the equilibrium equations,geometric equations and intrinsic structure relations of the spatially curved beam.Then the Laplace transform method,Furbinas method,dynamic stiffness matrix method and Laplace inverse transform method are applied to derive its control equations.The algorithm can be applied to calculate the inherent frequency of a spatially curved beam,as well as to analyze the effect of external loads on a spatially curved beam.(2)Mathematica software is applied to write the procedure of calculating the inherent frequency of variable curvature variable deflection variable section spatially curved beams into a program,and Visual Basic programming software is applied to establish a visual operation interface,and a software to calculate the inherent frequency of in-plane(in-plane and out-ofplane)and spatially curved beams is designed by calling Mathematica program.(3)The dimensionless frequencies of in-plane(parabolic,elliptical),out-plane(parabolic,sinusoidal)and variable-section planar curved beam(elliptical)in-plane and out-plane free vibration are solved separately,and the calculated results are compared with the literature results,and the accuracy of the method can be verified within the error tolerance.The effects of different boundary conditions,opening angles,long-span ratios and cross-sectional variation parameters on the frequency and their variation laws were also analyzed.(4)The inherent frequencies of equal/variable section spatial curve beams(cylindrical spiral beam,hyperbolic spiral beam and elliptical cylindrical spiral beam)are solved separately,and the calculated results are compared with the results of Ansys Workbench finite element software,which can verify the accuracy and feasibility of the method within the error allowance.The influence of different boundary conditions,helix angle,effective number of turns,section diameter and section variation parameters on the frequency and the variation law are also analyzed.