A New Series Method for Out-of-plane Free Vibration Analysis of Curved Beams with Variable Cross-sections
A numerical model for analysis of out-of-plane free vibration of curved beams is presented.In this model,the displacement is expressed by the improved Fourier series,and solved by the Rayleigh-Ritz method.First of all,the improved Fourier series method is used to express the three displacement functions of the curved beam in out-of-plane bending and torsional vibration,which can solve the problem of discontinuity of boundary derivatives of displacement functions.Secondly,artificial virtual springs are used to simulate the boundary conditions of the curved beam,and the constraint conditions on arbitrary boundaries are realized by changing the stiffness values of the additional transverse displacement constraint spring,the torsion constraint spring and the rotation constraint spring.The stiffness matrix and the mass matrix are obtained when the curved beam structure is in vibration.Finally,the frequency values of the out-of-plane free vibration of the plane curved beam are obtained by solving the matrix eigenvalue problem.This method overcomes the defect of some methods that vibration problems can only be solved under certain specific boundary conditions.Numerical examples show that the convergence and accuracy of the method are good.This method also analyzes the influence of different elastic constraints and section variation coefficient on out-of-plane free vibration frequency of the curved beam.It can be found that the dimensionless frequencies decrease with the increase of the central angle of circular curved beam with two ends clamped,and increase with increasing of the slenderness ratio.
vibration and wavefree vibrationcurved beamout-of-plane vibrationimproved Fourier series
万方数据
维普
