Techno Press
Techno Press

Structural Engineering and Mechanics
  Volume 47, Number 3, August10 2013 , pages 345-359
DOI: https://doi.org/10.12989/sem.2013.47.3.345
 


Exact solution for free vibration of curved beams with variable curvature and torsion
Li-li Zhu, Ying-hua Zhao and Guang-xin Wang

 
Abstract
    For the purpose of investigating the free vibration response of the spatial curved beams, the governing equations are derived in matrix formats, considering the variable curvature and torsion. The theory includes all the effects of rotary inertia, shear and axial deformations. Frobenius scheme and the dynamic stiffness method are then applied to solve these equations. A computer program is coded in Mathematica according to the proposed method. As a special case, the dynamic stiffness and further the natural frequencies of a cylindrical helical spring under fixed-fixed boundary condition are carried out. Comparison of the present results with the FEM results using body elements in I-DEAS shows good accuracy in computation and validity of the model. Further, the present model is used for reciprocal spiral rods with different boundary conditions, and the comparison with FEM results shows that only a limited number of terms in the resultant provide a relatively accurate solution.
 
Key Words
    curved beam; free vibration; variable curvature and torsion; dynamic stiffness; exact solution
 
Address
Li-li Zhu and Guang-xin Wang : School of Mechanical Engineering, Dalian Jiaotong University, Dalian 116028, P.R. China
Ying-hua Zhao : Institute of Road and Bridge Engineering, Dalian Maritime University, Dalian 116026, P.R. China
 

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