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http://dx.doi.org/10.12989/sem.2013.47.3.345

Exact solution for free vibration of curved beams with variable curvature and torsion  

Zhu, Li-Li (School of Mechanical Engineering, Dalian Jiaotong University)
Zhao, Ying-Hua (Institute of Road and Bridge Engineering, Dalian Maritime University)
Wang, Guang-Xin (School of Mechanical Engineering, Dalian Jiaotong University)
Publication Information
Structural Engineering and Mechanics / v.47, no.3, 2013 , pp. 345-359 More about this Journal
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.
Keywords
curved beam; free vibration; variable curvature and torsion; dynamic stiffness; exact solution;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
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