Solution for free vibration of spatial curved beams
ISSN: 0264-4401
Article publication date: 10 January 2020
Issue publication date: 11 May 2020
Abstract
Purpose
The purpose of this paper is to propose and analyze the free vibration response of the spatial curved beams with variable curvature, torsion and cross section, in which all the effects of rotary inertia, shear and axial deformations can be considered.
Design/methodology/approach
The governing equations for free vibration response of the spatial curved beams are derived in matrix formats, considering the variable curvature, torsion and cross section. Frobenius’ scheme and the dynamic stiffness method are applied to solve these equations. A computer program is coded in Mathematica according to the proposed method.
Findings
To assess the validity of the proposed solution, a convergence study is carried out on a cylindrical helical spring with a variable circular cross section, and a comparison is made with the finite element method (FEM) results in ABAQUS. Further, the present model is used for reciprocal spiral rods with variable circular cross section in different boundary conditions, and the comparison with FEM results shows that only a limited number of terms in the results provide a relatively accurate solution.
Originality/value
The numerical results show that only a limited number of terms are needed in series solutions and in the Taylor expansion series to ensure an accurate solution. In addition, with a simple modification, the present formulation is easy to extend to analyze a more complicated model by combining with finite element solutions or analyze the transient responses and stochastic responses of spatial curved beams by Laplace transformation or Fourier transformation.
Keywords
Acknowledgements
This study was supported by the National Natural Science Foundation of China [grant number 50905021]; the Foundation of the Youth Science and Technology of Dalian, China [grant number 2015R072]; the Research Foundation for Doctor of Liaoning Province, China [grant number 201601263]; the Natural Fund Guidance Scheme of Liaoning Province, China [grant number 20180551106]; and the Education Department’s Scientific Research Funding Project of Liaoning Province, China [grant number JDL2019010].
Citation
Wang, G., Zhu, L., Higuchi, K., Fan, W. and Li, L. (2020), "Solution for free vibration of spatial curved beams", Engineering Computations, Vol. 37 No. 5, pp. 1597-1616. https://doi.org/10.1108/EC-03-2019-0097
Publisher
:Emerald Publishing Limited
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