Natural Frequencies of a Very Large-Sag Extensible Cable

作者：Phanyasahachart Thongchai^*; Athisakul Chainarong; Chucheepsakul Somchai

来源：Journal of Engineering Mechanics, 2018, 144(2): 06017020.

DOI：10.1061/(ASCE)EM.1943-7889.0001409

• Dynamics of cables
• Nonlinear analysis
• Variational model formulation
• Galerkin finite element

This technical note presents a model formulation that can be used for analyzing the in-plane free vibration behaviors of a very large-sag extensible cable supported at the same and different levels. The formulation model developed in this study is based on a variational approach, which involves the virtual strain energy because of axial stretching, the virtual work done by cable self-weight, and by the inertia forces. The coupled equations of motion in the Cartesian coordinates are obtained by taking into account the difference of Euler's equations between equilibrium and displaced states. The Galerkin finite element method is used to obtain the mass and stiffness matrices and then the eigenvalue problem is solved. The numerical analysis results are given to demonstrate the dynamic free vibration on natural frequencies and mode shapes of various characteristics of cables from very small-sag to very large-sag cable configurations, the special case of a very large-sag cable was investigated and compared with the natural frequencies and mode shapes of the simple hanging chain.

• 出版日期2018-2