Large Amplitude Free Vibration of a Very Sag Marine Cable

Authors: O. Punjarat, S. Chucheepsakul, T. Phanyasahachart

Abstract:

This paper focuses on a variational formulation of large amplitude free vibration behavior of a very sag marine cable. In the static equilibrium state, the marine cable has a very large sag configuration. In the motion state, the marine cable is assumed to vibrate in in-plane motion with large amplitude from the static equilibrium position. The total virtual work-energy of the marine cable at the dynamic state is formulated which involves the virtual strain energy due to axial deformation, the virtual work done by effective weight, and the inertia forces. The equations of motion for the large amplitude free vibration of marine cable are obtained by taking into account the difference between the Euler’s equation in the static state and the displaced state. Based on the Galerkin finite element procedure, the linear and nonlinear stiffness matrices, and mass matrices of the marine cable are obtained and the eigenvalue problem is solved. The natural frequency spectrum and the large amplitude free vibration behavior of marine cable are presented.

Keywords: Axial deformation, free vibration, Galerkin Finite Element Method, large amplitude, variational method.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.3566403

References:

[1] H.M. Irvine and T.K. Caughey, “The Linear Theory of Free Vibrations of a Suspended Cable,” Pro. of the Royal Society of London Series, Vol. 341, pp. 229-315, 1974.
[2] M.S. Triantafyllou and L. Grinfogel, “Natural Frequencies and Modes of Inclined Cables,” ASCE Journal of Structural Engineering, Vol. 112, pp. 139-148, 1986.
[3] S. Chucheepsakul and T. Huang, “Effect of Axial Deformation on Natural Frequencies of Marine Cables,” Pro. of the 7th Int. Offshore and Polar Eng. Conf., USA, pp. 131-136, 1997.
[4] S. Chucheepsakul and N. Srinil, “Free Vibrations of Three-Dimensional Extensible Marine Cables with Specified Top Tension via a Variational Method,” J. Ocean Eng., Vol. 29, pp. 1067-1096, 2002.
[5] N. Srinil, G. Rega, and S. Chucheepsakul, “Large-amplitude three-dimensional free vibrations of inclined sagged elastic cables,” J. Nonlinear Dyn., Vol. 33(2), pp. 129–154, 2003.
[6] T. Phanyasahachart, C. Athisakul, and S. Chucheepsakul, “Natural Frequencies of a Very Large-sag Extensible Cable,” J. Eng. Mech., ASCE., Vol.14(2), pp. 1-7, 2017.
[7] T. Phanyasahachart, C. Athisakul, and S. Chucheepsakul, “Analysis of Large-sag Extensible Catenary with Free Horizontal Sliding at One End by Variational Approach,” Int. J. Struct. Stab. Dyn., Vol. 17, No.7, pp. 1-17, 2017.
[8] S. Chucheepsakul, T. Monprapussorn, and T. Huang, (2003), “Large Strain Formulations of Extensible Flexible Marine Pipes Transporting Fluid,” J. Fluid Struct., Vol. 17, pp. 185–224, 2003.
[9] O. Punjarat and S. Chucheepsakul, “Post-Buckling Model for Uniform Self-Weight Beam with an Application to Catenary Riser,” Int. J. Struct. Stab. Dyn., Vol. 19, No. 4, pp. 1-21, 2019.
[10] O. Punjarat, and S. Chucheepsakul, “Free Vibration of a Very-Large-Sag Extensible Catenary Riser,” Pro. of the 2019 World Congress on Adv. Struct. Eng. Mech., Korea, pp. 1–20, 2019.
[11] R.D. Cook, D.S. Malkus, and M.E. Plesha, (2002), Concept and Applications of Finite Element Analysis, 4th ed., Wiley & Sons, New York, USA, 2002.
[12] B.S. Sarma and T.K. Varadan, “Certain Discussions in the Finite Element Formulation of Nonlinear Vibration Analysis,” Comput Struct, Vol. 15, No. 6, pp. 61-70, 1982.