Theoretical Analysis of Mechanical Vibration for Offshore Platform Structures


A new class of support structures, called Periodic Structures, is introduced in this paper as a viable means for isolating the vibration transmitted from the sea waves to offshore platform structures through its legs. A passive approach to reduce transmitted vibration generated by waves is presented. The approach utilizes the property of periodic structural components that create stop and pass bands. The stop band regions can be tailored to correspond to regions of the frequency spectra that contain harmonics of the wave frequency, attenuating the response in those regions. A periodic structural component is comprised of a repeating array of cells, which are themselves an assembly of elements. The elements may have differing material properties as well as geometric variations. For the purpose of this research, only geometric and material variations are considered and each cell is assumed to be identical. A periodic leg is designed in order to reduce transmitted vibration of sea waves. The effectiveness of the periodicity on the vibration levels of platform will be demonstrated theoretically. The theory governing the operation of this class of periodic structures is introduced using the transfer matrix method. The unique filtering characteristics of periodic structures are demonstrated as functions of their design parameters for structures with geometrical and material discontinuities, and determine the propagation factor by using the spectral finite element analysis and the effectiveness of design on the leg structure by changing the ratio of step length and area interface between the materials is demonstrated in order to find the propagation factor and frequency response.

Share and Cite:

S. Asiri and Y. AL-Zahrani, "Theoretical Analysis of Mechanical Vibration for Offshore Platform Structures," World Journal of Mechanics, Vol. 4 No. 1, 2014, pp. 1-11. doi: 10.4236/wjm.2014.41001.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] A. Alghamdi, S. Asiri and A. Mohammed, “Wave Mechanics And Dynamic Response Of The Experimental Model For Offshore Platform With Periodic Legs,” Master Thesis, King Abdulaziz University, Jeddah, 2008.
[2] D. J. Mead, “Free Wave Propagation in Periodically Supported, Infinite Beams,” Journal of Sound and Vibration, Vol. 11, No. 2, 1970, pp. 181-197.
[3] L. Brillouin, “Wave Propagation in Periodic Structures,” Dover, New York, 1953.
[4] L. Brillouin, “Wave Propagation in Periodic Structures,” 2nd Edition, Dover, New York, 1946.
[5] D. J. Mead, “Vibration Response and Wave Propagation in Periodic Structures,” ASME Journal of Engineering for Industry, Vol. 93, No. 3, 1971, pp. 783-792.
[6] D. J. Mead, “Wave Propagation and Natural Modes in Periodic Systems: I. Mono-Coupled Systems,” Journal of Sound and Vibration, Vol. 40, No. 1, 1975, pp. 1-18.
[7] D. J. Mead and S. Markus, “Coupled Flexural-Longitudinal Wave Motion in a Periodic Beam,” Journal of Sound and Vibration, Vol. 90, No. 1, 1983, pp. 1-24.
[8] D. J. Mead, “Loss Factors and Resonant Frequencies of Periodic Damped Sandwiched Plates,” ASME Journal of Engineering for Industry, Vol. 98, No. 1, 1976, pp. 75-80.
[9] D. J. Mead, “A New Method of Analyzing Wave Propagation in Periodic Structures; Applications to Periodic Timoshenko Beams and Stiffened Plates,” Journal of Sound and Vibration, Vol. 104, No. 1, 1986, pp. 9-27.
[10] D. J. Mead, “Wave Propagation in Continuous Periodic Structures: Research Contributions from Southampton,” Journal of Sound and Vibration, Vol. 190, No. 3, 1996, pp. 495-524.
[11] D. J. Mead and N. S. Bardell, “Free Vibration of a Thin Cylindrical Shell with Periodic Circumferential Stiffeners,” Journal of Sound and Vibration, Vol. 115, No. 3, 1987, pp. 499-521.
[12] C. H. Hodges, “Confinement of Vibration by Structural Irregularity,” Journal of Sound and Vibration, Vol. 82, No. 3, 1982, pp. 441-444.
[13] C. H. Hodges and J. Woodhouse, “Vibration Isolation from Irregularity in a Nearly Periodic Structure: Theory and Measurements,” Journal of the Acoustical Society of America, Vol. 74, 1983, pp. 894-905.
[14] J. F. Doyle, “Wave Propagation in Structures,” Springer, New York, 1997.
[15] L. Cremer, M. Heckel and E. Ungar, “Structure-Borne Sound,” Springer-Verlag, New York, 1973.
[16] G. Gupta, “Natural Flexural Waves and the Normal Modes of Periodically-Supported Beams and Plates,” Journal of Sound and Vibration, Vol. 13, No. 1, 1970, pp. 89-111.
[17] M. Faulkner and D. Hong, “Free Vibrations of a Mono-Coupled Periodic System,” Journal of Sound and Vibration, Vol. 99, No. 1, 1985, pp. 29-42.
[18] D. J. Mead and Y. Yaman, “The Harmonic Response of Rectangular Sandwich Plates with Multiple Stiffening: A Flexural Wave Analysis,” Journal of Sound and Vibration, Vol. 145, No. 3, 1991, pp. 409-428.
[19] D. J. Mead, R. White and X. M. Zhang, “Power Transmission in a Periodically Supported Infinite Beam Excited at a Single Point,” Journal of Sound and Vibration, Vol. 169, No. 4, 1994, pp. 558-561.
[20] G. J. Kissel, “Localization Factor for Multichannel Disordered Systems,” Physical Review A, Vol. 44, No. 2, 1991, pp. 1008-1014.
[21] M. Ruzzene and A. Baz, “Attenuation and Localization of Wave Propagation in Periodic Rods Using Shape Memoryinserts,” Unpublished, 2000.
[22] M. Ruzzene and A. Baz, “Control of Wave Propagation in Periodic Composite Rods Using Shape Memory Inserts,” Journal of Vibration and Acoustics, Vol. 122, 2000, pp. 151-159.
[23] S. Asiri, A. Baz and D. Pines, “Active Periodic Struts for a Gearbox Support System,” Smart Materials Structures, Vol. 15, No. 6, 2006, pp. 1707-1714.
[24] S. Asiri, “Vibration Attenuation of Automotive Vehicle Engine Using Periodic Mounts,” International Journal of Vehicle Noise and Vibration, Vol. 3, No. 3, 2007, pp. 302-315.
[25] S. Asiri, M. Adbussalam and A. Alghamdi, “Dynamic Response of an Experimental Model for Offshore Platforms with Periodic Legs,” Journal of King Abdulaziz University Engineering Sciences, Vol. 20, No. 1, 2009, pp. 93-121.

Copyright © 2022 by authors and Scientific Research Publishing Inc.

Creative Commons License

This work and the related PDF file are licensed under a Creative Commons Attribution 4.0 International License.