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An analytical study on the static vertical stiffness of wire rope isolators

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Abstract

The vibrations caused by earthquake ground motions or the operations of heavy machineries can affect the functionality of equipment and cause damages to the hosting structures and surrounding equipment. A Wire rope isolator (WRI), which is a type of passive isolator known to be effective in isolating shocks and vibrations, can be used for vibration isolation of lightweight structures and equipment. The primary advantage of the WRI is that it can provide isolation in all three planes and in any orientation. The load-supporting capability of the WRI is identified from the static stiffness in the loading direction. Static stiffness mainly depends on the geometrical and material properties of the WRI. This study develops an analytical model for the static stiffness in the vertical direction by using Castigliano’s second theorem. The model is validated by using the experimental results obtained from a series of monotonic loading tests. The flexural rigidity of the wire ropes required in the model is obtained from the transverse bending test. Then, the analytical model is used to conduct a parametric analysis on the effects of wire rope diameter, width, height, and number of turns (loops) on vertical stiffness. The wire rope diameter influences stiffness more than the other geometric parameters. The developed model can be accurately used for the evaluation and design of WRIs.

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References

  1. U. Berardi, Modelling and testing of a dielectic electroactive polymer (DEAP) actuator for active vibration control, Journal of Mechanical Science and Technology, 27 (2013) 1–7.

    Article  Google Scholar 

  2. Q. Li, Y. Zhu, D. Xu, J. Hu, W. Min and L. Pang, A negative stiffness vibration isolator using magnetic spring combined with rubber membrane, Journal of Mechanical Science and Technology, 27 (2013) 813–824.

    Article  Google Scholar 

  3. H.-W. Chen, W.-X. Ji, Q.-J. Zhang, Y. Cao and S.-Y. Fan, A method for vibration isolation of a vertical axis automatic washing machine with a hydraulic balancer, Journal of Mechanical Science and Technology, 26 (2012) 335–343.

    Article  Google Scholar 

  4. M. Leblouba, S. Altoubat, M. E. Rahman and B. P. Selvaraj, Elliptical leaf spring shock and vibration mounts with enhanced damping and energy dissipation capabilities using lead spring, Shock and Vibration, 2015 (2015).

  5. T. M. Loyd, Damping phenomena in a wire rope vibration isolation system, Doctor of Philosophy, Aerospace Engineering, Auburn University (1989).

    Google Scholar 

  6. M. L. Tinker and M. A. Cutchins, Damping phenomena in a wire rope vibration isolation system, Journal of Sound and Vibration, 157 (1992) 7–18.

    Article  Google Scholar 

  7. G. F. Demetriades, M. C. Constantinou and A. M. Reinhorn, Study of wire rope systems for seismic protection of equipment in buildings, Engineering Structures, 15 (1993) 321–334.

    Article  Google Scholar 

  8. P. S. Balaji, L. Moussa, M. E. Rahman and L. Vuia, Experimental investigation on the hysteresis behavior of the wire rope isolators, Journal of Mechanical Science and Technology, 29 (2015) 1527–1536.

    Article  Google Scholar 

  9. G. Massa, S. Pagano, E. Rocca and S. Strano, Sensitive equipments on WRS-BTU isolators, Meccanica, 48 (2013) 1777–1790.

    Article  MATH  Google Scholar 

  10. P. Paolacci and R. Giannini, Study of the effectiveness of steel cable dampers for the seismic protection of electrical equipment, The 14th World Conference on Earthquake Engineering, Beijing, China (2008).

    Google Scholar 

  11. Wire rope Isolators, ITT Enidine Inc, New York, www. enidine.com (2014).

  12. R. G. Budynas, J. K. Nisbett and J. E. Shigley, Shigley’s mechanical engineering design, McGraw-Hill (2008).

    Google Scholar 

  13. S. Timoshenko, Strength of materials, Pt. 2: Advanced theory and problems, R. E. Krieger Publishing Company (1983).

    Google Scholar 

  14. Z. H. Zhu and S. A. Meguid, Nonlinear FE-based investigation of flexural damping of slacking wire cables, International Journal of Solids and Structures, 44 (2007) 5122–5132.

    Article  MATH  Google Scholar 

  15. Y. Prawoto and R. B. Mazlan, Wire ropes: Computational, mechanical, and metallurgical properties under tension loading, Computational Materials Science, 56 (2012) 174–178.

    Article  Google Scholar 

  16. X. Huang and O. Vinogradov, Extension of a cable in the presence of dry friction, Structural Engineering and Mechanics, 4 (1996) 313–329.

    Article  Google Scholar 

  17. X. Huang and O. G. Vinogradov, Dry friction losses in axially loaded cables, Structural Engineering and Mechanics, 4 (1996) 330–344.

    Article  Google Scholar 

  18. X. Huang and O. Vinogradov, Analysis of dry friction hysteresis in a cable under uniform bending, Structural Engineering and Mechanics, 2 (1994) 63–80.

    Article  Google Scholar 

  19. X. Li, S. Wang and J. Zhou, Analysis of elliptical Hertz contact of steel wires of stranded-wire helical spring, Journal of Mechanical Science and Technology, 28 (2014) 2797–2806.

    Article  Google Scholar 

  20. R. Hobbs and M. Raoof, Hysteresis in bridge strand, ICE Proceedings (1984) 445–464.

    Google Scholar 

  21. M. Raoof and T. J. Davies, Simple determination of the maximum axial and torsional energy dissipation in large diameter spiral strands, Computers & Structures, 84 (2006) 676–689.

    Article  Google Scholar 

  22. M. Raoof, Behaviour of large diameter wire ropes, International Journal of Offshore and Polar Engineering, 6 (1996) 119–226.

    Google Scholar 

  23. M. Raoof, The Prediction of axial damping in sprial strands, Journal of Strain Analysis for Engineering Design, 26 (1991) 221–229.

    Article  Google Scholar 

  24. S. A. Velinsky, Design and mechanics of multi-lay wire strands, Journal of Mechanisms, Transmissions, and Automation in Design, 110 (1988) 152–160.

    Article  Google Scholar 

  25. G. A. Costello and G. J. Butson, Simplified bending theory for wire rope, Journal of the Engineering Mechanics Division, 108 (1982) 219–227.

    Google Scholar 

  26. Y. J. Chiang, Characterizing simple-stranded wire cables under axial loading, Finite Elements in Analysis and Design, 24 (1996) 49–66.

    Article  MATH  Google Scholar 

  27. W. G. Jiang, M. S. Yao and J. M. Walton, A concise finite element model for simple straight wire rope strand, International Journal of Mechanical Sciences, 41 (1999) 143–161.

    Article  MATH  Google Scholar 

  28. E. Stanova, G. Fedorko, M. Fabian and S. Kmet, Computer modelling of wire strands and ropes Part I: Theory and computer implementation, Advances in Engineering Software, 42 (6) (2011) 305–315.

    Article  MATH  Google Scholar 

  29. E. Stanova, G. Fedorko, M. Fabian and S. Kmet, Computer modelling of wire strands and ropes part II: Finite element-based applications, Advances in Engineering Software, 42 (6) (2011) 322–331.

    Article  MATH  Google Scholar 

  30. ASTM A931-08 (2013) Standard test method for tension testing of wire ropes and strand, ASTM International, West Conshohocken, PA, www.astm.org (2013).

    Google Scholar 

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Authors and Affiliations

  1. Faculty of Engineering and Science, Curtin University Sarawak, Miri, 98009, Malaysia

    P. S. Balaji, M. E. Rahman & Lau Hieng Ho

  2. Department of Civil and Environmental Engineering, College of Engineering, University of Sharjah, P.O. Box, 27272, Sharjah, UAE

    Leblouba Moussa

Authors
  1. P. S. Balaji
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  2. Leblouba Moussa
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  3. M. E. Rahman
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  4. Lau Hieng Ho
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Corresponding author

Correspondence to M. E. Rahman.

Additional information

Moussa Leblouba received his State Engineer degree from the National School of Public Works, Algiers, Algeria in 2005. Then, he received his Ph.D. degree from the Technical University of Civil Engineering, Bucharest, Romania in 2009. He is currently an Assistant Professor at the Department of Civil and Environmental Engineering at the University of Sharjah, Sharjah, UAE since 2014. His research interests include structural dynamics, finite element analysis, and earthquake engineering.

Muhammad Ekhlasur Rahman received his Ph.D. degree from the University of Dublin, Trinity College Dublin, Ireland. He is currently an Associate Professor at the Department of Civil and Construction, Curtin University, Sarawak, Malaysia. His research interests include structural dynamics, finite element analysis, and construction materials.

P. S. Balaji received his B.E. degree in Aeronautical Engineering from the Anna University, Chennai, India. He obtained his M.Tech. degrees in Mechanical Design from the NIT, Allahabad, India. He is currently pursuing his Ph.D. degree at the Department of Civil and Construction Engineering, Curtin University, Sarawak, Malaysia. His area of research includes vibrations, finite element analysis, and composite materials.

Lau Hieng obtained his Bachelor of Engineering (Honors) and Ph.D. degrees from the Oxford Brookes University, Oxford, United Kingdom. He was the Head of the Civil and Construction Engineering Department from 2005 to 2011. He is currently a professional engineer registered with the Board of Engineers Malaysia. His area of research includes coldformed steel, connections, structural stability, and corrosion.

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Balaji, P.S., Moussa, L., Rahman, M.E. et al. An analytical study on the static vertical stiffness of wire rope isolators. J Mech Sci Technol 30, 287–295 (2016). https://doi.org/10.1007/s12206-015-1232-5

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  • DOI: https://doi.org/10.1007/s12206-015-1232-5

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