Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
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Wave Motion of Helical Springs with a Circular Section

원형 단면을 갖는 헬리컬 스프링에 대한 파동

  • Published : 2001.05.01
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Abstract

The governing partial differential equations of a helical spring with a circular section were derived from Frenet formulas and Timoshenko beam theory. These were solved to give the dispersion relationship between wave number and frequency along with wave form. Wave motions of helical springs are categorized by 4 regimes. In the first regime, the lower frequency area, the torsional and extensional waves of the spring are predominant and two waves are composite wave motions involving lateral motion of the coils and rotation of the coils about a horizontal axis. All waves are propagating in the second regime. The wave of the extensional motion of the spring and one wave of transverse motion of a wire change from travelling waves to near field waves in the third regime. Both waves excited by both axial and transverse motion are predominant in the fourth regime.

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References

  1. Love, A.E.M., 1899m 'The Propagation of Waves of Elastic Displacement along a Helical Wire,' Transaction of Cambridge Philosophy Society, 18, pp. 364-374
  2. Timoshenko, S.P., 1936, Theory of Elastic Stability, 1st Edn., NY, MacGraw Hill
  3. Wahl, A.M., 1963, Mechanical Springs, 2nd Edn., NY, MacGraw Hill
  4. Wittrick, W.H., 1966, 'On Elastic Wave Propagation in Helical Springs,' International Journal of Mechanical Sceince, 8, pp. 25-47 https://doi.org/10.1016/0020-7403(66)90061-0
  5. Jiang, W., Jones, W.K., Wang, T.L. and Wu, K.H., 1991, 'Free Vibration of Helical Springs,' Transaction of ASME, 58, 222
  6. Shinha, S.K. and Costello, G.A., 1978, 'The Numerical Solution of the Dynamic Response of Helical Springs,' International Journal of Numerical Methods in Engineering, 12, pp. 949 https://doi.org/10.1002/nme.1620120607
  7. 김도중, 이덕영, 1999, '원통형 스프링의 동특성 해석을 위한 헬리컬 로드 유한요소 개발,' 한국소음진동공학회지, 제9권, 제3호, pp. 544-553
  8. Mottershead, J.E., 1980, 'Finite elements for Dynamical Analysis of Helical Rod,' International Journalof Mechanical Science, 22, pp. 267-283 https://doi.org/10.1016/0020-7403(80)90028-4
  9. Pearson, D., 1982, 'The Transfer Matrix Method for the Vibration of Compressed Helical Springs,' Journal of Mechanical Engineering Science, 24, pp. 163-171 https://doi.org/10.1243/JMES_JOUR_1982_024_033_02
  10. Yildirim, V. and Ince, N., 1997, 'Natural Freqencies of Helical Spring of Arbitrary Shapes,' Journal of Sound and Vibration, 204(2), pp. 311-329 https://doi.org/10.1006/jsvi.1997.0940
  11. Pearson, D. and Wittrick, W.H., 1986, 'An Exact Solution for the Vibration of Helical Springs Using a Bernoulli-Euler Model,' International Journal of Mechanical Sciences, 28, pp. 83-96 https://doi.org/10.1016/0020-7403(86)90016-0
  12. Lee, J. and Thompson, D.J., 1999, 'Application of the Dynamic Stiffness Method to the Vibrationof Helical Springs,' ISVR Technical Memorandum No. 842, University of Southampton
  13. 이재형, 김성결, 허승진, Thompson, D.J., 2000, '동강성법을 이용한 코일 스프링의 진동 해석,' 한국소음진동공학회 창립10주년 기념소음진동학술대회논문집, pp. 1933-1938