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On axially symmetric modes in finite elastic cylinders
KTH, Superseded Departments, Vehicle Engineering.ORCID iD: 0000-0001-5760-3919
2000 (English)In: Proceedings of the 25th International Conference on Noise and Vibration Engineering, ISMA, Leuven, 2000, 1471-1478 p.Conference paper, Published paper (Refereed)
Abstract [en]

The resonance frequencies and mode shapes for axially symmetric modes in an elastic, finite, solid cylinder are examined by a waveguide model, where influences of boundary conditions, higher order modes, structure borne sound dispersion, cylinder diameter and length are investigated. The model is based on the dispersion relation for an infinite cylinder with the boundary conditions at the lateral surfaces satisfied by mode matching. The results are shown to converge. Comparisons with alternative and approximate theories are made. The presented model is shown to agree fully with more elaborate theories and with simplified theories for slender rods while diverging from the latter for increased diameter-to-length ratios. To a great extend, the increased influences of higher order modes and dispersion explain the discrepancies reported for the approximate theories.

Place, publisher, year, edition, pages
Leuven, 2000. 1471-1478 p.
Series
Proceedings of the 25th International Conference on Noise and Vibration Engineering, ISMA
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-82471ISBN: 9073802725 (ISBN); 9789073802728 (ISBN) (print)OAI: oai:DiVA.org:kth-82471DiVA: diva2:498263
Conference
ISMA 25
Note
References: Pochhammer, L., (1876) Journal FÃŒr Die Reine Und Angewandte Mathematik, 81, pp. 324-336; Chree, C., (1889) Transactions of the Cambridge Philosophical Society, 14, pp. 250-369; Love, A.E.H., (1927) A Treatise on the Mathematical Theory of Elasticity, Forth Edition, , Cambridge University Press; Adem, J., (1954) Quarterly of Applied Mathematics, 12, pp. 261-275; Onoe, M., McNiven, H.D., Mindlin, R.D., (1962) Journal of Applied Mechanics, 29, pp. 729-734; Snowdon, J.C., (1968) Vibration and Shock in Damped Mechanical Systems, , John Wiley & Sons; Graff, K.F., (1991) Wave Motion in Elastic Solids, , Reprint. Dover Publications; Bishop, R.E.D., (1952) Aeronautical Quarterly, 3, pp. 280-293; Kynch, G.J., (1957) British Journal of Applied Physics, 8, pp. 64-73; Mindlin, R.D., Herrmann, G., (1951) Proceedings of the First U.S. National Cong-ress of Applied Mechanics, pp. 187-191. , cop. 1952; Volterra, E., (1955) Ingenieur-Archiv, 23, pp. 410-420; Mindlin, R.D., McNiven, H.D., (1960) Journal of Applied Mechanics, 27, pp. 145-151; McNiven, H.D., Perry, D.C., (1962) Journal of the Acoustical Society of America, 34, pp. 433-437; Hutchinson, J.R., (1967) Journal of the Acoustical Society of America, 42, pp. 398-402; Hutchinson, J.R., (1972) Journal of the Acoustical Society of America, 51, pp. 233-240; Hutchinson, J.R., (1980) Journal of Applied Mechanics, 47, pp. 901-907; Hutchinson, J.R., (1981) Journal of Applied Mechanics, 48, pp. 923-928; Rasband, S.N., (1975) Journal of the Acoustical Society of America, 57, pp. 899-905; Rumerman, M., Raynor, S., (1971) Journal of Sound and Vibration, 15, pp. 529-543; Leissa, A.W., So, J., (1995) Journal of the Acoustical Society of America, 98, pp. 2122-2135; Leissa, A.W., So, J., (1995) Journal of the Acoustical Society of America, 98, pp. 2136-2141; Liew, K.M., Hung, K.C., (1995) International Journal of Solids and Structures, 32, pp. 3499-3513; Pickett, G., (1945) Journal of Applied Physics, 16, pp. 820-831; Gladwell, G.M.L., Vijay, D.K., (1975) Journal of Sound and Vibration, 42, pp. 137-145; Gladwell, G.M.L., Tahbildar, U.C., (1972) Journal of Sound and Vibration, 22, pp. 143-157; McMahon, G.W., (1970) Journal of the Acoustical Society of America, 48, pp. 307-312; Gaul, L., (1991) Mechanical Systems and Signal Processing, 5, pp. 13-24; Mittra, R., Lee, S.W., (1971) Analytical Techniques in the Theory of Guided Waves, , MacMillan Company; Zemanek Jr., J., (1972) Journal of the Acoustical Society of America, 51, pp. 265-283; Dahlquist, G., Björck, Å., (1974) Numerical Methods, , Prentice Hall; Ivansson, S., Karasalo, I., (1993) Journal of Sound and Vibration, 161, pp. 173-180; Miklowitz, J., (1984) The Theory of Elastic Waves and Waveguides, , North-Holland; Abramowitz, M., Stegun, I.A., (1972) Handbook of Mathematical Functions, , Ninth printing. Dover Publications NR 20140805Available from: 2012-02-11 Created: 2012-02-11 Last updated: 2012-02-12Bibliographically approved

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Kari, Leif

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