A spatial analysis of the generation and propagation of torsional waves in a cylindrical rod is presented. Starting from the classical linear equation of propagation and assuming a linear medium of propagation, the eigenfunctions of the propagation operator are calculated. Under the hypothesis of separation-of-variables type of solution, two ways of deriving the associated modes are performed. Given the normal mode basis, the behavior of a wavefront generated into the rod is examined. The application to the magnetostrictive generation of torsional waves is studied. Including the influence of eddy currents on the excitation and the geometry waveguide effects on the wave propagation, an analytical expression of mechanical losses during the first steps of propagation is given. A basic model of the interaction between a defect and the torsional guided waves is also proposed.

Topics
Waveguides, Eddy current, Wave propagation, Elastic waves, Fourier analysis, Functional equations
1.
J. D. Achenbach, Wave Propagation in Elastic Solids (North-Holland/American, Elsevier, 1973), Chap. 6.
2.
D. Royer and E. Dieulesaint, Ondes Élastiques dans les Solides (Masson, Paris, 1996), Vol. 1, pp. 289–297.
3.
R. N.
Thurston
, “
Elastic waves in rods and clad rods
,”
J. Acoust. Soc. Am.
64
,
1
–
37
(
1978
).
Google Scholar
Crossref
Search ADS
 
4.
P. Benoist-Guetal and M. Courbage, Mathématiques pour la Physique (Eyrolles, Paris, 1993), Vol. 3, Chap. 6.
5.
P. M. Morse and K. U. Ingard, Theoretical Acoustics (Princeton University Press, Princeton, 1986) pp. 191–222.
6.
N. S.
Tzannes
, “
Joule and Wiedeman effects. The simultaneous generation of longitudinal and torsional stress pulses in magnetostrictive materials
,”
IEEE Trans. Sonics Ultrason.
SU-13
,
33
–
41
(
1966
).
Google Scholar
 
7.
H.
Kwun
and
C.
Teller
, “
Magnetostrictive generation and detection of longitudinal, torsional and flexural waves in a steel rod
,”
J. Acoust. Soc. Am.
96
,
1202
–
1204
(
1994
).
Google Scholar
Crossref
Search ADS
 
8.
M.
Onoe
, “
Theory of ultrasonic delay lines for direct-current pulse transmission
,”
J. Acoust. Soc. Am.
34
,
1247
–
1254
(
1962
).
Google Scholar
Crossref
Search ADS
 
9.
R. Bozorth, Ferromagnetism (Van Nostrand, Princeton, 1951).
10.
W. Kaule, “Magnetostrictive ultrasonic testing of materials,” Proceedings of the 4th International Conference on Nondestructive Testing, London, 1963.
11.
A. Rothbart and L. Rosenberg, “A theory of pulse transmission along a magnetostrictive delay line,” Trans. IRE, PGUE-6, 1957.
12.
R. C.
Williams
, “
Theory of magnetostrictive delay lines for pulse and continuous wave transmission
,”
IEEE Trans. Ultrason. Eng.
UE-7
,
16
–
38
(
1959
).
Google Scholar
 
13.
F. Roddier, Distributions et Transformation de Fourier (Ediscience International, Paris, 1993), Chap. VIII, pp. 129–140.
14.
E. W.
Hobson
, “
On the representation of a function by series of Bessel’s functions
,”
Proc. London Math. Soc.
7
(
2
),
359
–
388
(
1909
).
Google Scholar
 
This content is only available via PDF.
© 2001 Acoustical Society of America.
2001
Acoustical Society of America
You do not currently have access to this content.