A semi-analytical finite element (SAFE) formulation is proposed to study the wave propagation characteristics of thin-walled members with an infinite length in the longitudinal (axial) direction. Common structural members are considered as an assemblage of thin plates. The ratio of the thickness of the plate to the wavelength in the axial direction is assumed to be small so that the plane-stress assumption is valid. Employing a finite element modeling in the transverse direction circumvents difficulties associated with the cross-sectional profile of the member. The dynamic behavior is approximated by dividing the plates into several line (one-dimensional) segments and representing the generalized displacement distribution through the segment by polynomial interpolation functions. By applying Hamilton’s principle, the dispersion equation is obtained as a standard algebraic eigenvalue problem. The reasonably good accuracy of the method is demonstrated for the lowest modes by comparing, where feasible, the results with analytical solutions. To demonstrate the method’s versatility, frequency spectra are also presented for I and L shaped cross sections.

Issue Section:
Technical Papers
Keywords:
finite element analysis, surface acoustic waves, acoustic waveguides, ultrasonic materials testing, structural acoustics
Topics:
Displacement, Eigenvalues, Finite element analysis, Interpolation, Plates (structures), Spectra (Spectroscopy), Stiffness, Structural elements (Construction), Wave propagation, Waves, Stress, Algebra, Hamilton's principle, Acoustics, Cross section (Physics), Modeling, Polynomials, Wavelength
1.
Bai, H., Shah, A. H., Popplewell, N., and Datta, S. K., (to appear), “Scattering of Guided Waves by Circumferential Cracks in Steel Pipes,” ASME J. Appl. Mech.
2.
Datta
,
S. K.
,
Shah
,
A. H.
, and
Karunasena
,
W.
,
1999
, “
Ultrasonic Waves and Material Defect Characterization in Composite Plates
,”
Mech. Compos. Mater.
,
6
, pp.
1
–
16
.
3.
Mindlin, R. D., 1960, “Waves and Vibrations in Isotropic, Elastic Solids,” Goodier, J. N. and Noff, N., eds., Proceedings of the 1st Symposium on Naval Structural Mechanics, Pergamon Press, Oxford, pp. 199–232.
4.
Newman
,
E. G.
, and
Mindlin
,
R. D.
,
1957
, “
Vibration of a Monoclinic Crystal Plate
,”
J. Acoust. Soc. Am.
,
29
, pp.
1206
–
1218
.
5.
Kaul
,
R. K.
, and
Mindlin
,
R. D.
,
1962a
, “
Vibrations of an Infinite, Monoclinic Crystal Plate at High Frequencies and Long Wavelengths
,”
J. Acoust. Soc. Am.
,
34
, pp.
1895
–
1901
.
6.
Kaul
,
R. K.
, and
Mindlin
,
R. D.
,
1962b
, “
Frequency Spectrum of a Monoclinic Crystal Plate
,”
J. Acoust. Soc. Am.
,
34
, pp.
1902
–
1910
.
7.
Dong
,
S. B.
, and
Huang
,
K. H.
,
1985
, “
Edge Vibrations in Laminated Composite Plates
,”
ASME J. Appl. Mech.
,
52
, pp.
433
–
438
.
8.
Datta
,
S. K.
,
Shah
,
A. H.
,
Bratton
,
R. L.
, and
Chakraborty
,
T.
,
1988
, “
Wave Propagation in Laminated Composite Plates
,”
J. Acoust. Soc. Am.
,
83
, pp.
2020
–
2026
.
9.
Gazis
,
D. C.
,
1959
, “
Three-Dimensional Investigation of the Propagation of Waves in Hollow Circular Cylinders,” I-Analytical Foundation, II-Numerical Results
,
J. Acoust. Soc. Am.
,
31
, pp.
568
–
578
.
10.
Huang
,
K. H.
, and
Dong
,
S. B.
,
1984
, “
Propagating Waves and Edge Vibrations in Anisotropic Cylinders
,”
J. Sound Vib.
,
96
, pp.
363
–
379
.
11.
Rattanawangcharoen
,
N.
,
Shah
,
A. H.
, and
Datta
,
S. K.
,
1992
, “
Wave Propagation in Laminated Composite Circular Cylinders
,”
Int. J. Solids Struct.
,
29
, pp.
767
–
781
.
12.
Mal, A. K., and Ting, T. C. T., eds., 1988, Wave Propagation in Structural Composites, ASME, New York.
13.
Datta, S. K., Achenbach, J. D., and Rajapakse, Y. S., eds., 1990, Elastic Waves and Ultrasonic Nondestructive Evaluation, North-Holland, Amsterdam.
14.
Kapania
,
R. K.
, and
Raciti
,
S.
,
1989
, “
Recent Advances in Analysis of Laminated Beam and Plates
,”
AIAA J.
,
27
, pp.
935
–
946
.
15.
Soldatos
,
K. P.
,
1994
, “
Review of Three-Dimensional Dynamic Analysis of Circular Cylinders and Cylindrical Shells
,”
Appl. Mech. Rev.
,
47
, pp.
501
–
516
.
16.
Chimanti
,
D. E.
,
1997
, “
Guided Waves in Plates and Their Use in Materials Characterization
,”
Appl. Mech. Rev.
,
50
, pp.
247
–
284
.
17.
Maji
,
A. K.
,
Satpathi
,
D.
, and
Kratochvil
,
T.
,
1997
, “
Acoustic Emission Source Location Using Lamb Wave Modes
,”
ASCE, J. Eng. Mech.
,
123
, pp.
154
–
161
.
18.
Cheung, Y. K., 1976, Finite Strip Method in Structural Analysis, Pergamon Press, New York.
19.
Daniel
,
A. N.
,
Doyle
,
J. F.
, and
Rizzi
,
S. A.
,
1996
, “
Dynamic Analysis of Folded Plate Structures
,”
ASME J. Vibr. Acoust.
,
118
, pp.
519
–
598
.
20.
Gibson, R. F., 1994, Principles of Composite Material Mechanics, McGraw-Hill, Inc., New York.
21.
Timoshenko, S. P., and Woinowsky, K., 1959, Theory of Plates and Shells, McGraw-Hill Inc., New York.
22.
Bathe, K. J., 1996, Finite Element Procedure, Prentice Hall, New Jersey.
23.
Zhu
,
J.
,
Shah
,
A. H.
, and
Datta
,
S. K.
,
1995
, “
Modal Representation of Two-dimensional Elastodynamic Green’s Functions
,”
ASCE, J. Eng. Mech.
,
121
, pp.
26
–
36
.
24.
Graff, K. F., 1975, Wave Motion in Elastic Solids, Oxford University Press, Ely House, London W. I.
25.
Taweel
,
H.
,
Dong
,
S. B.
, and
Kazic
,
M.
,
2000
, “
Wave Reflection from the Free End of a Cylinder with an Arbitrary Cross-section
,”
Int. J. Solids Struct.
,
37
, pp.
1701
–
1726
.
Copyright © 2001
 by ASME
You do not currently have access to this content.