Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
 Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IssuesArchive of Issues2015-1pp.81-95

Archive of Issues

Total articles in the database: 11223
In Russian (Èçâ. ÐÀÍ. ÌÒÒ): 8011
In English (Mech. Solids): 3212

<< Previous article | Volume 50, Issue 1 / 2015 | Next article >>
S.V. Kuznetsov, "Lamb Waves in a Clamped and a Partially Clamped Elastic Layer," Mech. Solids. 50 (1), 81-95 (2015)
Year 2015 Volume 50 Number 1 Pages 81-95
DOI 10.3103/S0025654415010082
Title Lamb Waves in a Clamped and a Partially Clamped Elastic Layer
Author(s) S.V. Kuznetsov (A. Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, pr. Vernadskogo 101, str. 1, Moscow, 119526 Russia, kuzn-sergey@yandex.ru)
Abstract The Lamb wave propagation in an anisotropic clamped or partially clamped (one side is free and the other side is clamped) elastic layer is studied by using the six-dimensional complex Cauchy formalism. The dispersion relations for Lamb waves in a clamped or partially clamped layer with arbitrary elastic anisotropy are obtained in closed form.
Keywords Lamb wave, anisotropy, dispersion, Cauchy formalism
References
1.  J. W. Rayleigh, "On the Free Vibrations of an Infinite Plate of homogeneous Isotropic Elastic Matter," Proc. Math. Soc. London 20, 225-234 (1889).
2.  H. Lamb, "On the Flexure of an Elastic Plate," Proc. Math. Soc. London 21, 70-90 (1889).
3.  H. Lamb, "On Waves in an Elastic Plate," Proc. Roy. Soc. A 93, 114-128 (1917).
4.  J. W. Rayleigh, "On Wave Propagation along the Plane Surface of an Elastic Solid," Proc. Math. Soc. London 17, 4-11 (1885).
5.  R. D. Mindlin, "Waves and Vibrations in Isotropic Elastic Plates," in The First Symposium on Naval Structural Mechanics, Ed. by J. N. Goodies and N. J. Hoff (Pergamon Press, Oxford, 1958), pp. 199-232.
6.  I. A. Viktorov, Physical Foundations of Application of Ultrasonic Rayleigh and Lamb Waves in Technology (Nauka, Moscow, 1966) [in Russian].
7.  H. Jeffreys, "The Surface Waves of Earthquakes," Geophys. J. Int. 3, 253-261 (1935).
8.  V. G. Gogoladze, "Rayleigh Wave Dispersion in a Layer," Trudy Seism. Inst. AN SSSR 119, 27-38 (1947).
9.  J. T. Wilson and O. Baykal, "On the North Atlantic Basin as Determined from Rayleigh Wave Dispersion," Bull. Seism. Soc. Am. 38, 41-53 (1948).
10.  M. B. Dobrin, "Dispersion in Seismic Surface Waves," Geophys. 16, 63-80 (1951).
11.  A. Freedman, "The Variation, with the Poisson Ratio, of Lamb Modes in a Free Plate. I: General Spectra," J. Sound Vibrat. 137, 209-230 (1990).
12.  A. Freedman, "The Variation, with the Poisson Ratio, of Lamb Modes in a Free Plate. II: At Transitions and Coincidence Values," J. Sound Vibrat. 137, 231-247 (1990).
13.  A. Freedman, "The Variation, with the Poisson Ratio, of Lamb Modes in a Free Plate. III: Behavior of Individual Modes," J. Sound Vibrat. 137, 249-266 (1990).
14.  Q. Zhu and W. G. Mayer, "On the Crossing Points of Lamb Wave Velocity Dispersion Curves," J. Acoust. Soc. Am. 93, 1893-1895 (1993).
15.  G. G. Stokes, "On the Theory of Oscillatory Waves," Trans. Cambridge Philos. Soc. 8, 441-455 (1847).
16.  J. W. Rayleigh, "On Progressive Waves," Proc. Math. Soc. London 9, 21-26 (1877).
17.  J. W. Rayleigh, Theory of Sound (Ulan Press, 2011).
18.  O. Reynolds, "On the Rate of Progression of Groups of Waves and the Rate at Which Energy is Transmitted by Waves," Nature 16, 343-344 (1877).
19.  K. Sezawa and K. Kanai, "On the Propagation of Rayleigh Waves in Dispersive Elastic Media," Bull. Earthquake Res. Inst. (Tokyo) 19, 549-553 (1941).
20.  Y. Sato, "Study on Surface Waves. II: Velocity of Surface Waves Propagated upon Elastic Plates," Bull. Earthquake Res. Inst. (Tokyo) 29, 223-261 (1951).
21.  F. Press and M. Ewing, "Theory of Air-Coupled Flexural Waves," J. Appl. Phys. 22, 892-899 (1951).
22.  F. Press and J. Oliver, "Model Study of Air-Coupled Surface Waves," J. Acoust. Soc. Am. 27, 43-46 (1955).
23.  I. Tolstoy, "Dispersion and Simple Harmonic Sources in Wave Ducts," J. Acoust. Soc. Am. 27, 897-910 (1955).
24.  I. Tolstoy and E. Usdin, "Wave Propagation in Elastic Plates: Low and High Mode Dispersion," J. Acoust. Soc. Am. 29, 37-42 (1957).
25.  K. Negishi, "Existence of Negative Group Velocities for Lamb Waves," Japanese J. Appl. Phys. 26, Suppl. 26-1, 171-173 (1987).
26.  M. A. Biot, "General Theorems on the Equivalence of Group Velocity and Energy Transport," Phys. Rev. 105, 1129-1137 (1957).
27.  M. J. S. Lowe, Plate Waves for the NDT of Diffusion Bonded Titanium, PhD Thesis (Imperial College, UK, 1992).
28.  R. H. Lyon, "Response of an Elastic Plate to Localized Driving Forces," J. Acoust. Soc. Am. 27, 259-265 (1955).
29.  Yu. I. Borovnitskii, "Orthogonality Relations for Lamb Waves," Akust. Zh. 18, 513-518 (1972) [Acoust. Phys. (Engl. Transl.)].
30.  B. A. Auld, Acoustic Fields and Waves in Solids, Vol. 2, 2nd ed., (Robert E. Krieger Publ. Company, Malabar, 1990).
31.  A. E. Vovk and V. V. Tyutenin, "Excitation of Normal Waves in Plane Elastic Waveguid by Prescribed Transverse Forces," Tr. Akust. Inst., No. IX, 5-26 (1969).
32.  L. Duquenne, E. Moulin, J. Assaad, and S. Grondel, "Transient Modeling of Lamb Waves Generated in Viscoelastic Materials by Surface Bonded Piezoelectric Transducers," J. Acoust. Soc. Am. 116, 133-141 (2004).
33.  M. B. Orazov, "The Completeness of the Eigenvectors and Associated Vectors of a Self-Adjoint Quadratic Bundle," Funkts. Anal. Ego Prilozhen. 10 (2), 82-83 (1976) [Func. Anal. Its Appl. (Engl. Transl.) 10 (2), 153-155 (1976)].
34.  D. D. Zakharov, "Orthogonality of 3D Guided Waves in Viscoelastic Laminates and Far Field Evaluation to a Local Acoustic Source," Int. J. Solids Struct. 45, 1788-1803 (2008).
35.  D. D. Zakharov, "Dirichlet-Neumann Conditions and the Orthogonality of Three-Dimensional Guided Waves in Layered Solids," Zh. Vych. Mat. Mat. Fiz. 50 (9), 1598-1612 (2010) [Comput. Math. Math. Phys. (Engl. Transl.) 50, 1522-1535 (2010)].
36.  W. Malischewsky, "Orthonormalization of Plane Surface and Body Waves (in German)," Cerlands Beiträge zur Geophys. 79, 468-474 (1970).
37.  S. Stange and W. Friederich, "Guided Wave Propagation across Sharp Lateral Heterogeneities: The Complete Wavefield at Plane Discontinuities," Geophys. J. Int. 109, 183-190 (1992).
38.  M. V. Keldysh, "On the Completeness of Eigenfunctions of Some Classes of Non-Self-Adjoint Linear Operators," Russ. Math. Surveys 26, 15-44 (1971).
39.  S. Agmon, "On the Eigenfunctions and on the Eigenvalues of General Elliptic Boundary Value Problems," Commun. Pure Appl. Math. 15, 119-147 (1962).
40.  M. J. S. Lowe and O. Diligent, "Low-Frequency Reflection Characteristics of the s0 Lamb Wave from a Rectangular Notch in a Plate," J. Acoust. Soc. Am. 111, 64-74 (2002).
41.  L. Brevdo, "On the Stability of Lamb Modes," Acta Mech. 117, 71-80 (1996).
42.  R. Stoneley, "The Seismological Implication of Aeolotropy in Continental Structures," Roy. Astronom. Soc. Monthly Notes. Geophys. Suppl. 5, 343-353 (1949).
43.  M. J. P. Musgrave, "On the Propagation of Elastic Waves in Aeolotropic Media. I. General Principles," Proc. Roy. Soc. Lond. A 226, 339-355 (1954).
44.  M. J. P. Musgrave, "On the Propagation of Elastic Waves in Aeolotropic Media. II. Media of Hexagonal Symmetry," Proc. Roy. Soc. Lond. A 226, 356-366 (1954).
45.  V. T. Buchwald, "Rayleigh Waves in Transversely Isotropic Media," Quart. J. Mech. Appl. Math. 14, 293-317 (1961).
46.  R. Stoneley, "The Propagation of Surface Elastic Waves in a Cubic Crystal," Proc. Roy. Soc. Lond. A 232, 447-458 (1955).
47.  G. F. Miller and M. J. P. Musgrave, "On the Propagation of Elastic Waves in Aeolotropic Media. III. Medial of Cubic Symmetry," Proc. Roy. Soc. Lond. A 236, 352-383 (1956).
48.  M. Mitra, "Propagation of Elastic Waves in an Infinite Plate of Cylindrically Aeolotropic Material," ZAMP 10, 579-583 (1959).
49.  D. L. Anderson, "Elastic Wave Propagation in Layered Anisotropic Media," J. Geophys. Res. 66, 2953-2963 (1961).
50.  L. P. Solie and B. A. Auld, "Elastic Waves in Free Anisotropic Plates," J. Acoust. Soc. Am. 54, 50-65 (1973).
51.  A. H. Nayfeh and D. E. Chimenti, "Free Wave Propagation in Plates of General Anisotropic Media," J. Appl. Mech. 56, 881-886 (1989).
52.  V. Dayal and V. K. Kinra, "Leaky Lamb Wave in an Anisotropic Plate. I: An Exact Solution and Experiments," J. Acoust. Soc. Am. 85, 2268-2276 (1989).
53.  A. Ben-Menahem and A. G. Sena, "Seismic Source Theory in Stratified Anisotropic Media," J. Geophys. Res. 95, 15.395-15.427 (1990).
54.  G. R. Liu, J. Tani, K. Watanabe, and T. Ohyoshi, "Lamb Wave Propagation in Anisotropic Laminates," J. Appl. Mech. 57, 923-929 (1990).
55.  W. Lin and L. M. Keer, "A Study of Lamb Waves in Anisotropic Plates," J. Acoust. Soc. Am. 92, 888-894 (1992).
56.  G. Neau, Lamb Waves in Anisotropic Viscoelastic Plates. Study of the Wave Fronts and Attenuation, PhD Thesis (L'Universite de Bordeaux, 2003).
57.  G. Neau, M. Deschamps, and M. J. S. Lowe, "Group Velocity of Lamb Waves in Anisotropic Plates: Comparison between Theory and Experiment," in Review of Progress in Quantitative NDE, Vol. 20, Ed. by D. O. Thompson and D. E, Chimenti (Amer. Inst. Phys., New York, 2001), pp. 81-88.
58.  L. Wang and F. G. Yuan, "Group Velocity and Characteristic Curves of Lamb Waves in Composites: Modeling and Experiments," Compos. Sci. Technol. 67, 1370-1384 (2007).
59.  S. V. Kuznetsov, "Surface Waves of Non-Rayleigh Type," Quart. Appl. Math. 61, 575-582 (2003).
60.  S. V. Kuznetsov, "Subsonic Lamb Waves in Anisotropic Plates," Quart. Appl. Math. 60, 577-587 (2002).
61.  S. A. Markus, "Low-Frequency Approximations for Zeroth-Order Modes of Normal Waves in Anisotropic Plates," Akust. Zh. 33, 1091-1092 (1998) [Acoust. Phys. (Engl. Transl.)].
62.  V. I. Alshits and V. N. Lyubimov, "Abnormal Dispersion of Surface Elastic Waves in Anisotropic Plate," Kristallogr. 33, 279-285 (1988) [Crystallogr. Rep. (Engl. Transl.)].
63.  A. N. Stroh, "Steady State Problem in Anisotropic Elasticity," J. Math. Phys. 41, 77-103 (1962).
64.  K. A. Ingebrigtsen and A. Tonning, "Elastic Surface Waves in Crystals," Phys. Rev. 184, 942-951 (1969).
65.  D. M. Barnett and J. Lothe, "Synthesis of the Sextic and the Integral Formalism for Dislocations, Green Functions, and Surface Waves in Anisotropic Elastic Solids," Phys. Norv. 7, 13-19 (1973).
66.  P. Chadwick and G. D. Smith, "Foundations of the Theory of Surface Waves in Anisotropic Elastic Materials," in Advances in Applied Mathematics, Vol. 17 (Acad. Press, New York, 1977), pp. 303-376.
67.  T. C. T. Ting nd D. M. Barnett, "Classifications of Surface Waves in Anisotropic Elastic Materials," Wave Motion 26, 207-218 (1997).
68.  T. C. T. Ting, "On Extraordinary Semisimple Matric N(v) for Anisotropic Elastic Materials," Quart. Appl. Math. 55, 723-738 (1997).
69.  Y. B. Fu, "Hamiltonian Interpretation of the Stroh Formalism in Anisotropic Elasticity," Proc. Roy. Soc. Ser. A 463, 3073-3087 (2007).
70.  K. Tanuma, Stroh Formalism and Rayleigh Waves (Springer, 2010).
71.  A. L. Shuvalov, "On the Theory of Wave Propagation in Anisotropic Plates," Proc. Roy. Soc. Lond. Ser. A 456, 2197-2222 (2000).
72.  V. Alshits, M. Deschamps, and G. Maugin, "Elastic Waves in Anisotropic Plates: Short-Wavelength Asymptotics of Dispersion Branches Vn(k)," Wave Motion 37, 273-292 (2003).
73.  R. V. Goldstein and S. V. Kuznetsov, "Surface Acoustic Waves in Testing of Layered Media. The Waves' Sensitivity to Variations in the Properties of Individual Layers," Prikl. Math. Mekh. 77 (1), 74-82 (2013) [J. Appl. Mat. Mech. (Engl. Transl.) 77 (1), 51-56 (2013)].
74.  S. V. Kuznetsov, "Love Waves in Stratified Monoclinic Media," Quart. Appl. Math. 62, 749-766 (2004).
75.  S. V. Kuznetsov, "SH-Waves in Laminated Plates," Quart. Appl. Math. 64, 153-165 (2006).
76.  S. V. Kuznetsov, "Low Waves in Nondestructive Diagnostics of Layered Composites," Acoust. Phys. 56, 877-892 (2010).
77.  C. Moler and Ch. V. Loan, "Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later," SIAM Review 45, 1-46 (2003).
78.  P. Hartman, Ordinary Differential Equations (SIAM, New York, 2002).
79.  M. C. Pease III, Methods of Matrix Algebra (Academic Press, London, 1965).
80.  J. W. Dunkin, "Computation of Model Solutions in Layered Elastic Media at High Frequencies," Bull. Seism. Soc. Am. 55, 335-358 (1965).
81.  D. Lébesque and L. Piché, "A Robust Transfer Matrix Formulation for the Ultrasonic Response of Multilayered Absorbing Media," J. Acoust. Soc. 92, 452-467 (1992).
82.  M. Castaings and B. Hosten, "Delta Operator Technique to Improve the Thomson-Haskell Method Stability for Propagation in Multilayered Anisotropic Absorbing Plate," J. Acoust. Soc. Am. 95, 1931-1941 (1994).
83.  M. J. S. Lowe, "Matrix Techniques for Modeling Ultrasonic Waves in Multilayered Media," IEEE Trans. Ultrasonics, Ferroelectr. Freq. Contr. 42, 525-542 (1995).
84.  L. Wang and S. I. Rokhlin, "Stable Reformulation of Transfer Matrix Method for Wave Propagation in Layered Anisotropic Media," Ultrasonics 39, 413-424 (2001).
85.  D. H. Bailey, "A Portable High Performance Multiprecision Package," in NASA RNR Technical Report, RNR-90-022 (1993), pp. 1-29.
86.  D. H. Bailey, "Automatic Translation of Fortran Programs to Multiprecision," in NASA RNR Technical Report, RNR-90-025 (1993), pp. 1-21.
87.  C. Y. Guo and L. Wheeler, "Extreme Poisson's Ratios and Related Elastic Crystal Properties," J. Mech. Phys. Solids 54, 690-707 (2006).
Received 25 September 2013
Link to Fulltext
<< Previous article | Volume 50, Issue 1 / 2015 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100