In the framework of the membrane theory of cylindrical shells, the localised vibration near the shell free edge is considered. This paper presents the development leading to the dispersion equations for finite length shells and for three types of boundary conditions. Based on the attained dispersion equations the localised membrane vibration conditions are analysed and remarks are offered.
References
1.
D.
Ensminger
, Ultrasonics, Fundamentals, Technology, Applications
(Marcel Dekker Publishing
, New York
, 1988
), pp. 1
–685
.2.
J.
Barshinger
, J. L.
Rose
, and M. J.
Avioli
, “Guided wave resonance tuning for pipe inspection
,” J. Pressure Vessel Technol.
124
, 303
–310
(2002
).3.
W. J.
Staszewski
, “Structural health monitoring using guided ultrasonic waves
,” in Advances in Smart Technologies in Structural Engineering
(Springer
, Berlin Heidelberg
, 2004
), pp. 117
–162
.4.
Z.
Su
and L.
Ye
, Identification of Damage Using Lamb Waves: From Fundamentals to Applications
(Springer Science & Business Media
, New York
, 2009
), Vol. 48, pp. 1
–346
.5.
Y. K.
Konenkov
, “A Rayleigh-type flexural wave
,” Acoust. J.
6
(1
), 122
–123
(1960
) (in Russian).6.
A. Y.
Ishlinskii
, “On a limiting process in the theory of the stability of elastic rectangular plates
,” Dokl. Akad. Nauk
95
, 477
–479
(1954
) (in Russian).7.
M. V.
Belubekyan
, “The problems of plates localized instability
,” in Proceedings of International Conference on Optimal Control, Stability and Durability Problems of Mechanical Systems
, Yerevan (1997
), pp. 95
–99
(in Russian).8.
M. V.
Belubekyan
and S. R.
Martirosyan
, “The localized instability of the elastic plate-strip streamlined by supersonic gas flow
,” in Proceedings of Armenian National Academy of Sciences, Mechanics
(2007
), Vol. 60
(1
), pp. 33
–37
.9.
B. K.
Sinha
, “Some remarks on propagation characteristics of ridge guides for acoustic waves at low frequencies
,” J. Acoust. Soc. Am.
56
, 16
–18
(1974
).10.
J.
McKenna
, G. D.
Boyd
, and R. N.
Thurston
, “Plate theory solution for guided flexural acoustic waves along the tip of a wedge
,” IEEE Trans. Sonics Ultrason.
21
, 178
–186
(1974
).11.
R. N.
Thurston
and J.
McKenna
, “Flexural acoustic waves along the edge of a plate
,” IEEE Trans. Sonics Ultrason.
21
, 296
–297
(1974
).12.
A. N.
Norris
, V. V.
Krylov
, and I. D.
Abrahams
, “Flexural edge waves and Comments on ‘A new bending wave solution for the classical plate equation,’ [J. Acoust. Soc. Am. 104, 2220–2222 (1998)]
,” J. Acoust. Soc. Am.
107
, 1781
–1784
(2000
).13.
J. B.
Lawrie
and J.
Kaplunov
, “Edge waves and resonance on elastic structures: An overview
,” Math. Mech. Solids
17
(1
), 4
–16
(2012
).14.
A.
Oliner
(ed.), “Acoustic surface waves
,” in Topics in Applied Physics
, Vol. 24 (Springer
, Berlin
, 1978
), pp. 1
–334
.15.
S. V.
Biryukov
, V. Y.
Gulyaev
, V. V.
Krylov
, and V. P.
Plessky
, “Surface acoustic waves in inhomogeneous media
,” in Wave Phenomena
, Vol. 20 (Springer
, Berlin
, 1995
), pp. 1
–388
.16.
M. V.
Wilde
, J. D.
Kaplunov
, and L. I.
Kossovich
, Edge and Interface Resonance Effects in Elastic Bodies
(Fizmatlit
, Moscow
, 2010
), 280
pp. (in Russian).17.
R. V.
Goldstein
and G. A.
Maugin
(eds.), “Surface waves in anisotropic and laminated bodies and defects detection
,” NATO Advanced Research Workshop
(Kluver Academic Publishers, 2004
).18.
I. D.
Abrahams
and A. N.
Norris
, “On the existence of flexural edge waves on submerged elastic plates
,” in Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences
, London, UK (2000
), Vol. 456, No. 1999.19.
M. V.
Belubekyan
, “Magnetoelastic vibrations localized in the vicinity of the free-edge of a thin plate
,” in Proceedings of Armenian National Academy of Sciences, Mechanics
, Yerevan, Armenia (2003
), Vol. 56(2).20.
M.
Belubekyan
, K.
Ghazaryan
, P.
Marzocca
, and C.
Cormier
, “Localized magnetoelastic, bending vibration of an electroconductive elastic plate
,” J. Appl. Mech.
74
, 1071
–1076
(2007
).21.
I. D.
Abrahams
and J. B.
Lawrie
, “Scattering of flexural waves by a semi-infinite crack in an elastic plate carrying an electric current
,” Math. Mech. Solids
17
(1
), 43
–58
(2012
).22.
G. T.
Piliposian
and K. B.
Ghazaryan
, “Localized bending vibrations of piezoelectric plates
,” J. Waves Random Complex Media
21
(3
), 418
–433
(2011
).23.
J.
Kaplunov
, D. A.
Prikazchikov
, G. A.
Rogerson
, and M. I.
Lashab
, “The edge wave on an elastically supported Kirchhoff plate
,” J. Acoust. Soc. Am.
136
(4
), 1487
–1490
(2014
).24.
J.
Kaplunov
, D. A.
Prikazchikov
, and G. A.
Rogerson
, “Edge bending wave on a thin elastic plate resting on a Winkler foundation
,” in Proceedings of the Royal Society A, Mathematical, Physical and Engineering Sciences
, London, UK (2016
), Vol. 472, No. 2190.25.
S.
Althobaiti
and D. A.
Prikazchikov
, “Edge bending waves on an orthotropic elastic plate resting on the Winkler-Fuss foundation
,” in Proceedings of National Academy of Sciences of Armenia Mechanics
, Yerevan, Armenia (2016
), Vol. 69(1)
, pp. 16
–24
.26.
J.
Kaplunov
and A.
Nobili
, “The edge waves on a Kirchhoff plate bilaterally supported by a two-parameter elastic foundation
,” J. Vib. Control
1
–9
(2015
).27.
M.
Belubekyan
, K.
Ghazaryan
, P.
Marzocca
, and C.
Cormier
, “Localized bending waves in a rib-reinforced elastic orthotropic plate
,” J. Appl. Mech.
74
, 169
–171
(2007
).28.
A.
Milanese
, P.
Marzocca
, M.
Belubekyan
, and K.
Ghazaryan
, “Effect of the stiffness and inertia of a rib reinforcement on localized bending waves in semi-infinite strips
,” Int. J. Solids Struct.
46
, 2126
–2135
(2009
).29.
M. I.
Destrade
and Y.
Fu
, “A wave near the edge of a circular disk
,” Open Acoust. J.
1
, 15
–18
(2008
).30.
R. A.
Bagdasaryan
, M. V.
Belubekyan
, and K. B.
Ghazaryan
, “Rayleigh-type waves in a semi-infinite closed cylindrical shell
,” in Wave Problems in Mechanics
, edited by A. I.
Vesnitskii
, V. I.
Erofeev
, and N.
Novgorod
(Nijnii Novgorod Branch of Mechanical Engineering Institute
, Nijnii, Novgorod
, 1992
), pp. 87
–93
.31.
M.
Belubekyan
, K.
Ghazaryan
, A.
Vardanov
, A.
Milanese
, and P.
Marzocca
, “Localized vibrations near the free-edge of a cylindrical shell
,” in Proceedings of 49th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference
(AIAA Publishing, Washington, DC, 2008
), pp. 1874
–1876
.32.
G. R.
Gulgazaryan
, L. G.
Gulgazaryan
, and R. D.
Saakyan
, “The vibrations of a thin elastic orthotropic circular cylindrical shell with free and hinged edges
,” J. Appl. Math. Mech.
72
, 312
–322
(2008
).33.
J. D.
Kaplunov
, L. I.
Kossovich
, and M. V.
Wilde
, “Free localized vibrations of a semi-infinite cylindrical shell
,” J. Acoust. Soc. Am.
107
, 1383
–1393
(2000
).34.
J. D.
Kaplunov
and M. V.
Wilde
, “Free interfacial vibrations in cylindrical shells
,” J. Acoust. Soc. Am.
111
, 2692
–2704
(2002
).35.
I. V.
Andrianov
and J.
Awrejcewicz
, “Edge-localized effects in buckling and vibrations of a shell with free in circumferential direction ends
,” Acta Mechanica
173
, 41
–47
(2004
).36.
M. V.
Belubekyan
, G. R.
Gulgazaryan
, and A. V.
Sahakyan
, “On a Rayleigh-type bending wave in semi-infinite closed cylindrical shell
,” in Proceedings of National Academy of Sciences of Armenia
, Mechanics, Yerevan, Armenia (1997
), Vol. 50
(3–4
), pp. 49
–55
(in Russian).37.
V. A.
Veshev
, I. I.
Klyukin
, D. P.
Kouzov
, and V. D.
Lukyanov
, “On oscillating energy propagation in a thin elastic plate of a finite width
,” Soc. Phys. Acoust.
23
, 129
–131
(1977
) (in Russian).38.
K.
Ghazaryan
, P.
Marzocca
, A.
Milanese
, and H.
Mkrtchyan
, “Localized bending vibration of a rectangular plate with one free and three clamped edges
,” in Proceedings of International Conference Topical Problems of Continuum Mechanics
, Institute of Mechanics, Yerevan, Armenia (2007
), pp. 479
–483
.39.
S.
Fluegge
, Stresses in Shells
, 2nd ed. (Springer
, Berlin
, 1973
), Vol. 1, pp. 1
–499
.40.
J. W.
Rayleigh
, “On waves propagated along the plane surface of an elastic solid
,” Proc. London Math. Soc.
17
(1
), 4
–11
(1885
).© 2017 Acoustical Society of America.
2017
Acoustical Society of America
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