The edge bending wave on a thin isotropic semi-infinite plate reinforced by a beam is considered within the framework of the classical plate and beam theories. The boundary conditions at the plate edge incorporate both dynamic bending and twisting of the beam. A dispersion relation is derived along with its long-wave approximation. The effect of the problem parameters on the cutoffs of the wave in question is studied asymptotically. The obtained results are compared with calculations for the reinforcement in the form of a strip plate.
References
1.
J.
Farkas
and K.
Jármai
, Optimum Design of Steel Structures
(Springer
, Heidelberg
, 2013
).2.
S. C.
Misra
, Design Principles of Ships and Marine Structures
(CRC Press
, Boca Raton, FL
, 2015
).3.
H.
Singh
, “Laterally loaded reinforced concrete stiffened plates: Analytical investigations
,” Pract. Period. Struct. Des. Construct.
17
(1
), 21
–29
(2012
).4.
I.
Elishakoff
and A.
Sternberg
, “Vibration of rectangular plates with edge-beams
,” Acta Mech.
36
(3–4
), 195
–212
(1980
).5.
D. A.
Pape
and A. J.
Fox
, “Deflection solutions for edge stiffened plates
,” in Proceedings of the 2006 IJME–INTERTECH Conference
.6.
E. J.
Sapountzakis
and J. T.
Katsikadelis
, “Analysis of plates reinforced with beams
,” Comput. Mech.
26
(1
), 66
–74
(2000
).7.
Y. K.
Lin
, Probabilistic Theory of Structural Dynamics
(McGraw-Hill Book Co
., New York
, 1967
).8.
L.
Dozio
and M.
Ricciardi
, “Free vibration analysis of ribbed plates by a combined analytical–numerical method
,” J. Sound Vib.
319
(1–2
), 681
–697
(2009
).9.
M.
Belubekyan
, K.
Ghazaryan
, P.
Marzocca
, and C.
Cormier
, “Localized bending waves in a rib-reinforced elastic orthotropic plate
,” J. Appl. Mech.
74
(1
), 169
–171
(2007
).10.
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
(10
), 2126
–2135
(2009
).11.
Y. K.
Konenkov
, “On normal modes of flexural waves in a plate
,” Sov. Phys. Acoust.
6
(1
), 57
–64
(1960
).12.
J. D.
Kaplunov
, L. Y.
Kossovich
, and M. V.
Wilde
, “Free localized vibrations of a semi-infinite cylindrical shell
,” J. Acoust. Soc. Am.
107
(3
), 1383
–1393
(2000
).13.
A. S.
Alzaidi
, J.
Kaplunov
, and L.
Prikazchikova
, “Elastic bending wave on the edge of a semi-infinite plate reinforced by a strip plate
,” Math. Mech. Solids
(published online 2019
).14.
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
(3
), 1781
–1784
(2000
).
[PubMed]
15.
J. B.
Lawrie
and J.
Kaplunov
, “Edge waves and resonance on elastic structures: An overview
,” Math. Mech. Solids
17
(1
), 4
–16
(2012
).16.
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
).17.
J.
Kaplunov
and A.
Nobili
, “The edge waves on a Kirchhoff plate bilaterally supported by a two-parameter elastic foundation
,” J. Vib. Control
23
(12
), 2014
–2022
(2017
).18.
J.
Kaplunov
, D. A.
Prikazchikov
, and G. A.
Rogerson
, “Edge bending wave on a thin elastic plate resting on a Winkler foundation
,” Proc. R. Soc. A
472
(2190
), 20160178
(2016
).19.
Y. K.
Konenkov
, “A Rayleigh-type flexural wave,” Sov
. Phys. Acoust.
6
, 122
–123
(1960
).20.
D. D.
Zakharov
, “Analysis of the acoustical edge flexural mode in a plate using refined asymptotics
,” J. Acoust. Soc. Am.
116
(2
), 872
–878
(2004
).© 2019 Acoustical Society of America.
2019
Acoustical Society of America
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