A system of periodic elastic strips (each one considered as a piece of a plate) is characterized by a matrix relation between the Bloch series of displacement and traction at the bottom side of the system. Both these mechanical fields are involved in the boundary conditions at the contact plane between the strips and the substrate supporting a Rayleigh wave. The analysis exploits the mechanical field expansion over the plate modes, including complex modes; numerical results satisfy the energy conservation law satisfactorily. The derived planar harmonic Green’s function provides an alternative tool for investigation of surface waves propagation under periodic elastic strips, with respect to pure numerical methods mostly applied in the surface acoustic wave devices literature. Perfect agreement of the presented theory with the experimentally verified perturbation model of thin strips is demonstrated.
Issue Section:
Research Papers
1.
Danicki
, E.
, 1992, “Generation and Bragg Reflection of Surface Acoustic Waves in Nearly Periodic System of Elastic Metal Strips on Piezoelectric Half-Space
,” J. Acoust. Soc. Am.
0001-4966, 93
, pp. 116
–131
.2.
Danicki
, E.
, 1984, “Perturbation Theory of Surface Acoustic Wave Reflection from a Periodic Structure With Arbitrary Angle of Incidence
,” Arch. Mech.
0373-2029, 36
, pp. 623
–638
.3.
Biriukov
, S. V.
, Martin
, G.
, and Polevoi
, V. G.
, 1995, “Derivation of COM Equations Using the Surface Impedance Method
,” IEEE Trans. Ultrason. Ferroelectr. Freq. Control
0885-3010, UFFC-42
, pp. 602
–611
.4.
Danicki
, E. J.
, 1998, “An Approximation to the Planar Harmonic Green’s Function at Branch Points in Wave-Number Domain
,” J. Acoust. Soc. Am.
0001-4966, 104
, pp. 651
–663
.5.
Besserer
, H.
, and Malishevsky
, P. S.
, 2004, “Mode Series Expansions at Vertical Boundaries in Elastic Waveguides
,” Wave Motion
0165-2125, 39
, pp. 41
–59
.6.
Karunasena
, W.
, Liew
, K. M.
, and Kitipornchai
, S.
, 1995, “Reflection of Plate Waves at Fixed Edge of a Composite Plate
,” J. Acoust. Soc. Am.
0001-4966, 98
, pp. 644
–651
.7.
Torvik
, P. J.
, 1971, “The Elastic Strip With Prescribed End Displacements
,” ASME J. Appl. Mech.
0021-8936, 38
, pp. 929
–936
.8.
Torvik
, P. J.
, 1967, “Reflection of Wave Trains in Semi-Infinite Plates
,” J. Acoust. Soc. Am.
0001-4966, 41
, pp. 346
–353
.9.
Gregory
, R. D.
, and Gladwel
, I.
, 1983, “The Reflection of a Symmetric Rayleigh-Lamb Wave at the Fixed or Free Edge of a Plate
,” J. Elast.
0374-3535, 13
, pp. 185
–206
.10.
Gregory
, R. D.
, and Gladwell
, I.
, 1982, “The Cantilever Beam Under Tension, Bending Or Flexure at Infinity
,” J. Elast.
0374-3535, 12
, pp. 317
–343
.11.
Dempsey
, J. P.
, and Sinclair
, G. B.
, 1979, “On the Stress Singularities in the Plane Elasticity of the Composite Wedge
,” J. Elast.
0374-3535, 9
, pp. 373
–391
.12.
Williams
, M. I.
, 1952, “Stress Singularities Resulting From Various Boundary Conditions in Angular Corners of Plates in Extension
,” ASME J. Appl. Mech.
0021-8936, 19
, pp. 526
–528
.13.
Bogy
, D. B.
, 1971, “Two Edge-Bonded Elastic Wedges of Different Materials and Wedge Angles Under Surface Traction
,” ASME J. Appl. Mech.
0021-8936, 38
, pp. 377
–386
.14.
Gregory
, R. D.
, 1979, “Green’s Function, Bi-Linear Forms, and Completeness of the Eigenfunctions for the Elastostatic Strip and Wedge
,” J. Elast.
0374-3535, 9
, pp. 283
–309
.15.
Danicki
, E. J.
, Hickernell
, F. S.
, and Mateescu
, I.
, 2005, “Closed-Form Solution for SPUDTS
,” IEEE Freq. Contr. Symp. Proc.
, 1
, pp. 152
–155
.16.
Danicki
, E. J.
, 2003, “Surface Acoustic Wave Diffraction in Spectral Theory of Interdigital Transducers
,” J. Acoust. Soc. Am.
0001-4966, 114
, pp. 813
–820
.17.
Pagneux
, V.
, 2006, “Revisiting the Edge Resonance for Lamb Waves in a Semi-Infinite Plate
,” J. Acoust. Soc. Am.
0001-4966, 120
, pp. 647
-656
.18.
Danicki
, E. J.
, 1999, “Resonant Phenomena in Bulk-Wave Scattering by In-Plane Periodic Cracks
,” J. Acoust. Soc. Am.
0001-4966, 105
, pp. 84
-92
.19.
Kundu
, T.
, Banerjee
, S.
, and Jata
, K. V.
, 2006, “An Experimental Investigation of Guided Vawe Propagation in Corrugated Plates Showing Stop Bands and Pass Bands
,” J. Acoust. Soc. Am.
0001-4966, 120
, pp. 1217
–1226
.20.
Quarry
, M. J.
, and Rose
, J. L.
, 1997, “Multimode Guided Wave Inspection of Piping Using Comb Transducers
,” Mater. Eval.
0025-5327, 45
, pp. 504
–508
.21.
Danicki
, E. J.
, 2002, “Scattering by Periodic Cracks and the Theory of Comb Transducers
,” Wave Motion
0165-2125, 35
, pp. 355
–370
.22.
Danicki
, E. J.
, 2007, “Spectral Theory of Interdigital Transducers
,” http://www.ippt.gov.pl/~edanicki/danickibook.pdfhttp://www.ippt.gov.pl/~edanicki/danickibook.pdf.Copyright © 2008
by American Society of Mechanical Engineers
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