Planar harmonic Green function for periodic elastic strips

• Autorzy: Danicki, E.
• Języki publikacji: EN

Abstrakty

EN

A system of periodic elastic strips (each one considered as a fragment of a plate) is characterized by a matrix relation between the Bloch series of displacements and stress at the bottom side of the system, which will remain in contact with the substrate supporting a propagating Rayleigh wave. The theory exploits the mechanical field representation in a spectral domain. It was found advantageous in formulation of the scattering problem for an elastic plate with stress-free cross-section, allowing us to apply ordinary boundary conditions instead of the variational ones. The result satisfies the energy conservation law with great accuracy, provided that sufficient number of complex modes are included in the solution. An algorithm is presented for modes evaluation; asymptotic properties of modes can be applied as well for higher modes. Perfect agreement of the proposed model with the experimentally verified perturbation model of thin strips is demonstrated.

Słowa kluczowe

PL

fala akustyczna powierzchniowa; funkcja Greena

EN

surface acoustic wave; Green's functions; planar harmonic Green's function; perturbation model; periodic system; periodic elastic strips

• Czasopismo: Journal of Technical Physics
• Rocznik: 2007
• Tom: Vol. 48, no 2
• Strony: 95-109
• Opis fizyczny: Bibliogr. 20 poz., rys., wykr.

Twórcy

autor

Danicki, E.

• Institute of Fundamental Technological Research, Polish Academy of Sciences, Świętokrzyska 21, 00-049 Warszawa, Poland,

Bibliografia

• 1. E. DANICKI, Perturbation theory of surface acoustic wave reflection from a periodic structure with arbitrary angle of incidence, Arch. Mech., 36 623-638 (1984).
• 2. E.J. DANICKI, F.S. HICKERNELL, I. MATEESCU, Closed-form solution for SPUDTs, IEEE Freq. Contr. Symp. Proc., ISBN 0-7803-9052-05, 152-155 (2005).
• 3. P.J. TORVIK, Reflection of wave trains in semi-infinite plates, J. Acoust. Soc. Am., 41, 346-353 (1967).
• 4. P.J. TORVIK, The elastic strip with prescribed end displacements, J. Appl. Mech., 38, 929-936 (1971).
• 5. R.D. GREGORY, I. GLADWELL, The reflection of a symmetric Rayleigh-Lamb wave at the fixed or free edge of a plate, J. Elasticity, 13, 185-206 (1983).
• 6. W. KARUNASENA, K.M. LIEW, S. KITIPORNCHAI, Reflection of plate waves at fixed edge of a composite plate, J. Acoust. Soc. Am., 98, 644-651 (1995).
• 7. H. BESSERER, P.S. MALISHEVSKY, Mode series expansions at vertical boundaries in elastic waveguides, Wave Motion, 39, 41-59 (2004).
• 8. R.D. GREGORY, I. GLADWELL, The cantilever beam under tension, bending or flexure at infinity, J. Elasticity, 12, 317-343 (1982).
• 9. J.P. DEMPSEY, G.B. SINCLAIR, On the stress singularities in the plane elasticity of the composite wedge, J. Elasticity, 9, 373-391 (1979).
• 10. M.I. WILLIAMS, Stress singularities resulting from various boundary conditions in angular corners of plates in extension, J. Appl. Mech., 19, 526-528 (1952).
• 11. D.B. BOGY, Two edge-bonded elastic wedges of different materials and wedge angles under surface traction, J. Appl. Mech., 38, 377-386 (1971).
• 12. R.D. GREGORY, Green's function, bi-linear forms, and completness of the eigenfunctions for the elastostatic strip and wedge, J. Elasticity 9, 283-309 (1979).
• 13. E.J. DANICKI, Surface acoustic wave diffraction in spectral theory of interdigital transducers, J. Acoust. Soc. Am., 114, 813-812 (2003).
• 14. E.J. DANICKI, Resonant phenomena in bulk-wave scattering by in-plane periodic cracks, J. Acoust. Soc. Am., 105, 84-92 (1999).
• 15. H.F. TIERSTEN, Linear Piezoelectric plate Vibration, Plenum Press, 1969.
• 16. http://www.mathworks.com
• 17. E.J. DANICKI, An approximation to the planar harmonic Green's function at branch points in wave-number domain, J. Acoust. Soc. Am., 104, 651-663 (1998).
• 18. E.J. DANICKI, Scattering by periodic cracks and the theory of comb transducers, Wave Motion, 35, 355-370 (2002).
• 19. E. DANICKI, Modeling of an elastic slab with periodic breaks, Arch. Mech., 53, 243-252 (2001).
• 20. H.F. TIERSTEN, Elastic surface waves guided by thin films, J. Appl. Phys., 40, 770-789 (1969).