- Physical Review Journals
All JournalsPhysics Magazine

Physical Review E

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Trapped Scholte modes supported by soft elastic cylindrical rods underwater

B. M. Staples, T. A. Starkey, A. P. Hibbins, and J. R. Sambles

PDF

Phys. Rev. E 113, 025505 – Published 13 February, 2026

DOI: https://doi.org/10.1103/sshw-sgcc

Abstract

This paper documents trapped Scholte modes; nonradiative surface acoustic modes that exist on fluid-loaded elastic cylindrical rods. Unlike previously reported surfacelike waves on cylindrical rods, the Scholte modes identified here are localized to the interface between the rod and the surrounding fluid. The study investigates plastic rods submerged in water, which allows exploration of the domain where the Scholte velocity is significantly slower than the speed of sound in water. The supported Scholte modes are shown to become increasingly localized to the solid-fluid interface at high frequencies, as their phase velocities tend toward that of the Scholte wave on a planar interface. This was modeled numerically using the finite element method and experimentally verified using cast acrylic rods underwater.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (42)

  1. H. Überall, Surface waves in acoustics, in Physical Acoustics: Principles and Methods, edited by W. P. Mason and R. N. Thurston (Academic Press, New York, London, 1973), Vol. 10.
  2. L. M. Brekhovskih, Waves in Layered Media (Academic Press, New York, London, 1960).
  3. M. J. S. Lowe, Disperse user manual, Disperse, 2nd ed., Non-destructive Testing Laboratory (Imperial College, London, 2013).
  4. R. A. Phinney, Propagation of leaking interface waves, Bull. Seismol. Soc. Am. 51, 527 (1961).
  5. C. Glorieux, and K. Van de Rostyne, On the character of acoustic waves at the interface between hard and soft solids and liquids, J. Acoust. Soc. Am. 110, 1299 (2001).
  6. V. G. Mozhaev and M. Weihnacht, Subsonic leaky Rayleigh waves at liquid-solid interfaces, Ultrasonics 40, 927 (2002).
  7. J. Zhu, J. S. Popovics, and F. Schubert, Leaky Rayleigh and Scholte waves at the fluid–solid interface subjected to transient point loading, J. Acoust. Soc. Am. 116, 2101 (2004).
  8. J. G. Scholte, The range and existence of Rayleigh and Stoneley waves, Geophys. Suppl. Mon. Not. R. Astron. Soc. 5, 120 (1947).
  9. J. H. Ansell, The roots of the Stoneley wave equation for solid-liquid interfaces, Pure Appl. Geophys. 94, 172 (1972).
  10. F. Padilla, M. de Billy, and G. Quentin, Theoretical and experimental studies of surface waves on solid-fluid interfaces when the value of the fluid sound velocity is located between the shear and the longitudinal ones in the solid, J. Acoust. Soc. Am. 106, 666 (1999).
  11. P. C. Vinh, Scholte-wave velocity formulae, Wave Motion 50, 180 (2013).
  12. W. L. Pilant, Complex roots of the Stoneley-wave equation, Bull. Seismol. Soc. Am. 62, 285 (1972).
  13. A. S. Ginzbarg and E. Strick, Stoneley-wave velocities for a fluid-solid interface, Bull. Seismol. Soc. Am. 48, 51 (1958).
  14. F. B. Cegla, P. Cawley, and M. J. S. Lowe, Material property measurement using the quasi-Scholte mode — A waveguide sensor, J. Acoust. Soc. Am. 117, 1098 (2005).
  15. H. Überall, Repulsion of phase-velocity dispersion curves and the nature of plate vibrations, J. Acoust. Soc. Am. 96, 908 (1994).
  16. F. B. Cegla, Ultrasonic waveguide sensors for fluid characterisation and remote sensing, Ph.D. thesis, Imerial College London, 2006.
  17. O. Önen, Dispersion and sensitivity analysis of quasi-Scholte wave liquid sensing by analytical methods, J. Sens. 2017, 1 (2017).
  18. S. N. Guzhev, Study of phase velocity and energy distribution of Stoneley waves at a solid-liquid interface, J. Acoust. Soc. Am. 95, 661 (1994).
  19. S. Nasr, J. Duclos, and M. Leduc, Scholte wave characterisation and it's decay for various materials, J. Acoust. Soc. Am. 87, 507 (1990).
  20. B. M. Staples, T. J. Graham, A. P. Hibbins, and J. R. Sambles, Coupled Scholte modes supported by soft elastic plates in water, Phys. Rev. E 103, 063002 (2021).
  21. G. Frisk, Creeping waves and lateral waves in acoustic scattering by large elastic cylinders (1975), https://apps.dtic.mil/sti/citations/ADA014412.
  22. G. Frisk, J. Dickey, and H. Überall, Surface wave modes on elastic cylinders, J. Acoust. Soc. Am. 58, 996 (1975).
  23. H. Überall, L. Dragonette, and L. Flax, Relation between creeping waves and normal modes of vibration of a curved body, J. Acoust. Soc. Am. 61, 711 (1977).
  24. R. Doolittle, H. Überall, and P. Uginčius, Sound scattering by elastic cylinders, J. Acoust. Soc. Am. 43, 1 (1968).
  25. G. Frisk and H. Überall, Creeping waves and lateral waves in acoustic scattering by large elastic cylinders, J. Acoust. Soc. Am. 59, 46 (1976).
  26. R. Doolittle, J. McNicholas, H. Überall, and P. Uginčius, Circumferential sound pulses on elastic cylinders, J. Acoust. Soc. Am. 42, 522 (1967).
  27. O. Grace and R. Goodman, Circumferential waves on solid cylinders, J. Acoust. Soc. Am. 39, 173 (1966).
  28. R. Goodman, R. Bunney, and S. Marshall, Observation of circumferential waves on solid aluminum, J. Acoust. Soc. Am. 42, 523 (1967).
  29. J. Dickey, G. Frisk, and H. Überall, Whispering gallery wave modes on elastic cylinders, J. Acoust. Soc. Am. 59, 1339 (1976).
  30. A. Stoyanov, H. Überall, F. Luppé, and G. Quentin, Observation of surface waves on a solid cylinder in a fluid, J. Acoust. Soc. Am. 85, 137 (1989).
  31. R. Thurston, Elastic waves at the surface of separation of two solids, Proc. R. Soc. A 106, 416 (1924).
  32. S. J. Hanna and R. O. Claus, Interface wave mode propagation in clad rod acoustic waveguides, J. Acoust. Soc. Am. 75, S78 (1984).
  33. R. Thurston, Elastic waves in rods and clad rods, J. Acoust. Soc. Am. 64, 1 (1978).
  34. A. Huber, The dispersion calculator - A free software for calculating dispersion curves of guided waves, eGNDT 29, 6 (2024).
  35. B. M. Staples, Control of flow-induced near-field noise through the use of metasurfaces, Ph.D. thesis, University of Exeter, 2026 (unpublished).
  36. V. Aubert, A simple acoustofluidic chip for microscale manipulation using evanescent Scholte waves, Lab Chip 16, 2532 (2016).
  37. E. García Neefjes, D. Nigro, R. C. Assier, and W. J. Parnell, Stress relaxation and thermo-visco-elastic effects in fluid-filled slits and fluid-loaded plates, J. Fluids Struct. 131, 104219 (2024).
  38. E. A. Campo, Selection of Polymeric Materials (William Andrew Publishing, Norwich, NY, 2008).
  39. J. M. G. Cowie, Polymers: Chemistry and Physics of Modern Materials (Intertext, Cheltenham, UK, 1973).
  40. M. Sinha and D. J. Buckley, Physical Properties of Polymers Handbook (Springer, New York, 2007).
  41. https://ore.exeter.ac.uk/.
  42. B. M. Staples, A. P. Hibbins, J. R. Sambles, T. A. Starkey, Raw data for “Trapped Scholte modes supported by soft elastic cylindrical rods underwater”. University of Exeter, Dataset, https://doi.org/10.24378/exe.30127165 (2026).

Outline

Information

Phys. Rev. E 113, 025505– Published 13 February, 2026
  • Received 22 September 2025
  • Accepted 14 January 2026
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation