Edge waves and resonance on elastic structures: An overview

Over 50 years have elapsed since the first experimental observations of dynamic edge phenomena on elastic structures, yet the topic remains a diverse and vibrant source of research activity. This article provides a focused history and overview of such phenomena with a particular emphasis on structures such as strips, rods, plates and shells. Within this context, some of the recent research highlights are discussed and the contents of this special issue of Mathematics and Mechanics of Solids on dynamical edge phenomena are introduced.

[1]  L. Librescu,et al.  Diffraction of harmonic flexural waves in a cracked elastic plate carrying electrical current , 2005, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[2]  Krylov,et al.  Flexural edge waves and comments on "A new bending wave solution for the classical plate equation" , 2000, The Journal of the Acoustical Society of America.

[3]  S. Timoshenko,et al.  THEORY OF PLATES AND SHELLS , 1959 .

[4]  Yibin Fu.  Existence and Uniqueness of Edge Waves in a Generally Anisotropic Elastic Plate , 2003 .

[5]  R. Porter.  Trapped waves in thin elastic plates , 2007 .

[6]  A. Norris,et al.  On the Existence of ° Exural Edge Waves on Submerged Elastic Plates , 2022 .

[7]  A. Krushynska.  Flexural edge waves in semi-infinite elastic plates , 2011 .

[8]  I. Gladwell,et al.  AXISYMMETRIC WAVES IN A SEMI-INFINITE ELASTIC ROD , 1989 .

[9]  V. Zernov,et al.  Three-dimensional edge waves in plates , 2008, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[10]  R. N. Thurston,et al.  Flexural Acoustic Waves Along the Edge of a Plate , 1974, IEEE Transactions on Sonics and Ultrasonics.

[11]  L. Rayleigh.  On Waves Propagated along the Plane Surface of an Elastic Solid , 1885 .

[12]  P. Torvik.  Reflection of Wave Trains in Semi‐Infinite Plates , 1967 .

[13]  J. Kaplunov,et al.  On three-dimensional edge waves in semi-infinite isotropic plates subject to mixed face boundary conditions , 2005 .

[14]  D. D. Zakharov.  Konenkov’s waves in anisotropic layered plates , 2002 .

[15]  E. Terentjev,et al.  Low–frequency acoustic waves in nematic elastomers , 2003, Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences.

[16]  P. Lu,et al.  Further studies on edge waves in anisotropic elastic plates , 2007 .

[17]  G. Piliposian,et al.  Localized bending waves in a transversely isotropic plate , 2010 .

[18]  Michael J. S. Lowe,et al.  Elastic waves guided by a welded joint in a plate , 2009, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[19]  J. Kaplunov,et al.  Eigenvalue of a semi-infinite elastic strip , 2006, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[20]  Yibin Fu,et al.  Edge waves in asymmetrically laminated plates , 2005 .

[21]  K. Cherednichenko.  An asymptotic expansion of the boundary-layer type for flexural waves along the curved edge of a Kirchhoff-Love elastic plate , 2007 .

[22]  J. Zemanek,et al.  An Experimental and Theoretical Investigation of Elastic Wave Propagation in a Cylinder , 1962 .

[23]  P. Cawley,et al.  Rapid, Long Range Inspection of Chemical Plant Pipework Using Guided Waves , 2004 .

[24]  K. Graff.  Wave Motion in Elastic Solids , 1975 .

[25]  R. D. Mindlin,et al.  Extensional Vibrations and Waves in a Circular Disk and a Semi-Infinite Plate , 1960 .

[26]  G. Maze,et al.  Edge resonance in semi-infinite thick pipe: numerical predictions and measurements. , 2008, The Journal of the Acoustical Society of America.

[27]  Richard V. Craster,et al.  Trapped modes in 3D topographically varying plates , 2008 .

[28]  E. Shaw.  On the Resonant Vibrations of Thick Barium Titanate Disks , 1956 .

[29]  V. Pagneux.  Revisiting the edge resonance for Lamb waves in a semi-infinite plate , 2006 .

[30]  A. Norris.  Flexural Edge Waves , 1994 .

[31]  W. Becker,et al.  Rayleigh type bending waves in anisotropic media , 2003 .

[32]  P. Lagasse,et al.  Acoustic flexural mode on a ridge of semi-infinite height , 1976 .

[33]  R. D. Mindlin,et al.  Extensional Waves Along the Edge of an Elastic Plate , 1963 .

[34]  B. Sinha.  Some remarks on propagation characteristics of ridge guides for acoustic surface waves at low frequencies , 1974 .

[35]  I. Thompson,et al.  On the existence of flexural edge waves on thin orthotropic plates. , 2002, The Journal of the Acoustical Society of America.

[36]  Akademii︠a︡ nauk Sssr,et al.  Soviet physics. Acoustics , 1992 .

[37]  R. D. Gregory,et al.  The reflection of a symmetric Rayleigh-Lamb wave at the fixed or free edge of a plate , 1983 .

[38]  I. Thompson,et al.  Diffraction of flexural waves by cracks in orthotropic thin elastic plates. Part II. Far field analysis , 2007, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[39]  W. M. Ewing,et al.  TWO‐DIMENSIONAL MODEL SEISMOLOGY , 1954 .

[40]  J. P. Sargent,et al.  Corrosion detection in welds and heat-affected zones using ultrasonic Lamb waves , 2006 .

[41]  J. Kaplunov,et al.  Dynamics of Thin Walled Elastic Bodies , 1997 .

[42]  B. Auld,et al.  A Variational Analysis of Edge Resonance in a Semi-Infinite Plate , 1977, IEEE Transactions on Sonics and Ultrasonics.

[43]  T. Weidl,et al.  Edge resonance in an elastic semi-strip , 1998 .

[44]  I. David Abrahams,et al.  A brief historical perspective of the Wiener–Hopf technique , 2007 .

[45]  D. Zakharov.  Analysis of the acoustical edge flexural mode in a plate using refined asymptotics , 2004 .

[46]  Edge resonance in an elastic semi-infinite cylinder , 2000 .

[47]  Free localized vibrations of a semi-infinite cylindrical shell , 2000, The Journal of the Acoustical Society of America.

[48]  Free interfacial vibrations in cylindrical shells. , 2002, The Journal of the Acoustical Society of America.

[49]  I. Thompson,et al.  Diffraction of flexural waves by cracks in orthotropic thin elastic plates. I Formal solution , 2005, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[50]  Numerical predictions and experiments on the free-plate edge mode. , 2003, Ultrasonics.

[51]  J. Oliver.  Elastic Wave Dispersion in a Cylindrical Rod by a Wide‐Band Short‐Duration Pulse Technique , 1957 .