Propagation of localised flexural vibrations along plate edges described by a power law
journal contributionposted on 13.04.2012 by Victor V. Krylov, A.L. Shuvalov
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Localised flexural vibrations propagating along sharp edges of elastic wedge-like structures are characterised by low propagation velocities (generally much lower than that of Rayleigh waves), and their elastic energy is concentrated in the area of about one wavelength from the edge. Such localised vibrations, also known as wedge acoustic waves, have been investigated in a number of papers (see, e.g. [1-14]) with regard to their possible applications to acoustic non-destructive testing of special engrneering constructrons and for better understanding vibrations of propellers, turbine blades and some civil engineering constructrons. They may be important also for the explanation of many as yet poorly understood phenomena in related fields of structural dynamics, physics, environmental acoustics and may result in many useful practical applications. ln particular, it is expected that ihese waves may play an important role in the dynamics of wedge-shaped offshore structures (such as piers, dams, wave-breakers, etc.), and in the formation of vibration patterns and resonance frequencies of propellers, turbine blades, disks, cutting tools and airfoils. They may be responsible for specific mechanisms of helicopter noise, wind turbine noise and ship propeller noise. Promising mechanical engineering applications of wedge elastic waves may include measurements of cuttrng edge sharpness, environmentally friendly water pumps and domestic ventilators utilising wave-generated flows. Another possible application earlier suggested by one of the present authors  may be the use of wedge waves for in-water propulsion of ships and submarines, the main principle of which being similar to that used in nature by fish of the ray family. lnitially these localised flexural waves have been investigated for wedges in contact with vacuum t1- 61. Later on, the existence of localised flexural elastic waves on the edges of wedge-like immersed structures has been predicted . This was followed by the experimental investigations of wedge waves in immersed structures which considered samples made of different materials and having different values of wedge apex angle [8,9]. Recently, finite element calculations have been carried out  for severaltypes of elastic wedges with the of apex angle varying in the range from 20 to 90 degrees. Also, the analytical theory based on geometrical-acoustics approach has been developed for the same range of wedge apex angle . ln the paper  deaiing with finite element calculations of the velocities and amplitudes of wedge waves, among other results, calculations have been carried out of the velocities of waves propagating along the edge of a cylindrical wedge-like structure bounded by a circular cylinder and a conical cavity. ln the paper tist different cylindrical and conical wedge-like structures have been investigated using geometrical acoustics approach.
- Aeronautical, Automotive, Chemical and Materials Engineering
- Aeronautical and Automotive Engineering