Propagation of localised flexural vibrations along plate edges described by a power law

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 [10] 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 [7]. 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 [10] 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 [11]. ln the paper [12] 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

Localised vibration modes in free anisotropic wedges

Propagation of flexural localized vibration modes along edges of anisotropic wedges is considered in the framework of the geometrical-acoustics approach. Its application allows for straightforward evaluation of the wedge-mode velocities in the general case of arbitrary elastic anisotropy. The velocities depend on the wedge apex angle and on the mode number in the same way as in the isotropic case, but there appears to be additional dependence on elastic coefficients. The velocities in tetragonal wedges ~with the midplane orthogonal to the four-fold axis! and in ‘‘weakly’’ monoclinic wedges are explicitly calculated and analyzed. Bounds of the wedge-wave velocity variation in tetragonal materials are established

Explicit asymptotic modelling of transient Love waves propagated along a thin coating

The official published version can be obtained from the link below.An explicit asymptotic model for transient Love waves is derived from the exact equations of anti-plane elasticity. The perturbation procedure relies upon the slow decay of low-frequency Love waves to approximate the displacement field in the substrate by a power series in the depth coordinate. When appropriate decay conditions are imposed on the series, one obtains a model equation governing the displacement at the interface between the coating and the substrate. Unusually, the model equation contains a term with a pseudo-differential operator. This result is confirmed and interpreted by analysing the exact solution obtained by integral transforms. The performance of the derived model is illustrated by numerical examples.This work is sponsored by the grant from Higher Education of Pakistan and by the Brunel University’s “BRIEF” research award

Surface acoustic waves in one-dimensional piezoelectric phononic crystals with a symmetric unit cell

International audienceThe paper studies the existence of surface acoustic waves in half-infinite one-dimensional piezoelectric phononic crystals consisting of perfectly bonded layers, which are arranged so that the unit cell is symmetric, i.e., is invariant with respect to inversion about its midplane. An example is a bilayered structure with exterior layer being half thinner than the interior layers of the same material. The layers may be generally anisotropic. The maximum possible number of surface acoustoelectric waves referred to a fixed wave number and a given full stop band is established for different types of electric boundary conditions at the mechanically free or clamped surface. In particular, it is proved that the phononic crystal-vacuum interface can support two surface waves in any full stop band. The same statement holds true in the case of a metallized surface of the crystal. This number is greater than that in a purely elastic case. In the presence of crystallographic symmetry, which decouples the sagittally and horizontally polarized surface waves, their separate admissible numbers are obtained. It is shown that the propagation along the normal to the surface is a special case, where the maximum number of surface waves is less than that along oblique directions

Interfacial acoustic waves in one-dimensional anisotropic phononic bicrystals with a symmetric unit cell

International audienceThe paper is concerned with the interfacial acoustic waves localized at the internal boundary of two different perfectly bonded semi-infinite onedimensional phononic crystals represented by periodically layered or functionally graded elastic structures. The unit cell is assumed symmetric relative to its midplane, whereas the constituent materials may be of arbitrary anisotropy. The issue of the maximum possible number of interfacial waves per full stop band of a phononic bicrystal is investigated. It is proved that, given a fixed tangential wavenumber, the lowest stop band admits at most one interfacial wave, while an upper stop band admits up to three interfacial waves. The results obtained for the case of generally anisotropic bicrystals are specialized for the case of a symmetric sagittal plane

Surface acoustic waves on one-dimensional phononic crystals of general anisotropy: Existence considerations

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Non-leaky surface acoustic waves in the passbands of one-dimensional phononic crystals

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Low-frequency dispersion of fundamental waves in anisotropic piezoelectric plates

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Approximation of the flexural velocity branch in plates

AbstractThe fitting of the flexural velocity branch by means of the Padé approximation is examined. Its use for free isotropic plates is elaborated and compared to other approaches. The flexural-velocity expansion into power series, which underlies the Padé implementation, is detailed. The generalization for fluid-loaded plates and inhomogeneous plates is outlined, and the impact of anisotropy is discussed in some detail