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

Stress analysis of helicopter main rotor torsion bar

The results of stress analysis for the main rotor torsion bar of the ANSAT helicopter based on the finite element method are presented. The analysis was performed for the base types of loading in the linear statement. The analysis results agree well with the experimental data. © Allerton Press, Inc., 2009

The Structure of Martian Magnetosphere at the Dayside Terminator Region as Observed on MAVEN Spacecraft

We analyzed 44 passes of the MAVEN spacecraft through the magnetosphere, arranged by the angle between electric field vector and the projection of spacecraft position radius vector in the YZ plane in MSE coordinate system (${\theta}$ E ). All passes were divided into 3 angular sectors near 0{\deg}, 90{\deg} and 180{\deg} ${\theta}$ E angles in order to estimate the role of IMF direction in plasma and magnetic properties of dayside Martian magnetosphere. The time interval chosen was from January 17 through February 4, 2016 when MAVEN was crossing the dayside magnetosphere at SZA ~ 70{\deg}. Magnetosphere as the region with prevailing energetic planetary ions is always found between the magnetosheath and the ionosphere. 3 angular sectors of dayside interaction region in MSE coordinate system with different orientation of the solar wind electric field vector E = -1/c V x B showed that for each sector one can find specific profiles of the magnetosheath, the magnetic barrier and the magnetosphere. Plume ions originate in the northern MSE sector where motion electric field is directed from the planet. This electric field ejects magnetospheric ions leading to dilution of magnetospheric heavy ions population, and this effect is seen in some magnetospheric profiles. Magnetic barrier forms in front of the magnetosphere, and relative magnetic field magnitudes in these two domains vary. The average height of the boundary with ionosphere is ~530 km and the average height of the magnetopause is ~730 km. We discuss the implications of the observed magnetosphere structure to the planetary ions loss mechanism.Comment: 24 pages, 13 figure