Three-dimensional edge waves in plates

This paper describes the propagation of three-dimensional symmetric waves localized near the traction-free edge of a semi-infinite elastic plate with either traction-free or fixed faces. For both types of boundary conditions, we present a variational proof of the existence of the low-order edge waves. In addition, for a plate with traction-free faces and zero Poisson ratio, the fundamental edge wave is described by a simple explicit formula, and the first-order edge wave is proved to exist. Qualitative variational predictions are compared with numerical results, which are obtained using expansions in three-dimensional Rayleigh–Lamb and shear modes. It is also demonstrated numerically that for any non-zero Poisson ratio in a plate with traction-free faces, the eigenfrequencies related to the first-order wave are complex valued

Eigenvalue of a semi-infinite elastic strip

A semi-infinite elastic strip, subjected to traction free boundary conditions, is studied in the context of in-plane stationary vibrations. By using normal (Rayleigh–Lamb) mode expansion the problem of existence of the strip eigenmode is reformulated in terms of the linear dependence within infinite system of normal modes. The concept of Gram's determinant is used to introduce a generalized criterion of linear dependence, which is valid for infinite systems of modes and complex frequencies. Using this criterion, it is demonstrated numerically that in addition to the edge resonance for the Poisson ratio ν=0, there exists another value of ν≈0.22475 associated with an undamped resonance. This resonance is best explained physically by the orthogonality between the edge mode and the first Lamé mode. A semi-analytical proof for the existence of the edge resonance is then presented for both described cases with the help of the augmented scattering matrix formalism

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

Elastodynamics of a coated half-space under a sliding contact

The paper deals with elastic wave propagating in a layer on a half-space induced by a vertical force. The focus is on the effect of a sliding contact along the interface and its comparative study with a perfect one. The effective boundary conditions substituting the presence of the layer are derived. The leading order term in these conditions corresponds to vertical inertia of the layer, whereas next order correction involves the effect of plate waves in the coating. Analysis of the associated dispersion relation confirms the existence of a Rayleigh-type wave, along with extensional and shear plate waves. An asymptotic hyperbolic-elliptic formulation for surface wave field is also presented. This includes a hyperbolic equation singularly perturbed by a pseudo-differential operator playing a role of a boundary condition for the elliptic equation governing decay over the interior. The sign of the coefficient at the pseudo-differential operator is demonstrated to be always negative, corresponding to a local maximum of the phase speed at zero wave number, and consequently to a distinct receding type of the Rayleigh-type wave quasi-front induced by an impulse load

High-frequency homogenization for periodic media

This article is available open access through the publisher’s website at the link below. Copyright @ 2010 The Royal Society.An asymptotic procedure based upon a two-scale approach is developed for wave propagation in a doubly periodic inhomogeneous medium with a characteristic length scale of microstructure far less than that of the macrostructure. In periodic media, there are frequencies for which standing waves, periodic with the period or double period of the cell, on the microscale emerge. These frequencies do not belong to the low-frequency range of validity covered by the classical homogenization theory, which motivates our use of the term ‘high-frequency homogenization’ when perturbing about these standing waves. The resulting long-wave equations are deduced only explicitly dependent upon the macroscale, with the microscale represented by integral quantities. These equations accurately reproduce the behaviour of the Bloch mode spectrum near the edges of the Brillouin zone, hence yielding an explicit way for homogenizing periodic media in the vicinity of ‘cell resonances’. The similarity of such model equations to high-frequency long wavelength asymptotics, for homogeneous acoustic and elastic waveguides, valid in the vicinities of thickness resonances is emphasized. Several illustrative examples are considered and show the efficacy of the developed techniques.NSERC (Canada) and the EPSRC

Photo- and electroluminescence of new organic semiconductors

The results of investigation of the luminescence under photo- and electroexcitation for four new compounds are presented. The spectral properties and photoluminescence are studied in ethanol, chloroform solutions and in films formed by thermovacuum deposition (TVD). The phosphorescence of compounds is investigated in ethanol at 77K temperature. The phosphorescence times of molecules are given. The electroluminescence is obtained in multilayered structure ITO/PEDOT/NPD/L /Ca/Al. It is shown, that spectral region of the photoluminescence of TVD films and electroluminescence coincide. Relations of electroluminescence efficiency with molecule structure, photoluminescence quantum yield and possibility of thermally activated delayed fluorescence are discussed

Воздействие наносекундных ультрафиолетовых лазерных импульсов на поверхность монокристаллов германия

For the first time, a detailed comprehensive study of the "dry" etching of dislocation and dislocation-free germanium samples on the {111}, {110} and {100} planes has been carried out. Etching was carried out by exposure to pulses of nanosecond UV laser radiation of subthreshold intensity (wavelength 355 nm, duration ~ 10 ns, energy density ~ 0.5–1.3 J/cm2, pulse repetition rate 100 Hz, divergence 1–2 mrad). Before and after laser heat treatment of the surface, the samples were examined using a Zygo optical profilometer and a scanning electron microscope. Features of the nature of damage to surfaces corresponding to different crystallographic planes of single crystals of industrial dislocation germanium are revealed. They are compared with data on subthreshold damages of typical dislocation-free crystals.It is shown that in dislocation samples of germanium on the {111} plane, it is possible to create a regime of exposure to radiation, leading to the formation of etch pits that are outwardly identical to dislocation pits detected during selective chemical etching. Their concentration corresponds in order of magnitude to the density of dislocations.On the {100} plane of dislocation samples, etching results were also found, which clearly have a crystallographic nature. At an energy density of the acting radiation ≥ 0.4 J/cm2, on the surfaces of dislocation ({100} plane) and dislocation-free germanium ({111}, {100}, {110} planes), only individual spots ~ 50 μm in size were registered, as well as individual microcraters ~ 0.1–1 μm in size, which do not have crystallographic features. The possibility of environmentally friendly detection of dislocations in germanium without the use of chemical reagents is shown.Впервые проведено подробное комплексное исследование «сухого» травления дислокационных и бездислокационных образцов германия на плоскостях {111}, {110}, {100}. Травление осуществляли путем воздействия импульсов наносекундного ультрафиолетового (УФ) лазерного излучения допороговой интенсивности (длина волны — 355 нм, длительность ~ 10 нс, плотность энергии ~ 0,5—1,3 Дж/см2, частота следования импульсов — 100 Гц, расходимость — 1—2 мрад). До и после лазерной термообработки поверхности образцы исследовали с помощью оптического профилометра Zygo и растрового электронного микроскопа. Выявлены особенности характера повреждения поверхностей, соответствующих различным кристаллографическим плоскостям монокристаллов промышленного дислокационного германия. Они сопоставлены с данными о допороговых повреждениях типовых бездислокационных кристаллов.Показано, что в дислокационных образцах германия на плоскости {111} возможно создание режима воздействия излучения, приводящего к формированию ямок травления, внешне идентичных дислокационным ямкам, выявляемым при селективном химическом травлении. Их концентрация по порядку величины соответствует плотности дислокаций.На плоскости {100} дислокационных образцов также обнаружены результаты травления, явно имеющие кристаллографическую природу. При плотности энергии воздействующего излучения ≥ 0,4 Дж/см2 на поверхностях дислокационного (плоскость {100}), и бездислокационного германия (плоскости {111}, {100}, {110}), были зарегистрированы лишь отдельные пятна размером ~ 50 мкм, а также отдельные микрократеры размером ~ 0,1—1 мкм, не имеющие кристаллографических признаков. Показана возможность экологичного выявления дислокаций в германии без использования химических реагентов