Evgeny Glushkov

3-D elastic stress singularity at polyhedral corner points

Abstract The three-dimensional stress singularity at the top of an arbitrary polyhedral corner is considered. Based on the boundary integral equations, the problem is reduced by the Mellin transform to a system of certain one-dimensional integral equations. The orders of stress singularity are spectral points of the integral operators while angular distribution and intensity factors are found as residues at those points. Numerical results are obtained by means of the Galerkin discretization scheme using expansions in terms of orthogonal polynomials with the proper weights. Some of the results illustrating the orders dependence on the elastic properties and corner geometry for a wedge-shaped punch and a crack, for an elastic trihedron and for a surface-breaking crack are given.

Forced wave propagation and energy distribution in anisotropic laminate composites.

Elastodynamic response of anisotropic laminate composite structures subjected to a force loading is evaluated based on the integral representations in terms of Greens matrices. Explicit and asymptotic expressions for guided waves generated by a given source are then obtained from those integrals by means of series expansions and the residue technique. Unlike to conventional modal expansions, such representations keep information about the source, giving an opportunity for a quantitative near- and far-field analysis of generated waves. An effective computer implementation is achieved by the use of fast and stable algorithms for the Green matrix, pole, and residue calculations. The potential of the model is demonstrated by examples of anisotropy manifestation in the directivity of radiated waves. The effect of main energy outflow in the direction of either upper- or inner-ply orientation depending on the source size and frequency is discussed.

Integral equation based modeling of the interaction between piezoelectric patch actuators and an elastic substrate

An integral equation based model for a system of piezoelectric flexible patch actuators bonded to an elastic substrate (layer or half-space) is developed. The rigorous solution to the patch–substrate dynamic contact problem extends the range of the models utility far beyond the bounds of conventional models that rely on simplified plate, beam or shell equations for the waveguide part. The proposed approach provides the possibility to reveal the effects of resonance energy radiation associated with higher modes that would be inaccessible using models accounting for the fundamental modes only. Algorithms that correctly account for the mutual wave interaction among the actuators via the host medium, for selective mode excitation in a layer as well as for body waves directed to required zones in a half-space, have also been derived and implemented in computer code.

Blocking property of energy vortices in elastic waveguides

Energy vortices in time-averaged energy flows of time-harmonic fields are considered. The purpose of the paper is to verify the supposition that the energy flux along an elastic waveguide with an obstacle is blocked completely at the stop frequencies by the vortices. It is hoped that this work will draw attention to the analogy between energy and fluid flows which is potentially fruitful for understanding various wave phenomena. The normal-mode diffraction by a surface punch on an elastic layer is taken as an example. For tracing energy streamlines in the near field up to the obstacle, a special efficient semianalytical approach has been developed. To illustrate the stated supposition, plots of transmission coefficients versus frequency and figures of the near-field streamline structures are given.

Energy vortices and backward fluxes in elastic waveguides

Abstract The behavior of energy fluxes in a multilayer halfspace is investigated under loading by harmonic stresses. The multilayering produces new phenomena compared to a homogeneous halfspace. In such system energy vortices and backward energy propagation are possible, which satisfy mathematical rigor and physical conditions of energy radiation. Various examples of these phenomena are given and the conditions under which they arise are formulated.

Natural resonance frequencies, wave blocking, and energy localization in an elastic half-space and waveguide with a crack

Sharp stopping of time-harmonic wave transmission in elastic structures with defects is considered as a manifestation of the well-known trapped mode effect. It is associated with natural resonance poles lying close to the real axis in the complex frequency plane. Nonresonant wave blocking may also occur due to antiphase combination of the incident and scattered waves. The present paper is aimed to give an insight into such phenomena using an analytically based computer model which strictly takes into account all wave interactions in a cracked structure. Numerical examples are restricted to the case of a line horizontal crack in a half-plane or in a layer (2D in-plane motion), that is, nevertheless, quite enough to demonstrate two kinds of the Rayleigh wave stopping mechanisms (resonant and nonresonant) as well as a possibility of pure real natural resonance frequencies and of a full blocking effect with energy localization.

Elastic wave excitation in a layer by piezoceramic patch actuators

A mathematical model of an electromechanical system excited by piezoceramic patch actuators is developed. The model is based on the solution to the dynamic contact problem for a set of flexible strips interacting with a free elastic layer. Unlike the conventional models, which describe the mechanical part by the dynamic equations for beams, plates, or shels, the proposed model, in addition to the first fundamental modes, also takes into account the higher normal modes of an elastic waveguide. Results obtained with the proposed model and with the simplified models prove to be in good agreement in the low-frequency range. Numerical examples illustrate resonance energy radiation associated with higher modes of the laminate strip-layer structure, as well as the possibility to control its directivity.

Wave energy trapping and localization in a plate with a delamination

The research aims at an experimental approval of the trapping mode effect theoretically predicted for an elastic plate-like structure with a horizontal crack. The effect is featured by a sharp capture of incident wave energy at certain resonance frequencies with its localization between the crack and plate surfaces in the form of energy vortices yielding long-enduring standing waves. The trapping modes are eigensolutions of the related diffraction problem associated with nearly real complex points of its discrete frequency spectrum. To detect such resonance motion, a laser vibrometer based system has been employed for the acquisition and appropriate visualization of piezoelectrically actuated out-of-plane surface motion of a two-layer aluminum plate with an artificial strip-like delamination. The measurements at resonance and off-resonance frequencies have revealed a time-harmonic oscillation of good quality above the delamination in the resonance case. It lasts for a long time after the scattered waves have left that area. The measured frequency of the trapped standing-wave oscillation is in a good agreement with that predicted using the integral equation based mathematical model.

Lamb wave excitation and propagation in elastic plates with surface obstacles: proper choice of central frequencies

Experimental and theoretical investigations of Lamb wave excitation and sensing using piezo patch transducers and the laser vibrometer technique have been performed, aiming at the development of adequate mathematical and computer models for the interpretation of sensing data and for the choice of optimal parameters for structural health monitoring. The proposed models are validated by experimental results. Furthermore, a methodology is presented which allows for the determination of central frequencies at which maximal values of the structural response spectrum can be expected in the case of wave propagation monitoring with laser vibrometry.

Resonance blocking and passing effects in two-dimensional elastic waveguides with obstacles

Resonance localization of wave energy in two-dimensional (2D) waveguides with obstacles, known as a trapped mode effect, results in blocking of wave propagation. This effect is closely connected with the allocation of natural resonance poles in the complex frequency plane, which are in fact the spectral points of the related boundary value problem. With several obstacles the number of poles increases in parallel with the number of defects. The location of the poles in the complex frequency plane depends on the defects relative position, but the gaps of transmission coefficient plots generally remain in the same frequency ranges as for every single obstacle separately. This property gives a possibility to extend gap bands by a properly selected combination of various scatterers. On the other hand, a resonance wave passing in narrow bands associated with the poles is also observed. Thus, while a resonance response of a single obstacle works as a blocker, the waveguide with several obstacles becomes opened in narrow vicinities of nearly real spectral poles, just as it is known for one-dimensional (1D) waveguides with a finite number of periodic scatterers. In the present paper the blocking and passing effects are analyzed based on a semi-analytical model for wave propagation in a 2D elastic layer with cracks or rigid inclusions.