Natalia Glushkova

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.

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.

Selective Lamb mode excitation by piezoelectric coaxial ring actuators

This paper describes an omnidirectional multi-element transducer for selective Lamb wave mode excitation. It is composed of several coaxial ring-shaped piezoelectric elements actuated by n-cycled sinusoidal tone bursts. Mode selection is achieved through a special choice of the amplitudes and time delays of the input driving signals. The method for the determination of these parameters is based on strict analytical consideration. In the limiting case of an infinite number of cycles and with a sufficient number of actuators one can generate a single required mode and completely eliminate all undesired ones. It is shown that within the range of applicability of a simplified model for the piezoelectric elements, i.e. when the actuating contact traction is replaced by a pair of concentrated opposite ring tangential forces, no time delays are needed, and the mode selection is achieved through an appropriate choice of the driving input-signal amplitudes applied in phase or out of phase to different transducer elements.

Surface and pseudo-surface acoustic waves piezoelectrically excited in diamond-based structures

Surface and pseudo-surface acoustic plane waves generated in two- and three-layer AlN/Diamond and AlN/Diamond/γ-TiAl structures by a point electric source are analyzed in the mathematical framework based on the Greens matrix integral representation and guided wave asymptotics derived using the residue technique. The attention is focused on the effect of pseudo-surface-to-surface wave degeneration at certain discrete values of h/λ (h is the thickness of the piezoelectric layer and λ is the wave-length). Earlier such optimal ratios were discovered and experimentally verified for the first pseudo-surface (Sezawa) wave mode in the AlN/Diamond structure. The present research reveals this effect for higher modes as well as examines its manifestation for three-layer structures with different diamond-to-AlN thickness ratios H/h.

Group velocity of cylindrical guided waves in anisotropic laminate composites

An explicit expression for the group velocity of wave packets, propagating in a laminate anisotropic composite plate in prescribed directions, is proposed. It is based on the cylindrical guided wave asymptotics derived from the path integral representation for wave fields generated in the composites by given localized sources. The expression derived is theoretically confirmed by the comparison with a known representation for the group velocity vector of a plane guided wave. Then it is experimentally validated against laser vibrometer measurements of guided wave packets generated by a piezoelectric wafer active sensor in a composite plate.

Wave energy transfer in elastic half-spaces with soft interlayers.

The paper deals with guided waves generated by a surface load in a coated elastic half-space. The analysis is based on the explicit integral and asymptotic expressions derived in terms of Greens matrix and given loads for both laminate and functionally graded substrates. To perform the energy analysis, explicit expressions for the time-averaged amount of energy transferred in the time-harmonic wave field by every excited guided or body wave through horizontal planes and lateral cylindrical surfaces have been also derived. The study is focused on the peculiarities of wave energy transmission in substrates with soft interlayers that serve as internal channels for the excited guided waves. The notable features of the source energy partitioning in such media are the domination of a single emerging mode in each consecutive frequency subrange and the appearance of reverse energy fluxes at certain frequencies. These effects as well as modal and spatial distribution of the wave energy coming from the source into the substructure are numerically analyzed and discussed.