Mikhail V. Golub

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.

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.

Propagation of Elastic Waves in Layered Composites with Microdefect Concentration Zones and Their Simulation with Spring Boundary Conditions

The possibility is studied of applying spring boundary conditions to describe propagation of elastic waves in layered composites with nonperfect contact of components or in the presence of groups of microdefects at the interface. Stiffnesses in spring boundary conditions are determined by crack density, the average size of microdefects, and the elastic properties of the materials surrounding them. In deriving the values of the effective stiffness parameters, the Baik-Thompson and Boström-Wickham approaches are applied, as well as the integral approach. The components of the stiffness matrices are derived from consideration of an incident, at a random angle to the interface, plane wave in the antiplane case, and at a normal angle in the plane case. The efficiency of this model and the possibility of using its results in the three-dimensional case are discussed.

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.

Blocking of traveling waves and energy localization due to the elastodynamic diffraction by a crack

The semianalytic methods developed for solving the problems of elastodynamic diffraction by a horizontal strip-like crack are used to analyze the transmission and reflection of Rayleigh waves in a half-plane and normal modes in a layer with the aim to determine the parameters of blocking and study the blocking mechanism. The resonance blocking is shown to be accompanied by energy localization near the crack. For the case of a crack in a half-plane, a possibility of nonresonance blocking is revealed. The transmission and reflection coefficients are analyzed as functions of frequency, crack size, and crack depth. Numerical examples of energy streamline and power distribution structures are given for the resonance and nonresonance blocking, as well as examples of the behavior of stress intensity factors at the crack tips.

Resonance blocking of traveling waves by a system of cracks in an elastic layer

Wave processes that occur in an elastic layer when waves traveling in it are diffracted by a system of horizontal cracks are investigated. Integral representations of wave fields are constructed in terms of the convolution of Green’s matrices and unknown jumps of displacements at the cracks. The displacement jumps are determined from the boundary integral equations, which are obtained from the initial boundary-value problem with the boundary conditions at crack faces being satisfied. The spectrum of the integral operator is studied for different variants of mutual crack arrangement and is compared with the spectrum of the corresponding operators for individual cracks; the relationship between the spectrum and the blocking effects is analyzed. The possibility of obtaining an extended frequency band of waveguide blocking in the case of groups of cracks is demonstrated.

In-plane time-harmonic elastic wave motion and resonance phenomena in a layered phononic crystal with periodic cracks

This paper presents an elastodynamic analysis of two-dimensional time-harmonic elastic wave propagation in periodically multilayered elastic composites, which are also frequently referred to as one-dimensional phononic crystals, with a periodic array of strip-like interior or interface cracks. The transfer matrix method and the boundary integral equation method in conjunction with the Bloch-Floquet theorem are applied to compute the elastic wave fields in the layered periodic composites. The effects of the crack size, spacing, and location, as well as the incidence angle and the type of incident elastic waves on the wave propagation characteristics in the composite structure are investigated in details. In particular, the band-gaps, the localization and the resonances of elastic waves are revealed by numerical examples. In order to understand better the wave propagation phenomena in layered phononic crystals with distributed cracks, the energy flow vector of Umov and the corresponding energy streamlines are visualized and analyzed. The numerical results demonstrate that large energy vortices obstruct elastic wave propagation in layered phononic crystals at resonance frequencies. They occur before the cracks reflecting most of the energy transmitted by the incoming wave and disappear when the problem parameters are shifted from the resonant ones.

Continuous wavelet transform application in diagnostics of piezoelectric wafer active sensors

Piezoelectric wafer active sensors (PWAS) are employed in a variety of structural health monitoring (SHM) applications. Failure of these might lead to significant problems, so monitoring of actuators themselves is necessary. While totally debonded PWAS can be detected easily, small debondings could still occur. In that case PWAS is still capable of generating ultrasound waves, but might lead to false diagnostic results since the underlying baseline measurements are not valid anymore. Therefore an experimental setup with a specimen of 16 partially debonded actuators has been used. Phenomena accompanying wave excitation by debonded actuators are examined. Collected knowledge is analyzed in order to identify existence, location and shape of a debonded part of the actuator. For a sufficiently debonded PWAS some interesting abnormalities have been detected for high frequencies. Wavelet analysis has revealed that the velocities of the motion and carrier frequencies depend on the shape of the debonded part of the PWAS.

Elastic Wave Propagation in Anisotropic and Functionally Graded Layered Phononic Crystals: Band-Gaps, Pass-Bands and Low Transmission Pass-Bands

This paper describes a mathematical model of plane wave propagation in anisotropic and functionally graded layered phononic crystals with finite and infinite number of unit-cells. Classification of pass-bands and band-gaps is presented based on asymptotic analysis of the wave-fields in periodic layered structures. Two kinds of band-gaps where the transmission coefficient decays exponentially with the number of unit-cells are specified. The so-called low transmission pass-bands are introduced in order to identify frequency ranges in which the transmission is low enough for engineering applications, but it does not tend to zero exponentially with the number of unit-cells approaching infinity. The results of the numerical simulation are presented in order to demonstrate wave propagation phenomena. The influence of the anisotropy and functionally graded interlayers on the band-gaps and pass-bands is analysed.

Wave propagation through an interface between dissimilar media with a doubly periodic array of arbitrary shaped planar delaminations

This paper considers the scattering of elastic waves by a doubly periodic array of three-dimensional planar delaminations at the interface between two dissimilar media. The delaminations are modelled in terms of the spring boundary conditions, which are employed to formulate a boundary integral equation. The problem is solved using the Bubnov–Galerkin scheme and the integral approach, taking into account geometrical periodicity. The effects of distribution and shape of periodic delaminations on wave transmission and diffraction are analysed. The specific phenomenon of pass-bands or an ‘opening’ interface for wave propagation by a periodic array of delaminations is revealed.