Nonlinear lamb waves in a metal plate with defects

Experimental results on the propagation of finite-amplitude Lamb waves in a solid plate made of polycrystalline aluminum alloy with defects are presented. The Lamb waves are recorded and visualized using a scanning laser vibrometer. The dependences of the higher harmonic amplitudes, both averaged over the plate surface and measured at a point far from the defect and at the site of the defect, on the fundamental frequency amplitude are studied. A threshold character of the higher harmonic generation and a power-law behavior of their amplitudes are revealed, the latter feature being unconventional for the nonlinearity associated with the anharmonicity of the crystal lattice of the material. The possibility of locating the distribution of individual defects from the measured spatial distribution of structural nonlinearity in the material under study is experimentally demonstrated. The results of the experiments are explained in terms of the bilinear medium model.     

Perturbation of fluid-guided waves induced by bending plates

In order to discover whether the interaction between flexural and dilatational waves in a fluid-filled rectangular duct may be the reason why one observes experimentally a dispersion in the speed of the plane wave inside the duct, a calculation is carried out by the finite element method both in the structure and in the fluid. The numerical results of the coupling problem agree qualitatively with the phenomenon observed, and it appears that the usual hypothesis of local reaction of the walls does not apply in all frequency ranges.     

The effect on bending waves by defects in pinned elastic plates

This paper presents solutions to a number of problems posed for the out-of-plane displacement of infinite thin elastic plates that are rigidly pinned in periodic configurations, but that possess a finite number of ‘defects’. We begin by considering a single one-dimensional periodic array of pins. We derive an analytic solution for the displacement produced by the forced oscillation of the central pin in the array, and this solution is shown to be closely connected to the problem of scattering of plane waves by an array when a finite number of pins are removed. Attention then focuses on doubly periodic rectangular arrays of pinned points possessing defects. Central to approaching such problems is an understanding of Bloch–Floquet waves in periodic arrays in the absence of defects and a simple method is described for computing the associated dispersion surfaces. The solutions to three problems are then sought: the trapping of localised waves by a finite number of missing pins; trapping of waves by entire rows of missing pins; and the wave radiation pattern due to the forcing of a single pin. All problems are treated analytically using bounded Green's functions for thin elastic plates, a discrete Fourier transform solution method and simple, explicit and rapidly convergent evaluations of the one- and two-dimensional lattice sums that arise.     

Nonlinear guided waves in plates: A numerical perspective

Harmonic generation from non-cumulative fundamental symmetric (_S0$S_0$) and antisymmetric (_A0$A_0$) modes in plate is studied from a numerical standpoint. The contribution to harmonic generation from material nonlinearity is shown to be larger than that from geometric nonlinearity. Also, increasing the magnitude of the higher order elastic constants increases the amplitude of second harmonics. Second harmonic generation from non-phase-matched modes illustrates that group velocity matching is not a necessary condition for harmonic generation. Additionally, harmonic generation from primary mode is continuous and once generated, higher harmonics propagate independently. Lastly, the phenomenon of mode-interaction to generate sum and difference frequencies is demonstrated.     

Reflection and transmission coefficients for guided waves reflected by defects in viscoelastic material plates

The paper presents a Fourier transform-based signal processing procedure for quantifying the reflection and transmission coefficients and mode conversion of guided waves diffracted by defects in plates made of viscoelastic materials. The case of the S(0) Lamb wave mode incident on a notch in a Perspex plate is considered. The procedure is applied to numerical data produced by a finite element code that simulates the propagation of attenuated guided modes and their diffraction by the notch, including mode conversion. Its validity and precision are checked by the way of the energy balance computation and by comparison with results obtained using an orthogonality relation-based processing method.     

Formation of nanometer ordered defect-deformational structures induced by energy fluxes in solids

A defect-deformational theory is constructed for the hierarchic formation of nanometer clusters in periodic structures of point defects under the action of an energy flux. The theoretical results obtained are compared with experimental results on the formation of nanometer pore lattices in metals under the action of particle beams and the laser-induced structural modification of semiconductor surfaces. Good agreement between the theory and experiment is obtained. Fiz. Tverd. Tela (St. Petersburg) 39, 2029–2035 (October 1997)     

Nonlinear induced reflection of light waves in semiconductors

A scheme of nonlinear optical four-wave mixing of two counterpropagating laser beams on the surface of a semiconductor is proposed and analyzed. It is shown that the density modulation of the electron-hole plasma current carriers in the light-induced grating manifests itself in the probe beam depolarization signal after the reflection from the surface, which is sensitive to the state of the surface and presence of complex molecules on it.     

Nonlinear scattering in BaTiO3 induced by two orthogonally polarized waves

A new nonlinear scattering effect is described which is induced by the simultaneous action of ordinary and extraordinary waves impigning on a BaTiO₃ crystal in the plane perpendicular to the c-axis. The scattered light of ordinary polarization propagates along a circular cone and the light intensity on this cone is nonuniform. We present a model that describes the experimental observations rather well, including phase matching conditions and the unusual intensity distribution of the scattered light.     

Remote characterization of defects in plates with viscoelastic coatings using guided waves

The remote inspection for defects in large metallic elements such as pipes, tubes and plates is a field where guided waves are being applied with success. There are a number of situations where a surface coating is added for corrosion protection or insulation purposes. Since the coating materials are usually viscoelastic, the guided wave inspection range may be severely reduced unless a proper mode and an adequate frequency range is selected. Previous authors found the existence of low-attenuated modes at certain frequency ranges, which were used to detect and locate defects at reasonably large distances. This paper studies the potential of guided waves for not only locating but also sizing defects in plates with viscoelastic coatings. A hybrid finite element-boundary element method which explicitly includes the attenuating characteristics of the coating is used to determine Lamb and SH mode conversion factors at corrosion defects under the coating. Through parametric studies and analysis of the numerical results, some trends and features are highlighted that could be used for sizing purposes.     

On the reflection of coupled Rayleigh-like waves at surface defects in plates

The reflection of coupled Rayleigh-like waves from surface defects in elastic plates is investigated experimentally and analyzed on the basis of an analytical model and finite difference simulations. The propagation of Rayleigh-like waves in plates is characterized by an energy transfer to the opposite plate side and back over a distance called the beat length. Experimental results clearly show this beating effect and its dependency on the frequency-thickness product, and excellent agreement is obtained with existing analytical predictions. The propagation and scattering are modeled separately for the fundamental A(0) and S(0) Lamb modes that constitute the incident Rayleigh-like wave. The reflection coefficients from surface slots are investigated using finite difference simulations and the reflected Rayleigh-like wave is obtained by superposition. The theoretical model reveals strong dependencies of the reflected field on the ratio between excitation distance and beat length and on the cutoff frequencies of specific higher Lamb modes. Standard pulse-echo measurements allow for the detection of small defects from a remote transducer location. Good agreement is obtained between the predicted and measured amplitude spectra of the reflected Rayleigh-like wave. The developed model allows for the evaluation of defect location and damaged plate side using a combination of time-of-flight and frequency measurements.     

Nonlinear longitudinal waves in the presence of the interaction between the strain and temperature fields and the field of nonequilibrium atomic defects

The propagation of nonlinear longitudinal waves in a plate is studied by taking into account the interaction of the longitudinal displacement component with the temperature field and the field of concentration of nonequilibrium atomic point defects. A nonlinear evolution equation is derived for describing the self-consistent thermoelastic longitudinal strain fields. It is shown that the thermoelastic effect on the strain waves manifests itself in the appearance of dissipative terms, which describe the heat transfer and the thermoelastic interaction caused by the strain-induced heat release due to the recombination of nonequilibrium atomic defects. The soliton solutions to the evolution equation are investigated, and the characteristic features of their damping are considered with allowance for the low-frequency and high-frequency losses.     

Circumferential thermoelastic waves in orthotropic cylindrical curved plates without energy dissipation

In this article, the propagation of guided thermoelastic waves in the circumferential direction of orthotropic cylindrical curved plates subjected to stress-free, isothermal boundary conditions is investigated in the context of the Green-Naghdi (GN) generalized thermoelastic theory (without energy dissipation). The coupled wave equations and heat conduction equation are solved by the Legendre orthogonal polynomial series expansion approach. The convergency of the method is discussed through a numerical example. The dispersion curves of thermal modes and elastic modes are illustrated simultaneously. Dispersion curves of the corresponding pure elastic cylindrical plate are also shown to analyze the influence of the thermoelasticity on elastic modes. The displacement, temperature and stress distributions are shown to discuss the differences between the elastic modes and thermal modes. A thermoelastic cylindrical plate with a different ratio of radius to thickness is considered to discuss the influence of the ratio on the characteristics of circumferential thermoelastic waves.     

Generation of flexural waves in plates by laser-initiated airborne shock waves

Results of the semi-analytical modelling of the interaction of laser-initiated airborne shock waves with an infinite horizontally positioned elastic plate are presented. The impact of the airborne shock waves on the plate is approximated by a cylindrically diverging surface force resulting from the pressure of the incident and reflected shock waves. This force is then represented in the wavenumber-frequency domain by means of Hankel and Fourier transforms that are carried out numerically so that the interaction problem can be solved using the Green’s function method. The resulting frequency spectra and time histories of generated flexural wave pulses are calculated for different values of laser pulse energy and for different heights of the laser beam focusing above the plate surface. The theoretical results obtained are compared with the results of laboratory measurements of the interaction of laser-generated acoustic shocks with a large plastic plate. The comparison shows reasonably good agreement between the semi-analytical predictions and data.     

3D analysis of interaction of Lamb waves with defects in loaded steel plates

The objective of the research presented here is the investigation of the interaction of guided waves with welds, defects and other non-uniformities in steel plates loaded by liquid. The investigation has been performed using numerical simulation for 2D and 3D cases by the finite differences method, finite element method and measurement of 3D distributions of acoustic fields. Propagation of the S(0) mode in a steel plate and its interaction with non-uniformities was investigated. It was shown that using the measured leaky wave signals in the water loading of the steel plate and by application of signal processing, the 3D ultrasonic field structure inside and outside of the plate can be reconstructed. The presence of leaky wave signals over the defect caused by the mode conversion of Lamb waves has been proved using the numerical modelling and experimental investigations. The developed signal and data processing enables to visualise dynamics of ultrasonic fields over the plate, and also to estimate spatial positions of defects inside the steel plates.     

Nonlinear nature of kinetic undamped waves induced by electrostatic turbulence in stimulated Raman backscattering

The influence of low-frequency waves of kinetic nature induced by electron trapping in backward Stimulated Raman Scattering (SRS) is investigated. Semi-lagrangian Vlasov-Maxwell simulations are carried out not only for periodic boundary conditions but also in the case of an open plasma with parabolic shape, in optical mixing. We provide a numerical example of generation of KEEN (kinetic electrostatic electron nonlinear) waves nonlinearly induced from the SRS through a mechanism we first here elucidate. In particular we identify a process of backward scattering of the SRS probe light from the so generated KEEN waves, which may provide a mechanism for the possible experimental observation and measurement of such nonlinear structures.     

Passivation of laser induced defects in silicon by low energy hydrogen ion implantation

It is well established that the pulsed-laser annealing of as-implanted Si introduces electrically active defects. The aim of this paper is to show that these defects can be neutralized by low-energy hydrogen ion implantation. The techniques used for the sample characterization are current-voltage measurements and capacitance transient spectroscopy.