Nonlinear Wave Modulation Research Articles

Non-Linear Vibro-Acoustic Wave Modulations - Analysis of Different Types of Low-Frequency Excitation

Signal processing method based on wavelet transform used in non-linear acoustic test is presented in the paper. The method is applied for sidebands identification in response signal acquired during vibro-acoustic modulation test of impacted carbon fiber reinforced plate (CFRP). The plate was impacted with known energy using drop-weight testing machine. The modulation effect in investigated specimen results from the interaction of low and high frequency excitation with damage. The paper investigates different than mono-harmonic low-frequency excitation usually used in non-linear acoustics tests. Application of aperiodic low-frequency excitation signal allows to omit the modal test, where natural frequency of the structure are estimated. However, this requires the use of dedicated signal processing methods.

Investigation of Nonlinear Vibro-Acoustic Wave Modulation Mechanisms in Composite Laminates

This paper investigates the effect of low-frequency vibration and the related temperature field on nonlinear vibro-acoustic wave modulations. Experimental modal analysis was used to find natural frequencies and mode shapes of a composite laminate plate with seeded delamination. Temperature distribution was analyzed with a thermographic camera in the vicinity of damage for the identified vibration modes. These frequencies of these vibration modes were then used for low-frequency excitation in nonlinear acoustic tests. The correlation between the thermal field and the observed wave modulations was analyzed.

Sub-inertial modulation of nonlinear Kelvin waves in the coastal zone

Abstract. Observational evidence is presented for interaction between nonlinear internal Kelvin waves at the ωt,i (where the ωt is the semidiurnal frequency and the ωi is the inertial frequency) and random oscillations of the background coastal current at the sub-inertial Ω frequency in the Japan/East Sea. Enhanced coastal currents at the sum ω+ and difference ω-frequencies ω±=ωt,i ± Ω have properties of propagating Kelvin waves, which suggests permanent energy exchange from the sub-inertial band to the mesoscale ω± band. This interaction may be responsible for a greater-than-predicted intensification, steepening and breaking of boundary-trapped Kelvin waves. The problem of interaction between the nonlinear Kelvin wave at the frequency ω and the low-frequency narrowband noise with representative frequency Ω≪ω is investigated using the theory of nonlinear weak dispersion waves.

Analysis of Vibro-Acoustic Modulations in Nonlinear Acoustics Used for Impact Damage Detection - Numerical and Experimental Study

The paper investigates experimentally the effect of low-frequency vibration on nonlinear vibro-acoustic wave modulations applied to the detection of Barely Visible Impact Damage (BVID) in a composite plate. Finite Element (FE) modeling was used in a pretest stage to identify different motion scenarios of delaminated surfaces and relate them to natural frequencies of the damaged plate. In particular the opening-closing and frictional sliding actions of the defected interfaces have been considered. Subsequently, the identified frequencies have been used for low frequency excitation in nonlinear acoustic experiments on a composite plate with impact damage.

SOLITARY WAVE MODULATION IN AN ARTERY WITH STENOSIS FILLED WITH A VISCOUS FLUID

In this study, the derivation of mathematical model for the wave modulation through an incompressible viscous fluid contained in a prestressed thin stenosed elastic tube is presented. The artery is assumed to be incompressible, prestressed thin walled elastic tube with a symmetrical stenosis, whereas the blood is considered to be incompressible and Newtonian fluid. By utilizing the nonlinear equations of tube and fluid, the weakly nonlinear wave modulation in such a medium is examined. Employing the reductive perturbation method and considering the long-wave approximation, we showed that the third-order term in the perturbation expansion is governed by the dissipative nonlinear Schrodinger equation with variable coefficient. Our results shown that this type of equation admits a downward bell-shape wave propagates to the right as time increases with decreasing wave amplitude.

Propagation of cylindrical and spherical electron-acoustic solitary wave packets in unmagnetized plasma

Investigation of nonlinear wave modulation of electron-acoustic solitary wave packets in planar as well as nonplanar geometry is carried out for an unmagnetized two temperature plasma composed of cold and hot (featuring q-nonextensive distribution) electrons with stationary ions. It is shown that in such plasma, propagation of EA wave packets is governed by a modified NLSE which accounts for the geometrical effect and the nonextensivity of the hot electron species. It is found that the nature of the modulational instabilities would be significantly modified due to the geometrical effects, density ratio α of the hot-to-cold electrons species as well as their temperature ratio θ. Also, there exists a modulation instability period for the cylindrical and spherical envelope excitations, which does not exist in the one-dimensional case. Furthermore, spherical EA solitary wave packets are more structurally stable to perturbations than the cylindrical ones. The relevance of the current study to EA wave modulation in auroral zone plasma is highlighted.

Modulation of nonlinear waves in an inviscid fluid (blood) contained in a stenosed artery

In this study, we have contributed to the derivation of mathematical model for the nonlinear waves modulation in an artery with the presence of a stenosis. Assume that the artery as an incompressible, prestressed thin walled elastic tube with a symmetrical stenosis and the blood as an incompressible inviscid fluid. Such a combination of a solid and fluid is considered to be a model for blood flow in a stenosed artery. By employing the nonlinear equations of tube and fluid as well as the knowledge of reductive perturbation method, we obtained the nonlinear Schr¨odinger (NLS) equation with variable coefficient as the governing equation for this model. Our results show that the solitary wave with the amplitude of one unit propagates to the left as travelling wave profile, ξ increases by preserving its bell-shape wave. As might be expected from physical consideration, the wave speed reaches its maximum value at the center of the stenosis and gets smaller and smaller as goes away from the center of the stenosis.

Estimation of Damage Location of Beam Subjected to Impact Hammer Excitation Based on Nonlinear Wave Modulation Phenomenon

This paper concerns the estimation method of damage location based on the nonlinear wave modulation demodulation which has attracted much attention in the field of structural health monitoring. When a structure containing a contact-type damage is subjected to a low-frequency vibration, a high-frequency wave which propagates through the damage may undergo amplitude and phase modulation at the damage location because the scatter characteristics of high-frequency waves in the vicinity of the damage may fluctuate in synchronization with the low-frequency vibration because of the contact acoustic nonlinearity. Since this modulation propagates through the structure with the group velocity, it may be possible to estimte damage location by measuring the modulation and performing an inverse analysis based on the wave propagation model. In this paper, a mathematical model of the modulation propagation on a Timoshenko beam is constructed, and by considering the damage as a source of the modulation, an estimation algorithm of damage location which utilizes the time difference between the modulated waves measured by sensor arrays located at both sides of the damage is proposed, and examined experimentally.

Modeling of nonlinear guided waves and applications to structural health monitoring

Research efforts on nonlinear guided wave propagation have increased dramatically in the last few decades because of the large sensitivity of nonlinear waves to structural condition (defects, quasi-static loads, instability conditions, etc...). However, the mathematical framework governing the nonlinear guided wave phenomena becomes extremely challenging in the case of waveguides that are complex in either materials (damping, anisotropy, heterogeneous, etc...) or geometry (multilayers, geometric periodicity, etc…). The present work develops predictions of nonlinear second-harmonic generation in complex waveguides by extending the classical Semi-Analytical Finite Element formulation to the nonlinear regime, and implementing it into a highly flexible, yet very powerful, commercial Finite Element code. Results are presented for the following cases: a railroad track, a viscoelastic plate, a composite quasi-isotropic laminate, and a reinforced concrete slab. In these cases, favorable combinations of primary wave modes and resonant double-harmonic nonlinear wave modes are identified. Knowledge of such combinations is important to the implementation of structural monitoring systems for these structures based on higher-harmonic wave generation. The presentation will also present a specific application of nonlinear guided waves for the monitoring of thermal stresses in rail tracks to prevent buckling.

NLS Equation with a Variable Coefficient in a Stenosed Elastic Tube Filled with an Averaged Inviscid Fluid

Wave modulation in an elastic tube has been studied by researchers since year 1979. In the present work, by considering the artery as a prestressed thin elastic tube with a symmetrical stenosis and the blood as an incompressible averaged inviscid fluid. We have studied the amplitude modulation of non-linear waves in such a composite medium by using the reductive perturbation method. The governing equations can be reduced to the non-linear Schrodinger (NLS) equation with variable coefficient. The progressive wave solution to the above non-linear evolution equation is then sought. The non-linear Schrodinger (NLS) equation with variable coefficient shows increasing shock wave propagates to the right as real time passed. Keywords: Elastic tube; stenosis; inviscid fluid; nonlinear Schrodinger equation. 2010 Mathematics Subject Classification: 35Q53

Higher‐Harmonic Generation Analysis in Complex Waveguides via a Nonlinear Semianalytical Finite Element Algorithm

Propagation of nonlinear guided waves is a very attracting phenomenon for structural health monitoring applications that has received a lot of attention in the last decades. They exhibit very large sensitivity to structural conditions when compared to traditional approaches based on linear wave features. On the other hand, the applicability of this technology is still limited because of the lack of a solid understanding of the complex phenomena involved when dealing with real structures. In fact the mathematical framework governing the nonlinear guided wave propagation becomes extremely challenging in the case of waveguides that are complex in either materials (damping, anisotropy, heterogeneous, etc.) or geometry (multilayers, geometric periodicity, etc.). The present work focuses on the analysis of nonlinear second‐harmonic generation in complex waveguides by extending the classical Semianalytical Finite Element formulation to the nonlinear regime, and implementing it into a powerful commercial Finite Element package. Results are presented for the following cases: a railroad track and a viscoelastic plate. For these case‐studies optimum combinations of primary wave modes and resonant double‐harmonic nonlinear wave modes are identified. Knowledge of such combinations is critical to the implementation of structural monitoring systems for these structures based on higher‐harmonic wave generation.

106 非定常低周波振動を用いた非線形波動変調現象に基づく損傷位置の推定(セッション2 同定技術)

This study concerns damage localization method based on nonlinear elastic wave modulation spectroscopy. When fragments of a contact-type damage is rupping and crapping in synchronization with the low-frequency vibration, a high-frequency wave which propagates through the damage may undergo amplitude and phase modulation at the damage location because the scatter characteristics of high -frequency waves in the vicinity of the damage may fluctuate in synchronization with the low-frequency vibration because of the contact acoustic nonlinearity. Since thi modulation propagates through the structure with the group velocity, it may be possible to estimate damage location by measurering the modulation and performing an inverse analysis based on the wave propagation model. In this paper a mathematical model of the phase modulation propagation on a Timoshenko beam is constructed, and by considering the damage as a source of the modulation wave, a localization algorithm which utilizes the time difference between the demodulated waves measured by sensor arrays located at both sides of the damage is proposed, and examind experimentally.

Delamination detection in composites using wave modulation spectroscopy with a novel active nonlinear acousto-ultrasonic piezoelectric sensor

A novel structural health monitoring (SHM) methodology, based on nonlinear wave modulation spectroscopy, is presented for the detection of delamination cracks in composites. The basic element is a novel active nonlinear acousto-ultrasonic piezoelectric sensor enabling low-cost and wide-frequency operational bandwidth. The active sensor configuration involves two piezoceramic wafer actuators, each one excited with a low- and high-frequency signal respectively, and a piezoceramic sensor, all permanently bonded on the tested structure. Experiments are conducted on two sets of composite strips containing delamination cracks of different sizes. Measured results illustrate first the efficiency of the nonlinear ultrasonics methodology to detect delamination cracks, as well as, the potential and benefits of the new active sensor. The sensitivity of the active sensor response to the crack size and the applied high-frequency carrier signals at the actuators, vary at various frequency and voltage levels indicating the appropriate testing setup. Additionally repeatability of proposed SHM methodology is studied.

Nonlinear acoustics for fatigue crack detection – experimental investigations of vibro-acoustic wave modulations

Vibro-acoustic nonlinear wave modulations are investigated experimentally in a cracked aluminum plate. The focus is on the effect of low-frequency vibration excitation on modulation intensity and associated nonlinear wave interaction mechanisms. The study reveals that energy dissipation – not opening–closing crack action – is the major mechanism behind nonlinear modulations. The consequence is that relatively weak strain fields can be used for crack detection in metallic structures. A clear link between modulations and thermo-elastic coupling is also demonstrated, providing experimental evidence for the recently proposed non-classical, nonlinear vibro-acoustic wave interaction mechanism.

Nonlinear piezoelectric impedance modulation induced by a contact-type failure and itsapplication in crack monitoring

In this paper, a self-sensing, sensitive and baseline-free structural health monitoringmethodology is developed, which aims to detect and characterize local structuralfailures of contact type, i.e. failures which arise along with the generation, growthand/or changes of imperfect solid–solid interfaces. The nonlinear piezoelectricimpedance modulation (NPIM) method presented is based on the ideas of two existingdamage detection principles; a piezoelectric impedance-based methodology anda nonlinear wave modulation spectroscopy. It uses a single piezoelectric activesensor bonded on the structural surface, which is driven by a high-frequencyharmonic voltage source. When the structure including a contact-type failureis subjected to a low-frequency dynamic load, the induced structural vibrationcauses a fluctuation of the scattering conditions for the high-frequency elasticwaves at the failure because of the contact acoustic nonlinearity (CAN). Thisnonlinear effect of vibro-acoustic interaction yields a significant fluctuation inthe driving-point impedance in the high-frequency range, which may lead to amodulation of the coupled electromechanical impedance (or admittance) of thepiezoelectric active sensor. Therefore, if the sensor is driven by a fixed amplitudehigh-frequency harmonic voltage source, modulation of the coupled admittance can beobserved as the amplitude modulation and phase modulation of the current flowingthrough the sensor. A simplified modeling study leads to the definition of a damageevaluation index that assesses the intensity of the stiffness fluctuation caused by theCAN. Experiments using cracked beam specimens are conducted to show how theNPIM can be observed and to examine the performance of the proposed method.

Perpendicular propagating electromagnetic envelope solitons in electron-positron-ion plasma

The nonlinear amplitude modulation of electromagnetic waves propagating perpendicular to the direction of ambient magnetic field in a uniform collisionless magnetized electron-positron-ion plasma is studied. The Krylov–Bogoliubov–Mitropolsky perturbation method is employed to derive nonlinear Schrödinger equation, which describes the amplitude dynamics of perturbed magnetic field. The modulation instability criterion reveals that the low frequency mode is always stable, whereas the high frequency mode becomes modulationally unstable for certain ranges of wave number and positron-to-electron density ratio. Furthermore, the positron-to-electron density ratio as well as the strength of ambient magnetic field is found to have significant effect on the solitary wave solutions of the nonlinear Schrödinger equation, namely, dark and bright envelope solitons.

A Hamiltonian approach to nonlinear modulation of surface water waves

Many wave phenomena in physics are described by weakly nonlinear nearly monochromatic solutions in the form of modulated wave packets. The examples include ocean waves as well as waves in optics and in plasmas. There are a number of approaches to deriving the envelope equations for these theories of amplitude modulation. In this paper, we give a unified approach, based on the principles of a Hamiltonian formulation of the equations of motion. Our principal example is the system of equations of free surface water waves, for which we give a new derivation of the classical nonlinear Schrödinger and Davey–Stewartson equations, as well as the higher-order Dysthe system. One consequence of our analysis from this point of view is that the Dysthe equation can be posed as a Hamiltonian partial differential equation.

Cylindrical and spherical ion-acoustic envelope solitons in multicomponent plasmas with positrons

The nonlinear wave modulation of planar and nonplanar (cylindrical and spherical) ion-acoustic envelope solitons in a collisionless unmagnetized electron-positron-ion plasma with two-electron temperature distributions has been studied. The reductive perturbative technique is used to obtain a modified nonlinear Schrödinger equation, which includes a damping term that accounts for the geometrical effect. The critical wave number threshold Kc, which indicates where the modulational instability sets in, has been determined for various regimes. It is found that an increase in the positron concentration (alpha) leads to a decrease in the critical wave number (Kc) until alpha approaches certain value alphac (critical positron concentration), then further increase in alpha beyond alphac increases the value of Kc. Also, it is found that there is a modulation instability period for the cylindrical and spherical wave modulation, which does not exist in the one-dimensional case.

Detecting barely visible impact damage detection on aircraft composites structures

Composites have many advantages as aircraft structural materials and for this reason their use is becoming increasingly widespread. Fragility of composite material to impact loading limits their application in aircraft structures. In particular, low velocity impacts can cause a significant amount of delamination, even though the only external indication of damage may be a very small surface indentation. This type of damage is often referred to as barely visible impact damage (BVID), and it can cause significant degradation of structural properties. If the damaged laminate is subjected to high compressive loading, buckling failure may occur. Therefore, there is the need to develop improved and more efficient means of detecting such damage. In this work a new NDT approach is presented, based on the monitoring of the nonlinear elastic material behaviour of damaged material. Two methods were investigated: a single-mode nonlinear resonance ultrasound (NRUS) and a nonlinear wave modulation spectroscopy (NWMS). The developed methods were tested on different composite plates with unknown mechanical properties and damage size and magnitude. The presence of the nonlinearities introduced by the damage was clearly identified using both techniques. The results showed that the proposed methodology appear to be highly sensitive to the presence of damage with very promising future applications.

123 非線形圧電インピーダンス変調とき裂モニタリングヘの応用

This paper concerns a structural health monitoring (SHM) methodology that can detect and characterize local structural damages in early stage, developed by combining the concepts of two existing SHM principles, a piezoelectric impedance-based methodology and a nonlinear wave modulation spectroscopy. When the structure is subjected to a dynamic load at low-frequencies, the nonlinear vibro-acoustic interaction between the low-frequency vibration and the high-frequency wave field in the vicinity of "contact-type" damages causes the change in the driving-point mobility at the high frequency range. Therefore, if the piezoelectric element bonded on the structural surface is driven by a fixed amplitude high-frequency harmonic voltage source, the nonlinear modulation of the coupled electro-mechanical admittance can be observed as the amplitude and phase modulation of the current flowing through the piezoelectric element. A simplified modeling study of this phenomenon successfully leads to a damage evaluation index that assesses the intensity of the modulation of the modal stiffness. Experiments using a cracked beam are conducted to see how the stiffness modulation can be observed and to examine the performance of the proposed method.