Wave Propagation in Functionally GradedPiezoelectric-piezomagnetic Rectangular Rings

In the present work, a wedge structure made of absorbing panels has been analyzed by making use of the matrizant analysis with the help of the Boundary-Condition-Transfer (BCT) algorithm. The rectangular panel wedge, as it is called in this manuscript, is simple in geometry. The theoretical model, based on the plane wave acoustical coupling between multiple interacting ducts of variable cross sectional area, is applied to predict the pressure reflection coefficient of the present wedge configuration. Bulk reaction and hence wave propagation in the wedge material has been assumed in the proposed model. An asymptotic solution using the Peano-Baker series of matrix calculus is derived for different variable area ducts and then solved with the aid of the boundary condition transfer algorithm. A brief parametric study is also included as an aid to designers.

Structural Health Monitoring (SHM) systems are widely regarded as capable of significantly reducing inspection costs of safety-critical structures in industries such as aerospace, nuclear, and oil and gas, among others. Successful SHM systems can be considered those which combine good sensitivity to defects, preferably with the capability of localization and identification, with a low sensor density. Techniques based on sparse arrays of sensors which generate and receive guided waves are among the most promising candidates. Guided waves propagate over large distances and certain modes have the ability to transmit through a variety of structural features leading to a relatively small number of distributed sensors being able to cover the structure. In complex structures, which contain high densities of structural elements, the timetraces obtained are often too complex to be directly interpreted due to the large number of overlapping reflections. In this case, the Baseline Subtraction technique becomes attractive. In this method a current signal from the structure is subtracted from a signal which has been acquired during the initial stages of operation of the structure. This eliminates the need for interpretation of the complex raw time signal and any defects will be clearly seen provided the amplitude of the residual signal obtained after subtraction of the baseline signal is sufficiently low when the structure is undamaged. However, it is well known that environmental effects such as stress, ambient temperature variations and liquid loading affect the velocity of guided waves; this modifies the time-traces and leads to high levels of residual signal if a single baseline, taken under different conditions, is used. Of these effects, temperature variations are the most commonly encountered and are critical since they affect not only the wave propagation but also the response of transducers. The present work aims to demonstrate the potential of guided wave health monitoring of large area complex structures. It starts with a general literature review on inspection and monitoring of large area structures, in which the advantages and disadvantages of this technique compared to other well-established SHM techniques 2 are presented. The design and behaviour of two different temperature-stable transducers generating high A0 or S0 mode purity in the sub-200kHz frequency region are described. The efficiency of different signal processing techniques aimed at reducing or eliminating the influence of temperature on wave propagation is evaluated and a temperature compensation signal processing strategy is proposed. Finally, a large metallic structure is used to demonstrate a sparse-array SHM system based on this signal processing strategy, and imaging algorithms are used to combine the information from a large number of sensor combinations, ultimately leading to the localization of defects artificially introduced in the structure.

SAW devices can be realized as sensors by coating a suitable sensing medium on the acoustic path of the device to detect various physical and chemical measurands. ZnO is a compound widely employed as sensing and wave propagation medium in SAW devices. In particular, high aspect ratio ZnO nanowires are a promising candidate as sensing medium for SAW gas sensors and UV detectors because of its favorable sensing properties, high surface-to-volume ratio and variety of growth techniques. In this thesis, high aspect ratio catalyst-free ZnO nanowires were directly grown as sensing medium on the surface of SAW devices for the first time through the self-seeding thermal evaporation method. Initially, growth of ZnO nanowires were conducted on blank 128°-YX LiNbO3 substrates and the alignment nature of the as-grown nanowires was studied. As-grown ZnO nanowires exhibited a crisscross aligned growth pattern due to step bunching of the polished LiNbO3 surface during the nanowire growth process. However, it was experimentally observed that nanoscale etching of the LiNbO3 surface could realize growth of well-aligned ZnO nanowires because of the added surface roughness. The thermal evaporation method was then adopted for direct growth of ZnO nanowires on SAW devices. High temperature stable Rayleigh mode SAW resonators were designed, and fabricated using Pt/Ti electrodes on 128°-YX LiNbO3 substrates to facilitate the on-chip nanowire growth conducted at 620°C. As a key part of the on-chip growth process, a mask and sleeve setup was used to protect one-half of the IDT aperture during the nanowire growth process to enhance post-growth device functionality. It was observed that the proposed device had approximately 3 times higher sensitivity to UV light of 365 nm wavelength as compared to the only previous report where 1-D ZnO nanostructures were directly grown on a LiNbO3 based SAW device using solution grown method for UV detection purposes. Further, FEM simulations were conducted to study the prospects of coupled resonance phenomenon towards enhancing the sensitivity of the ZnO nanowire integrated SAW device to conductivity changes in the sensing medium. It was observed that sensitivity increases by more than 200 times when the ZnO nanowire heights are adjusted such that the resonance frequency of the nanowires approaches the original resonance frequency of the SAW device. FEM simulations were also used to investigate the possibility of switching from Rayleigh waves to higher order Sezawa waves propagating on layered SAW devices to enhance the mass loading sensitivity of SAW sensors. As an example, it was shown that Sezawa waves propagating on a ZnO/Si layered SAW device has 2 to 8 times higher mass loading sensitivity as compared to Rayleigh waves propagating on the same device. The use of the self-seeding thermal evaporation method instead of the conventionally used solution grown method opens up possibilities towards scalable growth of catalyst-free ZnO nanowires without fusion among their roots which increases the surface area of the sensing medium. Moreover, on-chip growth of ZnO nanowires in the absence of a liquid medium has future prospects for in situ measurement of the SAW device response.

Propagation and radiation of electromagnetic waves in a lossless, reciprocal, chiral medium is studied in this thesis. Such a medium is described electromagnetically by the constitutive relations D = eE + iγB and H = iγE + (1/µ)B. The constants e, µ, γ are real and have values that are fixed by the size, shape, and the spatial distribution of the elements that collectively compose the medium. The plane wave propagation in an unbounded chiral medium is considered. The propagation constants are obtained and the polarization properties of electromagnetic waves in such a medium are discussed in detail. The problem of reflection from, and transmission through a semi-infinite chiral medium is solved by obtaining the Fresnel equations. The conditions for the total internal reflection of the incident wave from the interface, and the existance of the Brewster angle are obtained. The effects of the chirality on the polarization and intensity of the reflected wave from the chiral half-space are discussed and illustrated by employing the Stokes parameters. The propagation of electromagnetic waves through an infinite slab of chiral medium is formulated for oblique incidence and solved analytically for the case of normal incidence. The radiation emitted by an oscillating dipole in an unbounded, lossless, chiral medium is calculated. From the constitutive relations and from the time-harmonic Maxwell equations ∇ x E = iωB and ∇ x H = J - iωD, it is seen that the wave equation for such a medium is given by ∇ x ∇ x E - ω2µeE - 2ωµγ∇ x E = iωµJ where the source term J is the current density of the oscillating dipole and where E is the electric vector of the radiated field. The desired solution of this wave equation is found by the dyadic Green's function method, that is, by first constructing the dyadic Green's function Γ and then evaluating the expression E = iωµ∫Γ(r,r')•J(r')dV'. The dyadic Green's function Γ and the components of the radiated electric field E are obtained in closed form. The components of the radiated B, D, and H fields can be derived from knowledge of E by using the Maxwell equation B = (1/iω)∇ x E and the constitutive relations. The wave impedance of the medium and the radiation resistance of the dipole are also obtained. The effects of the chiral medium on the polarization and intensity of the dipole radiation are discussed.

The effect of liquid on the propagation of waves in a micropolar elastic layer with voids immersed in an infinite liquid has been investigated. In case I the frequency equations for symmetric and antisymmetric vibrations have been obtained and some special cases have been deduced. Case II is concerned with wave propagation in a micropolar elastic solid with voids. Reflection of micropolar elastic waves at the free surface of a micropolar elastic body with voids is discussed. In case III, propagation of Rayleigh waves in a micropolar elastic body with voids and particle motion for Rayleigh waves are discussed. Numerical computations of the amplitude ratios for different reflected waves have been performed and plotted against the angle of emergence. The frequency equation of Rayleigh wave propagation is obtained and phase velocity as a function of Poisson’s ratio, frequency ratio, non-dimensional micropolar constant and normalized wave number have been plotted graphically for a particular model.

In this article, wave propagation characteristics in magneto-electro-elastic (MEE) nanotube considering shell model is studied in the framework nonlocal theory. To account for the small-scale effects, the Eringen's nonlocal elasticity theory of is applied. Nonlocal governing equations of MEE nanotube have been derived utilizing Hamilton's principle. The results of this investigation have been accredited by comparing them of previous studies. An analytical solution of governing equations is used to obtain phase velocities and wave frequencies. The influences of different parameters, such as different mode, nonlocal parameter, length parameter, geometry, magnetic field and electric field on wave propagation responses of MEE nanotube are expressed in detail.

The various aspects of the propagation of long waves onto a shelf (i.e., reflection, transmission and propagation on the shelf) are examined experimentally and theoretically. The results are applied to tsunamis propagating onto the continental shelf. A numerical method of solving the one-dimensional Boussinesq equations for constant depth using finite element techniques is presented. The method is extended to the case of an arbitrary variation in depth (i.e., gradually to abruptly varying depth) in the direction of wave propagation. The scheme is applied to the propagation of solitary waves over a slope onto a shelf and is confirmed by experiments. A theory is developed for the generation in the laboratory of long waves of permanent form, i.e., solitary and cnoidal waves. The theory, which incorporates the nonlinear aspects of the problem, applies to wave generators which consist of a vertical plate which moves horizontally. Experiments have been conducted and the results agree well with the generation theory. In addition, these results are used to compare the shape, celerity and damping characteristics of the generated waves with the long wave theories. The solution of the linear nondispersive theory for harmonic waves of a single frequency propagating over a slope onto a shelf is extended to the case of solitary waves. Comparisons of this analysis with the nonlinear dispersive theory and experiments are presented. Comparisons of experiments with solitary and cnoidal waves with the predictions of the various theories indicate that, apart from propagation, the reflection of waves from a change in depth is a linear process except in extreme cases. However, the transmission and the propagation of both the transmitted and the reflected waves in general are nonlinear processes. Exceptions are waves with heights which are very small compared to the depth. For these waves, the entire process of propagation onto a shelf in the vicinity of the shelf is linear . Tsunamis propagating from the deep ocean onto the continental shelf probably fall in this class.

A numerical investigation of shock wave propagation in open atmosphere is presented to observe the shock wave decaying phenomena due to expansion in the free space. By examining different parameters (Pressure, velocity and density) of the upstream and downstream flow of the wave, it is possible to estimate the decaying phenomena of the wave strength. The governing equations described for compressible inviscid flow are discretized by the finite volume method. The three-dimensional Euler equations are solved by shock capturing method. Shock wave of Mach number 1.5 is allowed to flow through a shock tube and at different time intervals (35 μsec, 96 μsec, 121 μsec and 190 μsec), velocity, pressure and density variations along the center line of shock tube are investigated to observe the decay phenomenon across the shock front in open atmosphere.. The results have been compared with the Navier-Stokes Simulation (NS) results to establish the absence of viscous effects in the present flow. Due to absence of the solid boundary of the selected numerical domain in the free space, the fluid flow will act as non-viscous flow. The wave propagation in free space changes its propagation characteristics due to rapid expansion in all directions and at the same time the decay of the wave strength is observed.

R wave is short for Rayleigh wave. R wave,on which the effect of gravity is generally inevitable,has received considerably extensive attention and been widely used in many fields,such as geological exploration,nondestructive test,etc. The effects of gravity on R wave velocity for elastic parameters were further analyzed based on available R wave velocity function,and the applicable range of the approximate one was given as well. Wave propagation through quasi-half-space isotropic linear elastic medium with gravity,under the excitation of differentiated Gaussian pulse( DGP) was studied by finite difference time domain( FDTD) method with staggered grid discretization,and extended boundary conditions were introduced.Velocity values obtained were closer to the theoretical ones. Meanwhile,the influence of gravity on time domain,frequency domain response was discussed. By analyzing the theoretical and numerical results,it is necessary to take the effect of gravity into account in simulation for more accurate prediction.

The guided wave technique is commonly used in structural health monitoring as the guided waves can propagate far in the structures without much energy loss. The guided waves are conventionally generated by the surface-mounted piezoelectric wafer active sensor (PWAS). However, there is still lack of understanding of the wave propagation in layered structures, especially in structures made of anisotropic materials such as carbon fiber reinforced polymer (CFRP) composites. In this paper, the Rayleigh-Lamb wave strain tuning curves in a PWAS-mounted unidirectional CFRP plate are analytically derived using the normal mode expansion (NME) method. The excitation frequency spectrum is then multiplied by the tuning curves to calculate the frequency response spectrum. The corresponding time domain responses are obtained through the inverse Fourier transform. The theoretical calculations are validated through finite element analysis and an experimental study. The PWAS responses under the free, debonded and bonded CFRP conditions are investigated and compared. The results demonstrate that the amplitude and travelling time of wave packet can be used to evaluate the CFRP bonding conditions. The method can work on a baseline-free manner.

The propagation of elastic transient waves in a multi–layered medium subjected to in–plane loadings is investigated in this study. One of the objectives of this study is to develop an effective analytical method for determining transient full–field solutions in the layered medium. A matrix method is developed by expanding the matrix solution obtained directly from the boundary–value problem in the integral transform domain into a power series of the phase–related reflection and transmission matrix which characterizes the multiple reflections and transmissions of all waves in every layer. The transient response of the multi–layered medium is decomposed into infinite wave groups in which the waves are either reflected by, or transmitted through, the interfaces. The connection between the proposed matrix method and the generalized ray method is established for the layered medium in the transform domain. The matrix representation of the solution enables us to calculate the transient response of the layered medium without tracing the ray path manually. The obtained analytical solution can easily be applied to numerical calculations. The double inverse transform is performed based on Cagniard9s method and the theoretical transient solution for a layered half–space subjected to an in–plane dynamic force will be presented in part II. An experimental set–up that simulates the plane stress condition for a layered half–space was established to obtain the dynamic displacement response. The experimental result agrees well with the theoretical solution. The proposed methodology in this study can be extended to solve more complicated problems such as waves propagating in three–dimensional space.

The basic purpose of this work is to investigate experimentally the phase characteristics of radio waves propagated along the surface of the earth as proposed by K.A. Norton (reference 1). Norton's theory indicates that the ground wave phase at distances of the order of tens of miles is greater than the corresponding space wave phase by not more than 180 degrees. From a radio surveying point of view, range errors of tens of feet may result. To avoid difficulties inherent in the direct and absolute approach, that of comparison of optical surveying with radio surveying over actual terrain at normally used frequencies (200 kilocycles per second to 15 megacycles per second), a new technique is developed. It is proposed that the propagation of radio waves may be studied by use of appropriate scale models, permitting experiments otherwise impossible because of the gigantic size of the equivalent true scale systems. Further, relative measurements may be obtained directly in a model system by proper choice of paths as contrasted with the absolute measurements usually made in a full-scale system. The technique is demonstrated by a preliminary experimental confirmation of Norton's theory. Suggestions for technique improvement and for further investigation possibilities are given.

The objective of this investigation is to examine the buoyancy-driven gravitational spreading currents, especially as applied to ocean disposal of wastewater and the accidental release of hazardous fluids, such as liquefied natural gas. A series of asymptotic solutions are used to describe the displacement of a gravitationally driven spreading front during an inertial phase of motion and the subsequent viscous phase. Solutions are derived by a force scale analysis and a self-similar technique for flows in stagnant, homogeneous, or linearly density-stratified environments. The self-similar solutions for inertial-buoyancy currents are found using an analogy to the well-known shallow-water wave propagation equations and also to those applicable to a blast wave in gasdynamics. For the viscous-buoyancy currents the analogy is to the viscous long wave approximation to a nonlinear diffusive wave, or thermal wave propagation. Other similarity solutions describing the initial stage of motion of the flow formed by the collapse of a finite volume fluid are developed by analogy to the expansion of a gas cloud into a vacuum. For the case of a continuous discharge there is initially a starting jet flow followed by the buoyancy-driven spreading flow. The jet mixing zone in such flows is described using Prandtl's mixing length theory. Dimensional analysis is used to derive the relevant scaling factors describing these flows.

Natural or hydraulic fractures are of major importance for the productivity of hydrocarbon reservoirs. Besides fracture detection, also the aperture and extension of the fractures are essential for a correct reservoir productivity estimate. There are many ways to detect and measure fractures, such as borehole televiewers and electrical borehole scans. A practical approach to investigate fracture properties is by means of acoustic logging. In this thesis, borehole waves along fractured media are investigated theoretically and experimentally. Theoretically, the effect of a fracture intersecting a vertical borehole can be described by the introduction of a frequency-dependent (dynamic) borehole fluid compressibility which is measured in the laboratory. The dynamic fluid bulk modulus comprises the intrinsic fluid stiffness, the borehole wall distensibility, and the radial fluid seepage into the adjacent (horizontal) permeable zones. The latter two effects tend to diminish the intrinsic fluid’s stiffness, giving rise to a lower effective bulk modulus amplitude and thus to a lower wave speed in the borehole. The radial oscillatory fluid seepage causes viscous friction in the adjacent zones and results in a phase lag between the pressure increase and the compression of the borehole fluid, leading to attenuation of the borehole waves. This seepage effect is expressed in terms of a so-called borehole dynamic wall impedance specifying the radial fluid velocity at the borehole wall as a function of the borehole pressure variations. If a borehole wave travels down from an undamaged zone into a fracture zone, it will encounter an impedance contrast causing the wave to partially reflect and partially transmit, thus revealing the presence of permeable fracture zone adjacent to the borehole. Stoneley wave propagation in porous and fractured formations is studied experimentally by means of a vertical shock tube facility. In this set-up, shock waves in air are generated that travel downwards into a water-saturated cylindrical rock sample that has a borehole drilled along the center axis. In this way, high-energy borehole waves can be generated with excellent repeatability. A logging probe is installed in the borehole to measure the pressure profiles. Reflection from the water-sample interface and from the free water interface can be recorded by means of a fixed pressure transducer mounted in the wall of the shock tube above the sample in the water layer. The fractures in the formation are represented by small horizontal slits in composite cylinders whose upper and lower parts are separated by small spacer poles. In this way, a variable horizontal fracture (slit) aperture can be obtained. Obviously these fractures form an open connection between the borehole fluid and the fluid outside the cylinder. Also mandrel samples are used for horizontal slits that are not open to the fluid outside the cylinder, thus representing fractures with finite radial extension. Wave experiments show that varying fracture widths significantly alter the recorded Stoneley wave pressure signal at fixed depth. The reflection and transmission of borehole tube waves over 1 and 5 mm fractures are correctly predicted by theory. Other wave experiments show that attenuation in boreholes adjacent to porous zones without fractures can be predicted by theory. This technique even allows a direct measurement of the permeability, although the acoustically measured permeability and the permeability measured by falling-head technique still show a significant discrepancy. This technique is directly applicable to fractured porous reservoir core samples.

Earthquake represents one of most destructive geological hazards. In this thesis I will attempt to understand it through controlled laboratory experiments. The earthquake dynamic rupturing process itself is a complicated phenomenon, involving dynamic friction, wave propagation, and heat production. Because controlled experiments can produce results without assumptions needed in theoretical and numerical analysis, the experimental method is thus advantageous over theoretical and numerical methods. Our laboratory fault is composed of carefully cut photoelastic polymer plates (Homalite-100, Polycarbonate) held together by uniaxial compression. As a unique unit of the experimental design, a controlled exploding wire technique provides the triggering mechanism of laboratory earthquakes. Three important components of real earthquakes (i.e., pre-existing fault, tectonic loading, and triggering mechanism) correspond to and are simulated by frictional contact, uniaxial compression, and the exploding wire technique. Dynamic rupturing processes are visualized using the photoelastic method and are recorded via a high-speed camera. Our experimental methodology, which is full-field, in situ, and non-intrusive, has better control and diagnostic capacity compared to other existing experimental methods. Using this experimental approach, we have investigated several problems: dynamics of earthquake faulting occurring along homogeneous faults separating identical materials, earthquake faulting along inhomogeneous faults separating materials with different wave speeds, and earthquake faulting along faults with a finite low wave speed fault core. We have observed supershear ruptures, rupture speed transition, directionality of rupture in faults with a material contrast, self-healing slip pulses in faults with a finite core, crack-like to pulse-like rupture transition in faults with a finite core.