Mode Conversion Phenomena Research Articles

Ultrasonic guided wave scattering in a plate overlap

Guided wave scattering in a plate overlap is investigated by numerical calculations and experimental measurements of transmission and reflection factors from the overlap region. In the numerical study, a hybrid boundary element-finite element method is used to calculate the guided wave scattered field from the overlap region. Transmission and reflection factors are calculated for incident A0 and S0 Lamb and n0 shear horizontal waves, including higher modes generated through mode conversion phenomena. In addition, parametric studies of transmission and reflection factors in this problem are performed numerically over various incident modes, frequencies, and overlap lengths. For verification and comparison with numerical results, experiments were conducted to measure the transmission and reflection factors for incident Lamb and shear horizontal waves in steel plates with two different overlap areas. The experimental results agree well with the numerical calculations. The numerical and experimental results show that it is highly feasible to carry out efficient Lamb wave nondestructive evaluation (NDE) in overlapped plates and in multilayer structures with various lap joints by selecting various modes and tuning frequency.

Full wave simulations of fast wave mode conversion and lower hybrid wave propagation in tokamaks

Fast wave (FW) studies of mode conversion (MC) processes at the ion–ion hybrid layer in toroidal plasmas must capture the disparate scales of the FW and mode converted ion Bernstein and ion cyclotron waves. Correct modeling of the MC layer requires resolving wavelengths on the order of k⊥ρi∼1 which leads to a scaling of the maximum poloidal mode number, Mmax, proportional to 1/ρ* (ρ*≡ρi/L). The computational resources needed scale with the number of radial (Nr), poloidal (Nθ), and toroidal (Nφ) elements as Nr * Nφ * Nθ3. Two full wave codes, a massively-parallel-processor (MPP) version of the TORIC-2D finite Larmor radius code [M. Brambilla, Plasma Phys. Controlled Fusion 41, 1 (1999)] and also an all orders spectral code AORSA2D [E. F. Jaeger et al., Phys. Plasmas 9, 1873 (2002)], have been developed which for the first time are capable of achieving the resolution and speed necessary to address mode conversion phenomena in full two-dimensional (2-D) toroidal geometry. These codes have been used in conjunction with theory and experimental data from the Alcator C-Mod [I. H. Hutchinson et al., Phys. Plasmas 1, 1511 (1994)] to gain new understanding into the nature of FWMC in tokamaks. The massively-parallel-processor version of TORIC is also now capable of running with sufficient resolution to model planned lower hybrid range of frequencies experiments in the Alcator C-Mod.

Transient dynamic responses of a cracked solid subjected to in-plane loadings

Transient dynamic responses of an elastic cracked solid subjected to in-plane surface loadings are investigated in this study. Two vertical cracks, a surface-breaking crack and a sub-surface crack, are considered. The frequency responses of the plane strain problem are calculated by the computational mechanics combining the finite element method with the boundary integral equation. The finite element method is used for the near-field enclosing the crack, while the boundary integral equation is applied for the far-field to satisfy the Sommerfeld radiation condition. The transient responses are then obtained using fast Fourier transform. Surface displacements, crack opening displacements, and dynamic stress intensity factors are presented to show the significant effects of the cracks. The interaction between the elastic waves and the cracks as well as the mode conversion phenomena can be observed and understood through the numerical simulations.

Acoustic properties of wood in tridimensional representation of slowness surfaces

Mechanical behaviour of wood considered as an orthotropic solid can be determined with ultrasonic technique. The propagation phenomena in wood are complex and theoretically are regulated by Christoffel's equation. Three type of waves can propagate in wood. During the propagation phenomena three slowness sheets are observed, corresponding to a fast longitudinal wave (inner sheet) and two shear waves, one fast and one slow (outer sheet). These waves are submitted continuously to mode conversion phenomena. The polarization angle changes when the propagation direction is out of the principal directions of symmetry of the material. In this article an analysis of the propagation phenomena in tridimensional representation is performed for different wood species. This approach contributes to the understanding of dynamic aspects of particle displacement associated with the wave fronts propagation. Globally, the anisotropy of each species, expressed by their acoustical behaviour is well represented.

Estimation of ultrasonic guided wave mode conversion in a plate with thickness variation

The hybrid boundary element method aimed at analyzing Lamb wave scattering from defects can provide us with an excellent numerical tool for tackling complicated mode conversion phenomena under waveguide thickness variation. In this paper, utilization of hybrid boundary element modeling for specific Lamb wave mode incidence situations with special energy distributions along the structural cross section is proposed for estimating reflection and transmission from various scatterers, such as a step discontinuity and tapered parts of a waveguide, etc. Interaction of individual Lamb wave modes with scatterers that represent arbitrary thickness variation along the direction of guided wave propagation is investigated by calculating the scattered fields for varying incident modes, frequency, and scatterer shape. The mode conversion phenomena through step discontinuity in a plate are also experimentally explored. The theoretical predictions of reflection and transmission by boundary element methods and the utility of dispersion curves are compared with experiments for specific modes. Results in this paper can be used to improve inspection sensitivity and penetration power for a variety of practical NDE applications, notably those in which thickness variation is found. In addition, the feasibility of inspecting sections located behind a waveguide thickness variation region and subsequent mode control will also be discussed.

Application of ultrasound reflection tomography for nondestructive evaluation of objects with a complex geometry

In the case of solid objects with complex geometry, conventional ultrasound tomography techniques tend not to be efficient enough. The objective of the paper is the development and experimental verification of an ultrasound tomography approach suitable for objects with non-flat boundaries. The reconstructed images in ultrasound reflection tomography usually are imperfect because of ultrasound wavefront curvature, which is significantly affected by wave refraction and mode conversion phenomena at the boundaries. In order to achieve better resolution of reconstructed images in the ultrasound reflection tomography, the curvature of the wavefronts has to be known and taken into account performing backprojection. Ultrasonic wavefronts were reconstructed from measured ultrasonic wave parameters. Obtained results were taken into account performing backprojection in the ultrasound refection tomography. When the curvature of the wavefront is known, the shape and the size of the defects can be reconstructed with greater accuracy. In order to determine accuracy of the proposed method, computer simulations and experimental measurements have been carried out and sources of possible errors were detected. From the results presented it can be seen that the method proposed increases accuracy of the ultrasonic reflection tomography.

Full-wave analysis of asymmetric CPW-microstrip overlap transitions for MMIC interconnects and packaging

In this letter, an asymmetric overlay transition between a CPW and a microstrip is studied. The mode conversion phenomenon is characterized by an efficient spectral-domain analysis associated with the matrix pencil posttreatment and described by a generalized scattering matrix. © 1997 John Wiley & Sons, Inc. Microwave Opt Technol Lett 16: 328–332, 1997.

Shielded edge-coupled coplanar waveguide structures: Modes and field configurations

In this article we present the dispersion characteristics as well as frequency-dependent field configuration and characteristic impedance for edge-coupled, shielded, coplanar waveguide structures. The structures studied include conductor-backed and suspended configurations. Phenomena such as mode conversion and dispersion of the dominant modes are explained. The characteristic impedance behavior is shown to be directly related to the phenomenon of mode conversion. The analysis uses the method of lines. © 1996 John Wiley & Sons, Inc.

A boundary element solution for a mode conversion study on the edge reflection of Lamb waves

The boundary element method, well known for bulk wave scattering, is extended to study the mode conversion phenomena of Lamb waves from a free edge. The elastodynamic interior boundary value problem is formulated as a hybrid boundary integral equation in conjunction with the normal mode expansion technique based on the Lamb wave dispersion equation. The present approach has the potential of easily handling the geometrical complexity of general guided wave scattering with improved computational efficiency due to the advantage of the boundary-type integral method. To check the accuracy of the boundary element program, vertical shear wave diffraction, due to a circular hole, is solved and compared with previous analytical solutions. Edge reflection factors for the multibackscattered modes in a steel plate are satisfied quite well with the principle of energy conservation. In the cases of A0, A1, and S0 incidence, the variations of the multireflection factors show similar tendencies to the existing results for glass. It is observed that the reflection of an incident wave becomes close to zero over a certain frequency range seen through energy interaction with other reflected modes, and increases again beyond this minimum point due to reverse mode conversion. The reflections of the higher symmetric incident modes, S1 and S2, are also investigated. It turns out that S1 mode is an unusual mode which is nearly unaffected by the mode conversion in the Lamb wave edge reflection.

Analysis of the film thickness dependence of a single-phase unidirectional transducer using the coupling-of-modes theory and the finite-element method

A coupling-of-modes (COM) analysis is given for the film thickness dependence of a single-phase undirectional transducer (SPUDT), while the finite-element method (FEM) is employed for evaluating all the coefficients of COM equations. The relationship between the directivity and dispersion curves of the transducer is discussed. The theoretical analysis shows that when the electrode finger thickness increases through a threshold value, a mode conversion phenomenon occurs and the value of the reflection phase changes from the positive to the negative. This result predicts that the forward direction of a film thickness difference type SPUDT will move conversely when the electrode film thickness increases through the threshold thickness. A prototype step-type SPUDT, fabricated on 128 degrees Y-X LiNbO(3) substrate, showed a directivity of 10 dB/transducer at 481.5 MHz, and a low-loss surface acoustic wave (SAW) filter showed a minimum insertion loss of 3.8 dB.

Mechanical characterization of a unidirectional composite by ultrasonic methods

The anisotropy of fibrous composite materials makes it difficult to determine their elastic constants nondestructively. Quantitative ultrasonic methods were studied to determine elastic constants of a transversely isotropic laminate. Comprehensive relationships of the measured ultrasonic data and material properties were developed. The mode conversion phenomenon at the specimen–liquid interface with oblique incidence ultrasonic immersion testing provided all the necessary information. Determination of elastic constants was possible by measuring wave speeds and critical angles. Phase velocities were determined by the multiple reflection technique utilizing ultrasonic spectroscopy. A special scanning technique was developed to determine the phase velocities and wave propagation angles in the anisotropic plane from the measured group velocities. The method developed was applied to the characterization of a unidirectional graphite/epoxy composite.

Low-loss optical branching waveguides consisting of anisotropic materials

Low-loss branching waveguides of the mode-conversion type consisting of anisotropic materials are proposed, and their basic wave-guiding characteristics are studied by means of coupled-mode theory. Two mode-conversion sections are introduced on both input and output sides of a conventional symmetric branching waveguide. Each arm of the branching waveguides is assumed to be a single-mode slab waveguide except for the tapered section. A coupled-mode system of equations describing mode-conversion phenomena with respect to the transverse magnetic (TM) mode in the branching waveguides is derived from the field expansion in terms of local normal modes. A Runge-Kutta-Gill method is used to numerically solve the coupled-mode equations. It is found that the proposed branching waveguides suffer mode-conversion losses to a much lesser extent than conventional branching waveguides. >

Shear wave imaging for deep nondestructive evaluation

Deep subsurface high resolution shear wave imaging using a conventional acoustic microscope and lens is presented. The technique is based on mode conversion phenomena which occur when a focused acoustic beam is incident from water at a material surface. A theoretical framework for the interpretation of the experimental results is discussed. Experimental results are presented using a 50 MHz acoustic lens with a 28 o aperture and 11.5 mm working distance in water

Applications of ultrasonic mode conversion techniques

Ultrasonic inspection of austenitic and dissimilar metal welds is usually performed using compressional wave angle beam probes. The dual wave mode character of those probes and the mode conversion phenomena which occur upon sound reflections (e.g. when inspection beyond half-skip is attempted) are often considered as complications which restrict the possibilities of those ultrasonic inspections. In this paper, however, several situations related to defect orientation and/or geometrical restraints to the inspection are described, in which the dual mode character and mode conversion can be—and have been—applied beneficially.

Experimental study of mode-conversion at slots

Studies of mode conversion phenomena, have been undertaken, using ultrasonic mode conversion techniques. The approach was first investigated using laser techniques to identify the likely mechanisms. This was followed by immersion experiments using either conventional piezoelectric transducers or pulsed laser generation. It will be shown that mode conversion of an incident longitudinal wave to either shear or Rayleigh waves at a surface defect may have practical application to materials evaluation.

Parametric studies on the effect of defect characteristics on their detection and sizing by ultrasound

This paper describes the experimental results of the characterisation of the ultrasonic response produced by planar ‘diffusion welded’ defects, inspected with the pulse-echo technique with probes at angles of inclination of 45°, 60° and 70°. In particular, the amplitude and time locus curves for orthogonal scanning lines at the defect plane and passing through its middle have been determined. In general, a diffuse presence of effects linked to mode conversion phenomena of the ultrasonic wave incident on the defect was observed, which in many cases made interpretation of the results more complicated. For the embedded vertical defects (tilt angle equal to zero) it was possible to determine the curves giving the echo maximum amplitude as a function of the defect depth; these curves have a regular behaviour which follows the line of the DAC curve quite well. Even for surface defects which can be detected by the corner effect, one finds quite regular behaviour as a function of the various parameters (defect height, probe angle, tilt angle), while it is more complicated to interpret the results for the embedded inclined defects (tilt angle different from zero), probably because of the different contributions of the mode conversion phenomena in the individual cases.

Surface-plasmon-polariton mode conversion on rough interfaces.

We have observed mode conversion in the structure that supports two surface-plasmon polaritons. This mode-conversion phenomenon shows up as the emission from both modes, when either of the modes is excited, and is due to intrinsic roughness of the interfaces. We present an outline of a first-order (in roughness) Green's-function-based theory that yields a simple expression for the scattering cross section and which is in good agreement with the experimental data. Implications of these results for light-emitting tunnel junctions are discussed.

Body to Rayleigh wave mode-conversion at steps and slots

The efficient excitation of Rayleigh waves at surface discontinuities due to body wave incidence has potential as a method for the detection and sizing of surface breaking defects. In this paper, the mode-conversion phenomenon at several types of surface features is studied in detail, using numerical models which employ finite-difference methods. The emphasis is on examining the spectral content of the Rayleigh wave field in order to arrive at a method for relating the spectral information to the defect dimensions. The numerical results are backed up by experimental observations.

Design Theory of a Multimode Rectangular Waveguide Taper with Truncated Gaussian Mode Conversion Distribution Function

Rectangular waveguides are mainly single-mode guides because different types of standard waveguides are manufactured /available for the use over a particular frequency band. For example, the WG-16 type of guides are to be used only in the X-band. The guide dimensions are so chosen that they will not support the spurious modes, if generated. Thus, the mode conversion phenomenon in rectangular waveguides particularly that in a tapered section has not been considered by any previous investigator. But, if the tapered section joins two different types of waveguides and/or subjected to the higher of the input frequencies, they will begin to support the higher order modes and in such cases, the losses due to mode conversion will exceed that due to the reflection alone. Thus in such cases, it becomes necessary to design tapers of minimum lengths which will keep the spurious-mode level to a pre-determined low value.

Solutions of a fourth-order differential equation describing mode conversion in a magnetized plasma

Solutions of the equation ε2u(4)+zu(2)+αu(1)+β1u −β22zu=0, where α, β1, β22 are constants, ε2≪1, and z is the independent variable, are obtained using the Laplace integral technique. This equation describes the propagation of high frequency electrostatic waves near plasma resonance in a magnetized plasma with a longitudinal density gradient and is a generalization of an equation studied by Wasow and by Rabenstein in the context of boundary layer phenomena. The solutions of this fourth-order equation in which the associated second-order equation (i.e., ε2=0) exhibits both a singularity (at z=0) and a turning point (at z=β1/β22) fall readily into two classes. One class resembles Airy functions and exists only for ε2 not equal to zero. In the other class, the solutions are related to confluent hypergeometric functions and can be viewed as solutions of the second-order equation with small corrections proportional to ε2. Using the integral representations of solutions, it is demonstrated that each class of solutions can generate the other when the independent variable crosses the singular point. This is the physical phenomenon of mode conversion. Asymptotic descriptions of both classes of solutions are given and the form of the solutions near the singular point is expressed as a power series.