Hanyin Cui

Characteristics of group velocities of backward waves in a hollow cylinder

It is known that modes in axially uniform waveguides exhibit backward-propagation characteristics for which group and phase velocities have opposite signs. For elastic plates, group velocities of backward Lamb waves depend only on Poissons ratio. This paper explores ways to achieve a large group velocity of a backward mode in hollow cylinders by changing the outer to inner radius ratio, in order that such a mode with strong backward-propagation characteristics may be used in acoustic logging tools. Dispersion spectra of guided waves in hollow cylinders of varying radii are numerically simulated to explore the existence of backward modes and to choose the clearly visible backward modes with high group velocities. Analyses of group velocity characteristics show that only a small number of low order backward modes are suitable for practical use, and the radius ratio to reach the highest group velocity corresponds to the accidental degeneracy of neighboring pure transverse and compressional modes at the wavenumber k = 0. It is also shown that large group velocities of backward waves are achievable in hollow cylinders made of commonly encountered materials, which may bring cost benefits when using acoustic devices which take advantage of backward-propagation effects.

Excitation mechanisms and dispersion characteristics of guided waves in multilayered cylindrical solid media

This paper first reviews a method of simulating the propagation characteristics of guided waves in multilayered coaxial cylindrical elastic solid media. Secondly, this method is used to investigate the properties of the guided waves for the ultrasonic long-range non-destructive evaluation techniques for rockbolts. To do so, the special case of non-leaky guided modes in open waveguides is considered. The method explains how the complex dispersion function is converted into a real function: hence the bisection technique can be employed to search for all the real roots. The model is used to (i) characterize the low dispersion range and anomalous dispersion of normal and Stoneley modes and (ii) analyze the excitation mechanisms of guided waves from axisymmetric and non-axisymmetric acoustic sources. The results are used to select suitable excitation frequency ranges associated with dominant modes with large amplitudes, low dispersion, and distinguishable propagation velocities to reduce signal distortion. The results suggest the lowest order flexural mode, excited by a radial force source, has potential to be used in practice. Also, the highly dispersive Stoneley mode propagating along a cylindrical interface is defined and distinguished from the normal mode using two properties, velocity high-frequency asymptotes and amplitude distributions along the radial direction.

Anomalous dispersion of flexural guided waves in clad rods

In clad rods, the dispersion properties of firstorder flexural [F(1, 1)] modes can differ from other modes. Normal and Stoneley modes and the existence criteria for four F(1, 1) modes are investigated. We focus on low-frequency anomalous dispersion, which occurs only in F(1, 1) modes and is sensitive to shear velocity.

Anomalous dispersion of guided wave in cylindrical multi-layered solid media

This paper presents an investigation into the dispersion of guided waves in cylindrical multi-layered solid media. This will aid in the design of ultrasonic transmission rods, consisting of a metal rod surrounded by a sheath, used in liquid metal cleanliness measurements. The aim is to understand the material parameters which define the regions of normal and anomalous dispersion, such that the sheath material and transmitted frequency range can be designed to improve measurement of the surrounding medium. Three models were created for infinite length rods: (1) in a vacuum, (2) embedded in an infinite medium, and (3) surrounded by an infinite medium connected via an adhesive intermediary layer (i.e. single-, double-and three-layered models). The dispersion equations were transformed into real functions and solved numerically using the bisection technique, to give robust solutions of the phase and group velocities for all propagating modes. Simulations were performed for a variety of adhesive layers and infinite medium material properties. In the single-layered model (1) it was found that only first order modes show the attributes of anomalous dispersion. In the double-layered model (2) the materials were chosen to satisfy the Stoneley wave existence criterion and the rod density was chosen to be greater than the outer medium. In this case only the Stoneley modes were predicted to exhibit signs of anomalous dispersion. These were found to exist in two distinct frequency bands. In the three-layered model (3) the Stoneley mode was found to exhibit anomalous dispersion when the density of the inner rod was larger than that of the adhesive layer, whereas the flexural normal modes required both the shear velocity and density of the rod to be greater than those of the adhesive layer. These results suggest that the high-frequency anomalous dispersion regions could be related to the interface wave properties to aid in transmission rod design.

Guided modes with multiple zero-group-velocity points in fluid-filled cylindrical pipes

It is known that guided modes in isotropic hollow cylinders exhibit backward wave propagation with negative group velocity. And interferences between backward and forward waves generate zero-group-velocity (ZGV) resonances with a finite wavenumber but vanishing group velocity. These ZGV resonances can be applied for non-destructive evaluation (NDE) of hollow pipes. In this paper, influences of a fluid-loading on ZGV resonances in pipes are studied for the possible application of integrity inspections of oil transportation pipelines. From numerically simulated frequency-wavenumber spectra of axisymmetric guided modes, in addition to the backward mode with a single ZGV point, certain branches change the sign of their slopes for twice (i.e., two ZGV points in one branch). Such multiple ZGV modes might be caused by the strong repulsion between the backward mode with a single ZGV point that is propagating in the hollow pipe and a number of longitudinal modes in the fluid cylinder. It is found that, from wave structure analyses, ZGV points correspond to relatively large displacement amplitudes at the pipe’s inner and outer interfaces. It indicates that guided modes with multiple ZGV points can be sensitive to the surface features of fluid-filled pipes, which is useful for NDE application.

Stoneley waves in three-layered cylindrical solid media

This paper considers the propagation of Stoneley modes along the interfaces of three-layered concentric cylindrical solid media in order to assist in the design of ultrasonic transmission rods. The phase velocity dispersion curves and amplitude distributions are numerically analyzed. The modes are analogous to non-dispersive Stoneley waves and are confined to the vicinities of the two interfaces at high frequency. A key finding is that the peak amplitude location for each mode transfers between the two interfaces as a function of frequency. A simplified model is introduced, giving the peak amplitude locations of each mode in different frequency ranges efficiently.

Backward waves with double zero-group-velocity points in a liquid-filled pipe

Hollow cylinders often exhibit backward propagation modes whose group and phase velocities have opposite directions, and these exhibit a minimum possible frequency at which the group velocity vanishes at a nonzero wavenumber. These zero-group-velocity (ZGV) points are associated with resonant conditions in the medium. On the basis of ZGV resonances, a non-contact and laser ultrasound technique has been developed to measure elastic constants of hollow pipes. This paper provides a theoretical and numerical investigation of the influence of the contained liquid on backward waves and associated ZGV modes, in order to explore whether this ZGV technique is suitable for in-service non-destructive evaluations of liquid-filled pipes. Dispersion spectra and excitation properties have been analyzed. It is found that the presence of the liquid causes an increased number of backward modes and ZGVs which are highly excitable by a point source. In addition, several guided modes twice undergo a change of sign in the slopes of their dispersion curves, leading to two ZGV points. This phenomenon of double ZGVs in one backward wave, which is caused by strong mode repulsions, has not been found in isotropic hollow cylinders, but it can be observed in a fluid-filled thin-walled pipe.

Influence of flow speed on guided waves in a liquid filled pipe

Liquid-filled pipes that are widely used in industries must be regularly inspected for the structure integrity. Elastic guided waves are suitable for long-range pipe inspections. In this paper, the influences of the flowing speed and temperature of the fluid flow on the propagation properties of guided waves in pipes filled with flowing high temperature liquid metals are investigated. The dispersion equation is theoretically derived applying coordinate transformations, and then simplified to get its approximation form, and finally numerically solved to obtain dispersion curves. The aim is to choose the suitable guided modes for nondestructive evaluation (NDE) of pipes, which are nonsensitive to the flow speed and the varying temperature of the fluid flow inside the pipe.

Comparison of dispersive relation of the oil well with that of the fluid cylinder and the hollow in solid

Acoustical well logging is a widely used technique in oil fields to investigate the formation outside wells and the quality of wells. The knowledge of the acoustical behavior of the wells is important to the technique and has been widely studied. The wells are usually modeled as a fluid filled cylindrical borehole in an infinite solid medium. This structure with an infinite section, sometimes called as open waveguide, is more difficult to study than the typical acoustical waveguide with finite section and free or rigid boundaries. In this presentation the well is studied as a coupled vibration system consisted of the fluid cylinder inside the well and the solid formation outside the well. The dispersive relations of 3 systems, i.e., the circular fluid cylinder with rigid boundary, the circular hollow in solid medium and the fluid filled borehole in solid, are numerically calculated and compared.

Temperature influence on guided waves in a liquid-filled pipe

The varying temperature of liquid sodium is a vital factor affecting the development of a non-destructive evaluation (NDE) ultrasonic technique for health monitoring of sodium-cooled fast reactor (SFR). The main pipe of the secondary loop of SFR is a waveguide in which numerous guided modes exhibit. In this paper, temperature influence on dispersion characteristics of guided waves in a liquid sodium filled pipe model is investigated. It is analyzed that mode coupling between guided modes in a liquid cylinder and in a hollow pipe yields guided modes in a pipe filled with liquid. The aim is to select promising guided modes and suitable excitation frequency ranges, which are non-sensitive to the sodium temperature, low dispersion, and group velocity distinguishable, for NDE application.