Standing Shear Waves Research Articles

Standing shear waves in nonlinear gel-like media under static shear stress

Standing shear waves in a resonator in the form of layer of gel-like medium placed between two rigid plates are studied. The bottom plate is fixed to the vibrator and oscillates in the horizontal direction with a preset amplitude. Two rubber threads attached to the upper plate can displace the plate by a specified value in the horizontal direction. The change in the tension of the threads creates an additional static deformation of the elastic layer resulting in the effective shear elasticity increase. The measured static stress-strain dependence of the elastic layer can be described by the cubic parabola. We measured the dependences of the resonance frequency on the static deformation of the layer. For static deformations of the layer less than 0.3 h (h—is the layer thickness), the resonance frequency increases linearly, that can be explained by a linear growth of the elastic force of rubber threads. In the deformation range of 0.3-1 h, an additional shift of the resonance frequency caused by the nonline...

WE‐E‐9A‐01: Ultrasound Elasticity

Principles and techniques of ultrasound‐based elasticity imaging will be presented, including quasistatic strain imaging, shear wave elasticity imaging, and their implementations in available systems. Deeper exploration of quasistatic methods, including elastic relaxation, and their applications, advantages, artifacts and limitations will be discussed. Transient elastography based on progressive and standing shear waves will be explained in more depth, along with applications, advantages, artifacts and limitations, as will measurement of complex elastic moduli. Comparisons will be made between ultrasound radiation force techniques, MR elastography, and the simple A mode plus mechanical plunger technique. Progress in efforts, such as that by the Quantitative Imaging Biomarkers Alliance, to reduce the differences in the elastic modulus reported by different commercial systems will be explained.Dr. Hall is on an Advisory Board for Siemens Ultrasound and has a research collaboration with them, including joint funding by R01CA140271 for nonlinear elasticity imaging.Learning Objectives: Be reminded of the long history of palpation of tissue elasticity for critical medical diagnosis and the relatively recent advances to be able to image tissue strain in response to an applied force. Understand the differences between shear wave speed elasticity measurement and imaging and understand the factors affecting measurement and image frame repletion rates. Understand shear wave propagation effects that can affect measurements, such as essentially lack of propagation in fluids and boundary effects, so important in thin layers. Know characteristics of available elasticity imaging phantoms, their uses and limitations. Understand thermal and cavitational limitations affecting radiation force‐based shear wave imaging. Have learning and references adequate to for you to use in teaching elasticity imaging to residents and technologists. Be able to explain how elasticity measurement and imaging can contribute to diagnosis of breast and prostate cancer, staging of liver fibrosis, age estimation of deep veinous fhrombosis, confirmation of thermal lesions in the liver after RF ablation.

Standing shear waves in rubberlike layered media

Standing shear waves arising in layered media the shear modulus of which varies in a stepwise manner at the plain boundaries between the layers are considered. A general solution is obtained for the shear wave amplitudes in a resonator with an N-layer structure the lower boundary of which performs harmonic vibrations while a finite-mass plate is attached to the upper boundary. Results of calculations and measurements are presented for a resonator with a structure in which nondeformable metal layers alternate with elastic rubberlike polymer layers. It is shown that the resonance frequencies of such a resonator can be controlled by changing the number of layers and their thicknesses. It is demonstrated, both experimentally and theoretically, that, from the resonance curve of a resonator with a two-layer structure, it is possible to determine the shear modulus of one of the layers under the condition that the elasticity of the other layer is known. The method of separation into a finite number of layers is used to analyze the resonance characteristics of a one-dimensional resonator filled with a rubberlike medium the properties of which continuously vary in the direction perpendicular to the shear displacements. The choice of the number of layers depending on the type of inhomogeneity is analyzed.

Spatial stress and strain distributions of viscoelastic layers in oscillatory shear

One of the standard experimental probes of a viscoelastic material is to measure the response of a layer trapped between parallel surfaces, imposing either periodic stress or strain at one boundary and measuring the other. The relative phase between stress and strain yields solid-like and liquid-like properties, called the storage and loss moduli, respectively, which are then captured over a range of imposed frequencies. Rarely are the full spatial distributions of shear and normal stresses considered, primarily because they cannot be measured except at boundaries and the information was not deemed of particular interest in theoretical studies. Likewise, strain distributions throughout the layer were traditionally ignored except in a classical protocol of Ferry, Adler and Sawyer, based on snapshots of standing shear waves. Recent investigations of thin lung mucus layers exposed to oscillatory stress (breathing) and strain (coordinated cilia), however, suggest that the wide range of healthy conditions and environmental or disease assaults lead to conditions that are quite disparate from the “surface loading” and “gap loading” conditions that characterize classical rheometers. In this article, we extend our previous linear and nonlinear models of boundary stresses in controlled oscillatory strain to the entire layer. To illustrate non-intuitive heterogeneous responses, we characterize experimental conditions and material parameter ranges where the maximum stresses migrate into the channel interior.

Standing waves in an elastic layer loaded with a finite mass

Standing shear waves in a plane-parallel rubberlike layer fixed without slippage between two rigid plates with finite masses are investigated. The lower plate, which underlies the layer, oscillates in the direction parallel to its surface under an external harmonic force, whereas the upper plate freely overlies the layer. It is shown both theoretically and experimentally that such a system exhibits resonances at frequencies the values of which depend on the mass of the free plate and the shear modulus of the layer. The shapes of the resonance curves are calculated and measured for different values of parameters of the layer and different masses of the upper plate. From the measured resonance curves, it is possible to determine the dynamic shear modulus and the shear viscosity of the rubberlike material.

SPHEROIDAL AND TORSIONAL MODES OF QUASISTATIC SHEAR OSCILLATIONS IN THE SOLID GLOBE MODELS OF NUCLEAR PHYSICS AND PULSAR ASTROPHYSICS

The past three decades of investigation on nuclear physics and pulsar astrophysics have seen gradual recognition that elastodynamic approach to the continuum mechanics of nuclear matter provides proper account of macroscopic motions of degenerate Fermi-matter constituting interior of the nuclear material objects, the densest of all known today. This paper focuses on one theoretical issue of this development which is concerned with oscillatory behavior of a viscoelastic solid globe in the regime of quasistatic, force-free, noncompressional oscillations less investigated in the literature compared to oscillations in the regime of standing shear waves. We show that in this case the problem of computing frequency and lifetime of spheroidal and torsional modes of nonradial shear vibrations damped by viscosity can be unambiguously resolved by working from the energy balance equation and taking advantage of the Rayleigh's variational method. The efficiency of this method is demonstrated by solid globe models of nuclear physics and pulsar astrophysics dealing with oscillations of a spherical mass of a viscoelastic Fermi-solid with homogeneous and nonhomogeneous profiles of the bulk density, the shear modulus, and the shear viscosity.

Lattice resonances of a planar array of spherical inclusions: An experimental study

This paper is concerned with an experimental investigation of the excitation of lattice resonances in a single periodic (square) array of glass inclusions embedded in an elastic matrix. A normally-incident plane longitudinal wave is used to excite the resonances. The excitation of the lattice resonances is identified through a comparison of the transmission and reflection spectra of the periodic layer with those of an equivalent random layer. At the lattice-resonant frequencies, standing shear waves are excited within the plane of the layer along certain directions of lattice symmetry. These waves are measured along five different symmetry directions by the use of shear wave transducers. The transmission and reflection spectra reveal at least three lattice resonances; these are corroborated by the shear wave spectra.

The observation of viscous waves in a He I film

The transverse acoustic impedance of a 4He film has been measured at 3.11 K and 20.5 MHz and shows the occurence of standing shear waves in the film. This is in good agreement with calculations using transmission line theory and gives a new method of measuring the thickness of liquid films.