Guided Waves in a Fluid with Continuously Variable Velocity Overlying an Elastic Solid: Theory and Experiment

1960 ◽  
Vol 32 (1) ◽  
pp. 81-87 ◽  
Author(s):  
Ivan Tolstoy
Keyword(s):  
Guided Waves ◽  
Elastic Solid ◽  
Variable Velocity ◽  
Theory And Experiment

scholarly journals Mechanical cloak design by direct lattice transformation

2015 ◽  
Vol 112 (16) ◽  
pp. 4930-4934 ◽  
Author(s):  
Tiemo Bückmann ◽  
Muamer Kadic ◽  
Robert Schittny ◽  
Martin Wegener
Keyword(s):  
Lattice Theory ◽  
Solid Mechanics ◽  
Elastic Solid ◽  
Lattice Points ◽  
Coordinate Transformations ◽  
Constituent Material ◽  
Elasticity Tensors ◽  
Complex Boundary ◽  
Direct Lattice ◽  
Theory And Experiment

Spatial coordinate transformations have helped simplifying mathematical issues and solving complex boundary-value problems in physics for decades already. More recently, material-parameter transformations have also become an intuitive and powerful engineering tool for designing inhomogeneous and anisotropic material distributions that perform wanted functions, e.g., invisibility cloaking. A necessary mathematical prerequisite for this approach to work is that the underlying equations are form invariant with respect to general coordinate transformations. Unfortunately, this condition is not fulfilled in elastic–solid mechanics for materials that can be described by ordinary elasticity tensors. Here, we introduce a different and simpler approach. We directly transform the lattice points of a 2D discrete lattice composed of a single constituent material, while keeping the properties of the elements connecting the lattice points the same. After showing that the approach works in various areas, we focus on elastic–solid mechanics. As a demanding example, we cloak a void in an effective elastic material with respect to static uniaxial compression. Corresponding numerical calculations and experiments on polymer structures made by 3D printing are presented. The cloaking quality is quantified by comparing the average relative SD of the strain vectors outside of the cloaked void with respect to the homogeneous reference lattice. Theory and experiment agree and exhibit very good cloaking performance.

Dispersion Correction for Acoustic Multipole Logging on Guided Waves in Transversely Isotropic Medium

2014 ◽  
Vol 687-691 ◽  
pp. 732-735
Author(s):  
Li Zhang ◽  
H.X. Chen ◽  
M.X. Hao ◽  
X. Gao
Keyword(s):  
Perturbation Method ◽  
Isotropic Medium ◽  
Dispersion Characteristic ◽  
Guided Waves ◽  
Principal Axis ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Transversely Isotropic Medium ◽  
New Perturbation ◽  
Perturbation Solutions

A new and effective analytical perturbation method is presented for the multipole acoustic logging in a transversely isotropic medium (TIM) whose symmetric principal axis is parallel to the borehole axis although the exact solutions could be found. In this paper, the new perturbation method is adopted to simulate the dispersion characteristic in a borehole surrounded by a TIM for the first time. The TIM is regarded as a reference unperturbed isotropic state added to the perturbations, and three perturbation quantities about moduli deviated from the isotropic medium are introduced. By selecting a group of displacement potentials and a cylindrical coordinate system oriented along the borehole axis, the zero-, first-order and second-order perturbation solutions of the multipole acoustic field are derived for the weak transversely isotropic elastic solid which has its symmetric principal axis parallel to the borehole axis. The acoustic fields inside and outside the borehole excited by a multipole source are investigated. The dispersion characteristics in the borehole are numerically simulated by the perturbation method in the range of the second perturbation solutions. It is found that the dispersion characteristic by the perturbation method inside the borehole excited by monopole, dipole sources and quadrupole source are similar to obtained by the exact solution.

scholarly journals A THEORETICAL STUDY ON PROPAGATION OF GUIDED WAVES IN A FLUID LAYER OVERLYING A SOLID HALF-SPACE

2018 ◽  
Author(s):  
Haidang Phan
Keyword(s):  
Half Space ◽  
Guided Waves ◽  
Fluid Layer ◽  
Elastic Solid ◽  
Wave Mode ◽  
Ultrasonic Guided Waves ◽  
Harmonic Load ◽  
Closed Form Solutions ◽  
Time Harmonic ◽  
Potential Applications

Ultrasonic guided waves propagating in a fluid layer of uniform thickness bonded to an elastic solid half-space is theoretically investigated in this article. Based on the boundary conditions set for the joined configuration, a characteristic dispersion equation is found and new expressions for free guided waves are introduced. Closed-form solutions of guided waves generated by a time-harmonic load are derived by the use of elastodynamics reciprocity theorems. Through calculation examples, it is shown that the obtained computation of the lowest wave mode approaches the result of the Rayleigh wave in the solid half-space as the layer thickness approaches zero. The aim of the present work is to improve the understanding of wave motions in layered half-spaces for potential applications in the area of bone quantitative ultrasound

Potential Function for Acoustic Multipole Logging on Guided Waves in Transversely Isotropic Medium

2014 ◽  
Vol 716-717 ◽  
pp. 1318-1321
Author(s):  
Li Zhang ◽  
G.H. Wang ◽  
J.J. Lu
Keyword(s):  
Perturbation Method ◽  
Isotropic Medium ◽  
Dispersion Characteristic ◽  
Guided Waves ◽  
Principal Axis ◽  
Elastic Solid ◽  
Transversely Isotropic ◽  
Transversely Isotropic Medium ◽  
Axis Parallel ◽  
New Perturbation

A new and effective analytical perturbation method is presented for the multipole acoustic logging in a transversely isotropic medium (TIM) whose symmetric principal axis is parallel to the borehole axis although the exact solutions could be found. In this paper, the new perturbation method is adopted to simulate the dispersion characteristic in a borehole surrounded by a TIM for the first time. The TIM is regarded as a reference unperturbed isotropic state added to the perturbations, and three perturbation quantities about moduli deviated from the isotropic medium are introduced. By selecting a group of displacement potentials and a cylindrical coordinate system oriented along the borehole axis, the zero-, first-order and second-order perturbation solutions of the multipole acoustic field are derived for the weak transversely isotropic elastic solid which has its symmetric principal axis parallel to the borehole axis. It is found that the dispersion characteristic by the perturbation method inside the borehole excited by monopole, dipole sources and quadrupole source are similar to obtained by the exact solution.

Guided Waves in a Multi-Layered Cylindrical Elastic Solid Medium

2007 ◽  
Vol 24 (10) ◽  
pp. 2883-2886 ◽  
Author(s):  
Zhang Bi-Xing ◽  
Cui Han-Yin ◽  
Xiao Bo-Xun ◽  
Zhang Cheng-Guang
Keyword(s):  
Guided Waves ◽  
Solid Medium ◽  
Elastic Solid

Guided Waves Along Fluid-Filled Cracks in Elastic Solids and Instability at High Flow Rates

2012 ◽  
Vol 79 (3) ◽  
Author(s):  
Eric M. Dunham ◽  
Darcy E. Ogden
Keyword(s):  
Guided Waves ◽  
Flow Direction ◽  
Constant Width ◽  
Fluid Velocity ◽  
Elastic Solid ◽  
Momentum Balance ◽  
General Function ◽  
Sound Waves ◽  
Flow Rates ◽  
Barotropic Equation

We characterize wave propagation along an infinitely long crack or conduit in an elastic solid containing a compressible, viscous fluid. Fluid flow is described by quasi-one-dimensional mass and momentum balance equations with a barotropic equation of state, and the wall shear stress is written as a general function of width-averaged velocity, density, and conduit width. Our analysis focuses on small perturbations about steady flow, through a constant width conduit, at an unperturbed velocity determined by balancing the pressure gradient with drag from the walls. Short wavelength disturbances propagate relative to the fluid as sound waves with negligible changes in conduit width. The elastic walls become more compliant at longer wavelengths since strains induced by opening or closing the conduit are smaller, and the fluid compressibility becomes negligible. As wavelength increases, the sound waves transition to crack waves propagating relative to the fluid at a slower phase velocity that is inversely proportional to the square-root of wavelength. Associated with the waves are density, velocity, pressure, and width perturbations that alter drag. At sufficiently fast flow rates, crack waves propagating in the flow direction are destabilized when drag reduction from opening the conduit exceeds the increase in drag from increased fluid velocity. This instability may explain the occurrence of self-excited oscillations in fluid-filled cracks.

Electrostatic optics and aberration correction in the 1940s and today

1992 ◽  
Vol 50 (1) ◽  
pp. 6-7
Author(s):  
Gertrude F. Rempfer
Keyword(s):  
Electron Microscope ◽  
Focal Point ◽  
Focal Length ◽  
High Vacuum ◽  
Electron Optics ◽  
Applied Physics ◽  
Electrostatic Lenses ◽  
Commercial Instrument ◽  
The University ◽  
Theory And Experiment

I became involved in electron optics in early 1945, when my husband Robert and I were hired by the Farrand Optical Company. My husband had a mathematics Ph.D.; my degree was in physics. My main responsibilities were connected with the development of an electrostatic electron microscope. Fortunately, my thesis research on thermionic and field emission, in the late 1930s under the direction of Professor Joseph E. Henderson at the University of Washington, provided a foundation for dealing with electron beams, high vacuum, and high voltage.At the Farrand Company my co-workers and I used an electron-optical bench to carry out an extensive series of tests on three-electrode electrostatic lenses, as a function of geometrical and voltage parameters. Our studies enabled us to select optimum designs for the lenses in the electron microscope. We early on discovered that, in general, electron lenses are not “thin” lenses, and that aberrations of focal point and aberrations of focal length are not the same. I found electron optics to be an intriguing blend of theory and experiment. A laboratory version of the electron microscope was built and tested, and a report was given at the December 1947 EMSA meeting. The micrograph in fig. 1 is one of several which were presented at the meeting. This micrograph also appeared on the cover of the January 1949 issue of Journal of Applied Physics. These were exciting times in electron microscopy; it seemed that almost everything that happened was new. Our opportunities to publish were limited to patents because Mr. Farrand envisaged a commercial instrument. Regrettably, a commercial version of our laboratory microscope was not produced.

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