scholarly journals Diffraction by a rigid strip in a plate modelled by Mindlin theory

2020 ◽  
Vol 476 (2243) ◽  
pp. 20200648
Author(s):  
Ian Thompson
Keyword(s):  
Boundary Conditions ◽  
Low Frequency ◽  
Mindlin Plate ◽  
Flexural Wave ◽  
Far Field ◽  
Matrix Problem ◽  
Frequency Limit ◽  
Scalar Problem ◽  
Simple Method ◽  
Kirchhoff Model

We consider a plane flexural wave incident on a semi-infinite rigid strip in a Mindlin plate. The boundary conditions on the strip lead to three Wiener–Hopf equations, one of which decouples, leaving a scalar problem and a 2 × 2 matrix problem. The latter is solved using a simple method based on quadrature. The far-field diffraction coefficient is calculated and some numerical results are presented. We also show how the results reduce to the simpler Kirchhoff model in the low-frequency limit.

A Refinement of Mindlin Plate Theory Using Simultaneous Rotary Inertia and Shear Correction Factors

2018 ◽  
Vol 140 (3) ◽  
Author(s):  
Andrew N. Norris
Keyword(s):  
High Frequency ◽  
Plate Theory ◽  
Low Frequency ◽  
Rotary Inertia ◽  
Mindlin Plate ◽  
Flexural Wave ◽  
Correction Factors ◽  
Flexural Mode ◽  
Mode Dispersion ◽  
Mindlin Plate Theory

We revisit Mindlin's theory for flexural dynamics of plates using two correction factors, one for shear and one for rotary inertia. Mindlin himself derived and considered his equations with both correction factors, but never with the two simultaneously. Here, we derive optimal values of both factors by matching the Mindlin frequency–wavenumber branches with the exact Rayleigh–Lamb dispersion relations. The thickness shear resonance frequency is obtained if the factors are proportional but otherwise arbitrary. This degree-of-freedom allows matching of the main flexural mode dispersion with the exact Lamb wave at either low or high frequency by choosing the shear correction factor as a function of Poisson's ratio. At high frequency, the shear factor takes the value found by Mindlin, while at low frequency, it assumes a new explicit form, which is recommended for flexural wave modeling.

Borehole flexural modes in transversely isotropic formations: Low-frequency asymptotic velocity

Geophysics ◽  
2009 ◽  
Vol 74 (4) ◽  
pp. E149-E158 ◽  
Author(s):  
Xiao He ◽  
Hengshan Hu
Keyword(s):  
Low Frequency ◽  
Transversely Isotropic ◽  
Shear Velocity ◽  
Petroleum Engineering ◽  
Flexural Wave ◽  
Branch Points ◽  
Frequency Limit ◽  
Reflection Function ◽  
Flexural Mode ◽  
A Value

Dipole acoustic logging is widely used for in situ measurement of formation shear velocity. This technique is based on the theoretical result in isotropic formations that the velocity of the dispersive flexural mode approaches the shear velocity at the low-frequency limit. Transversely isotropic (TI) formations frequently are encountered in petroleum engineering, so it is necessary to determine if shear velocity along the borehole can be determined from the low-frequency flexural wave in TI cases. The flexural wave in a borehole parallel to the symmetry axis of a TI formation is investigated. The borehole acoustic field is formulated in the frequency-wavenumber domain as the sum of a direct field from the source and a reflected field from the borehole wall. Poles and branch points of the reflection coefficient are analyzed, and component waves contributed by those singularities are calculated. The dispersion feature of the flexural mode in some TI formations differs from isotropic cases. The low-frequency limit of flexural-mode velocity trends to a value lower than the shear velocity when parameters of the formation satisfy [Formula: see text], where [Formula: see text] and [Formula: see text] are Thomsen parameters and [Formula: see text] and [Formula: see text] are the elastic moduli. That asymptotic value corresponds to a newly found branch point of the reflection function. Numerical results show that the low-frequency flexural wave travels slower than the shear wave in the synthetic full waveforms in Mesaverde clayshale 5501. Extracting the shear velocity from the flexural arrival leads to inaccuracy on the order of 10% in this formation.

Evaluation of Special Hearing Aids for Deaf Children

1971 ◽  
Vol 36 (4) ◽  
pp. 527-537 ◽  
Author(s):  
Norman P. Erber
Keyword(s):  
Hearing Aids ◽  
High Frequency ◽  
Hearing Aid ◽  
Low Frequency ◽  
Acoustic Stimulation ◽  
Deaf Children ◽  
Frequency Range ◽  
Frequency Limit ◽  
Unpublished Studies ◽  
Published Research

Two types of special hearing aid have been developed recently to improve the reception of speech by profoundly deaf children. In a different way, each special system provides greater low-frequency acoustic stimulation to deaf ears than does a conventional hearing aid. One of the devices extends the low-frequency limit of amplification; the other shifts high-frequency energy to a lower frequency range. In general, previous evaluations of these special hearing aids have obtained inconsistent or inconclusive results. This paper reviews most of the published research on the use of special hearing aids by deaf children, summarizes several unpublished studies, and suggests a set of guidelines for future evaluations of special and conventional amplification systems.

Onset of size effects in lattice thermal conductivity and lifetime of low-frequency thermal phonons

2012 ◽  
Vol 1404 ◽  
Author(s):  
A.A. Maznev
Keyword(s):  
Thin Film ◽  
Thermal Conductivity ◽  
Size Effects ◽  
Lattice Thermal Conductivity ◽  
Low Frequency ◽  
Square Root ◽  
Relaxation Rates ◽  
Frequency Limit ◽  
Conductivity Of Thin Films ◽  
Closed Form Formula

ABSTRACTThe onset of size effects in phonon-mediated thermal transport along a thin film at temperatures comparable or greater than the Debye temperature is analyzed theoretically. Assuming a quadratic frequency dependence of phonon relaxation rates in the low-frequency limit, a simple closed-form formula for the reduction of the in-plane thermal conductivity of thin films is derived. The effect scales as the square root of the film thickness, which leads to the prediction of measurable size-effects even at “macroscopic” distances ~100 μm. However, this prediction needs to be corrected to account for the deviation from the ω−2 dependence of phonon lifetimes at sub-THz frequencies due to the transition from Landau-Rumer to Akhiezer mechanism of phonon dissipation.

scholarly journals Nonlinear interaction between acoustic gravity waves

1996 ◽  
Vol 14 (3) ◽  
pp. 304-308 ◽  
Author(s):  
P. Axelsson ◽  
J. Larsson ◽  
L. Stenflo
Keyword(s):  
Gravity Waves ◽  
Nonlinear Interaction ◽  
Low Frequency ◽  
Resonant Interaction ◽  
Coupling Coefficients ◽  
Symmetric Form ◽  
Frequency Limit ◽  
Acoustic Gravity Waves

Abstract. The resonant interaction between three acoustic gravity waves is considered. We improve on the results of previous authors and write the new coupling coefficients in a symmetric form. Particular attention is paid to the low-frequency limit.

Determination of Electric and Magnetic Properties of Commercial LTCC Soft Ferrite Material

2011 ◽  
Vol 8 (1) ◽  
pp. 1-9 ◽  
Author(s):  
Nelu Blaž ◽  
Andrea Marić ◽  
Goran Radosavljević ◽  
Nebojša Mitrović ◽  
Ibrahim Atassi ◽  
...  
Keyword(s):  
Electrical Properties ◽  
Low Frequency ◽  
Hysteresis Loops ◽  
Frequency Range ◽  
Dispersion Parameters ◽  
Simple Method ◽  
Component Design ◽  
Microwave Engineering ◽  
Characterization Procedure

This paper offers an effective, accurate, and simple method for permittivity and permeability determination of an LTCC (low temperature cofired ceramic) ferrite sample. The presented research can be of importance in the fields of ferrite component design and application, as well as for RF and microwave engineering. The characterization sample is a stack of LTCC tapes forming a toroid. Commercially available ferrite tape ESL 40012 was used and standard LTCC processing was applied for the sample fabrication. For the first time, the electrical properties of a ferrite toroid sample of ESL 40012 LTCC ferrite tape is presented at various frequencies. The electrical properties of LTCC ferrite materials, permittivity and specific resistivity, are shown in a frequency range from 10 kHz to 1 MHz using the capacitive method. The hysteresis properties of this material are also determined. B-H hysteresis loops were measured applying a maximum excitation of 2 kA/m and frequencies of 50 Hz, 500 Hz, and 1000 Hz. Permeability is determined in the frequency range from 10 kHz to 1 GHz and a characterization procedure is divided in two segments, for low and high frequencies. Low frequency measurements (from 10 kHz to 1 MHz) are performed using LCZ meter and discrete turns of wire, while a short coaxial sample holder and vector network analyzer were used for the higher frequency range (from 300 kHz to 1 GHz). In addition, another important factor required for the practical design of devices is presented, the temperature variation of the permeability dispersion parameters.

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