scholarly journals Explicit Analytic Solution for the Plane Elastostatic Problem with a Rigid Inclusion of Arbitrary Shape Subject to Arbitrary Far-Field Loadings

2021 ◽  
Author(s):  
Ornella Mattei ◽  
Mikyoung Lim
Keyword(s):  
Rigid Inclusion ◽  
Arbitrary Shape ◽  
Analytic Solution ◽  
Far Field ◽  
Explicit Analytic Solution ◽  
Elastostatic Problem

scholarly journals Breaking the acoustic diffraction limit with an arbitrary shape acoustic magnifying lens

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Ali Abdolali ◽  
Hooman Barati Sedeh ◽  
Mohammad Hosein Fakheri ◽  
Chen Shen ◽  
Fei Sun
Keyword(s):  
Arbitrary Shape ◽  
Design Principle ◽  
Focused Ultrasound ◽  
Effective Medium Theory ◽  
Wide Spectrum ◽  
Diffraction Limit ◽  
Far Field ◽  
Biomedical Sensors ◽  
Focused Ultrasound Surgery ◽  
Unit Cells

AbstractBased on the transformation acoustics methodology, the design principle for achieving an arbitrary shape magnifying lens (ASML) is proposed. Contrary to the previous works, the presented ASML is competent of realizing far-field high resolution images and breaking the diffraction limit, regardless of the position of the utilized sources. Therefore, objects locating within the designed ASML can be properly resolved in the far-field region. It is shown that the obtained material through the theoretical investigations becomes an acoustic null medium (ANM), which has recently gained a significant attention. Besides the homogeneity of ANM, which makes it an implementable material, it is also independent of the perturbation in the geometry of the lens, in such a way that the same ANM can be used for different structural topologies. The obtained ANM has been implemented via acoustics unit cells formed by membranes and side branches with open ends and then was utilized to realize an ASML with the aid of effective medium theory. It is shown that the far-field results of an ideal ASML abide well with the results of the implemented sample, validating the proposed design principle. The presented acoustic magnifying lens has a wide spectrum of possible applications ranging from medical imaging, and biomedical sensors to focused ultrasound surgery.

scholarly journals An analytical and experimental investigation of aerofoil–turbulence interaction noise for plates with spanwise-varying leading edges

2019 ◽  
Vol 865 ◽  
pp. 137-168 ◽  
Author(s):  
Lorna J. Ayton ◽  
Paruchuri Chaitanya
Keyword(s):  
Noise Reduction ◽  
Analytic Solution ◽  
Piecewise Linear ◽  
Separation Of Variables ◽  
Leading Edge ◽  
Test Case ◽  
Far Field ◽  
Mean Flow ◽  
Flat Plates ◽  
Leading Edges

This paper presents an analytic solution for gust–aerofoil interaction noise for flat plates with spanwise-varying periodic leading edges in uniform mean flow. The solution is obtained by solving the linear inviscid equations via separation of variables and the Wiener–Hopf technique, and is suitable for calculating the far-field noise generated by any leading edge with a single-valued piecewise linear periodic spanwise geometry. Acoustic results for homogeneous isotropic turbulent flow are calculated by integrating the single-gust solution over a wavenumber spectrum. The far-sound pressure level is calculated for five test-case geometries; sawtooth serration, slitted $v$-root, slitted $u$-root, chopped peak and square wave, and compared to experimental measurements. Good agreement is seen over a range of frequencies and tip-to-root ratios (varying the sharpness of the serration). The analytic solution is then used to calculate the propagating pressure along the leading edge of the serration for fixed spanwise wavenumbers, i.e. only the contribution to the surface pressure which propagates to the far field. Using these results, two primary mechanisms for noise reduction are discussed; tip and root interference, and a redistribution of energy from cuton modes to cutoff modes. A secondary noise-reduction mechanism due to nonlinear features is also discussed and seen to be particularly important for leading edges with very narrow slits.

Some problems concerning the production of a linear shear flow using curved wire-gauze screens

1976 ◽  
Vol 76 (4) ◽  
pp. 689-709 ◽  
Author(s):  
I. P. Castro
Keyword(s):  
Shear Flow ◽  
Incompressible Fluid ◽  
Experimental Work ◽  
Arbitrary Shape ◽  
Practical Problem ◽  
Analytic Solution ◽  
Linear Shear ◽  
Wire Gauze ◽  
The Common ◽  
Small Shear

The flow of an incompressible fluid through a curved wire-gauze screen of arbitrary shape is reconsidered. Some inconsistencies in previously published papers are indicated and the various approximations and linearizations (some of which are necessary for a complete analytic solution) are discussed and their inadequacies demonstrated. Attention is concentrated on the common practical problem of calculating the screen shape required to produce a linear shear flow and experimental work is presented which supports the contention that the theoretical solutions proposed by Elder (1959)–subsequently discussed by Turner (1969) and Livesey & Laws (1973)-and Lau & Baines (1968) are inadequate, although, for the case of small shear, Elder's theory appears to be satisfactory. Since, in addition, there are inevitable difficulties concerning both the value of the deflexion coefficient appropriate to any particular screen and inhomogeneities in the screen itself, it is concluded that the preparation of a curved screen to produce the commonly required moderate to large linear shear flow is bound to be somewhat empirical and should be attempted with caution.

Explicit Analytic Solution for Inverse Kinematics of Bioloid Humanoid Robot

2012 ◽  
Author(s):  
J. Victor Nunez ◽  
Abraham Briseno ◽  
Dora A. Rodriguez ◽  
J. Manuel Ibarra ◽  
Victor M. Rodriguez
Keyword(s):  
Inverse Kinematics ◽  
Humanoid Robot ◽  
Analytic Solution ◽  
Explicit Analytic Solution

General analytic solution for far-field phase and amplitude control, with a phase-only spatial light modulator

2014 ◽  
Vol 39 (7) ◽  
pp. 2137 ◽  
Author(s):  
Lewis Z. Liu ◽  
Kevin O’Keeffe ◽  
David T. Lloyd ◽  
Simon M. Hooker
Keyword(s):  
Spatial Light Modulator ◽  
Analytic Solution ◽  
Far Field ◽  
Field Phase ◽  
Light Modulator ◽  
Amplitude Control

scholarly journals NUMERICAL CALCULATION OF SEICHE MOTIONS IN HARBOURS OF ARBITRARY SHAPE

1982 ◽  
Vol 1 (18) ◽  
pp. 11
Author(s):  
P. Gaillard
Keyword(s):  
Finite Element ◽  
Numerical Calculation ◽  
Arbitrary Shape ◽  
Wave Pattern ◽  
Offshore Structures ◽  
Experimental Investigations ◽  
Far Field ◽  
Method Of Calculation ◽  
Long Wave ◽  
Element Technique

A new method of calculation of wave diffraction around islands, offshore structures, and of long wave oscillations within offshore or shore-connected harbours is presented. The method is a combination of the finite element technique with an analytical representation of the wave pattern in the far field. Examples of application are given, and results are compared with other theoretical and experimental investigations.

Approximate explicit analytic solution of the Elenbaas-Heller equation

2016 ◽  
Vol 120 (6) ◽  
pp. 063304 ◽  
Author(s):  
Meng-Ran Liao ◽  
Hui Li ◽  
Wei-Dong Xia
Keyword(s):  
Analytic Solution ◽  
Explicit Analytic Solution
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