scholarly journals Acoustic trapped modes in a three-dimensional waveguide of slowly varying cross section

2013 ◽  
Vol 469 (2149) ◽  
pp. 20120384 ◽  
Author(s):  
Simon N. Gaulter ◽  
Nicholas R. T. Biggs
Keyword(s):  
Cross Section ◽  
Turning Point ◽  
Harmonic Wave ◽  
Three Dimensional ◽  
Longitudinal Direction ◽  
Interior Layer ◽  
Oscillatory Behaviour ◽  
Trapped Modes ◽  
Trapped Mode ◽  
Time Harmonic

In this paper, we develop an asymptotic scheme to approximate the trapped mode solutions to the time harmonic wave equation in a three-dimensional waveguide with a smooth but otherwise arbitrarily shaped cross section and a single, slowly varying ‘bulge’, symmetric in the longitudinal direction. Extending previous research carried out in the two-dimensional case, we first use a WKBJ-type ansatz to identify the possible quasi-mode solutions that propagate only in the thicker region, and hence find a finite cut-on region of oscillatory behaviour and asymptotic decay elsewhere. The WKBJ expansions are used to identify a turning point between the cut-on and cut-off regions. We note that the expansions are non-uniform in an interior layer centred on this point, and we use the method of matched asymptotic expansions to connect the cut-on and cut-off regions within this layer. The behaviour of the expansions within the interior layer then motivates the construction of a uniformly valid asymptotic expansion. Finally, we use this expansion and the symmetry of the waveguide around the longitudinal centre, x =0, to extract trapped mode wavenumbers, which are compared with those found using a numerical scheme and seen to be extremely accurate, even to relatively large values of the small parameter.

scholarly journals Wave Propagation in X-Section Piles for Low Strain Integrity Testing: Three-Dimensional Effects

2020 ◽  
Vol 2020 ◽  
pp. 1-10
Author(s):  
Yanling Zhang ◽  
Yuming Fan ◽  
Zheng Li ◽  
Chenglong Wang ◽  
Xuanming Ding
Keyword(s):  
Wave Propagation ◽  
Cross Section ◽  
Three Dimensional ◽  
Longitudinal Direction ◽  
Propagation Characteristic ◽  
Scale Model ◽  
Geometrical Parameters ◽  
Response Characteristics ◽  
Dimensional Effects ◽  
Velocity Response

X-section cast-in-place concrete pile (referred to as XCC pile) has a different velocity response compared with circular section pile in the low strain testing due to the special cross section. Full-scale model tests of XCC pile were conducted to reveal the velocity response characteristics. The time-domain velocity responses on the pile top were obtained, which showed obvious three-dimensional effects because of the different high-frequency interferences. The test results were compared with the numerical results to validate the numerical model. Furthermore, numerical simulations were conducted to investigate the propagation characteristic of velocity waves along the longitudinal direction in the pile. The results indicated that the wave propagation was complicated as a result of the superposition of the incident wave and the reflected wave. The effects of the geometrical parameters of cross section on the three-dimensional effects of velocity responses were also studied. Three-dimensional effects would be more significant with a larger arc distance. However, the effects of arc angle were not obvious.

SAF file: It's really three dimensional file

2018 ◽  
Vol 14 (1) ◽  
pp. 1
Author(s):  
Prof. Dr. Jamal Aziz Mehdi
Keyword(s):  
Cross Section ◽  
Root Canal ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Circular Motion ◽  
Root Canal Treatment ◽  
Metal Core ◽  
Rotating Blade

The biological objectives of root canal treatment have not changed over the recentdecades, but the methods to attain these goals have been greatly modified. Theintroduction of NiTi rotary files represents a major leap in the development ofendodontic instruments, with a wide variety of sophisticated instruments presentlyavailable (1, 2).Whatever their modification or improvement, all of these instruments have onething in common: they consist of a metal core with some type of rotating blade thatmachines the canal with a circular motion using flutes to carry the dentin chips anddebris coronally. Consequently, all rotary NiTi files will machine the root canal to acylindrical bore with a circular cross-section if the clinician applies them in a strictboring manner

ANALYSIS OF THE GENERAL EQUATIONS OF THE TRANSVERSE VIBRATION OF A PIECEWISE UNIFORM VISCOELASTIC PLATE

2020 ◽  
Vol 7 (3) ◽  
pp. 52-56
Author(s):  
MMATMATISA JALILOV ◽  
◽  
RUSTAM RAKHIMOV ◽  
Keyword(s):  
Cross Section ◽  
Transverse Vibration ◽  
Three Dimensional ◽  
Viscoelastic Plate ◽  
Constant Thickness ◽  
Regional Problem ◽  
Rigid Contact ◽  
Under Construction ◽  
Derivatives Of ◽  
Theoretical Results

This article discusses the analysis of the general equations of the transverse vibration of a piecewise homogeneous viscoelastic plate obtained in the “Oscillation of inlayer plates of constant thickness” [1]. In the present work on the basis of a mathematical method, the approached theory of fluctuation of the two-layer plates, based on plate consideration as three dimensional body, on exact statement of a three dimensional mathematical regional problem of fluctuation is stood at the external efforts causing cross-section fluctuations. The general equations of fluctuations of piecewise homogeneous viscoelastic plates of the constant thickness, described in work [1], are difficult on structure and contain derivatives of any order on coordinates x, y and time t and consequently are not suitable for the decision of applied problems and carrying out of engineering calculations. For the decision of applied problems instead of the general equations it is expedient to use confidants who include this or that final order on derivatives. The classical equations of cross-section fluctuation of a plate contain derivatives not above 4th order, and for piecewise homogeneous or two-layer plates the elementary approached equation of fluctuation is the equation of the sixth order. On the basis of the analytical decision of a problem the general and approached decisions of a problem are under construction, are deduced the equation of fluctuation of piecewise homogeneous two-layer plates taking into account rigid contact on border between layers, and also taking into account mechanical and rheological properties of a material of a plate. The received theoretical results for the decision of dynamic problems of cross-section fluctuation of piecewise homogeneous two-layer plates of a constant thickness taking into account viscous properties of their material allow to count more precisely the is intense-deformed status of plates at non-stationary external loadings.

Boundary element method in numerical study of three-dimensional Stokes flows in channels of arbitrary shape

2012 ◽  
Vol 9 (1) ◽  
pp. 94-97
Author(s):  
Yu.A. Itkulova
Keyword(s):  
Boundary Element Method ◽  
Boundary Element ◽  
Cross Section ◽  
Numerical Study ◽  
Three Dimensional ◽  
Cylindrical Tube ◽  
Variable Cross Section ◽  
Variable Cross ◽  
Periodic Flows ◽  
Element Method

In the present work creeping three-dimensional flows of a viscous liquid in a cylindrical tube and a channel of variable cross-section are studied. A qualitative triangulation of the surface of a cylindrical tube, a smoothed and experimental channel of a variable cross section is constructed. The problem is solved numerically using boundary element method in several modifications for a periodic and non-periodic flows. The obtained numerical results are compared with the analytical solution for the Poiseuille flow.

On the Flexural-Torsional Behavior of a Straight Elastic Beam Subject to Terminal Moments

1993 ◽  
Vol 60 (2) ◽  
pp. 498-505 ◽  
Author(s):  
Z. Tan ◽  
J. A. Witz
Keyword(s):  
Coordinate System ◽  
Cross Section ◽  
Equilibrium Equation ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Elastic Beam ◽  
Cartesian Coordinate System ◽  
Kinematic Constraints ◽  
Torsional Behavior ◽  
Cartesian Coordinate

This paper discusses the large-displacement flexural-torsional behavior of a straight elastic beam with uniform circular cross-section subject to arbitrary terminal bending and twisting moments. The beam is assumed to be free from any kinematic constraints at both ends. The equilibrium equation is solved analytically with the full expression for curvature to obtain the deformed configuration in a three-dimensional Cartesian coordinate system. The results show the influence of the terminal moments on the beam’s deflected configuration.

Long waves in a straight channel with non-uniform cross-section

2015 ◽  
Vol 770 ◽  
pp. 156-188 ◽  
Author(s):  
Patricio Winckler ◽  
Philip L.-F. Liu
Keyword(s):  
Boundary Layer ◽  
Wave Propagation ◽  
Cross Section ◽  
Three Dimensional ◽  
Channel Cross Section ◽  
Cross Sectional ◽  
New Model ◽  
One Dimensional ◽  
Uniform Channel ◽  
The Cross

A cross-sectionally averaged one-dimensional long-wave model is developed. Three-dimensional equations of motion for inviscid and incompressible fluid are first integrated over a channel cross-section. To express the resulting one-dimensional equations in terms of the cross-sectional-averaged longitudinal velocity and spanwise-averaged free-surface elevation, the characteristic depth and width of the channel cross-section are assumed to be smaller than the typical wavelength, resulting in Boussinesq-type equations. Viscous effects are also considered. The new model is, therefore, adequate for describing weakly nonlinear and weakly dispersive wave propagation along a non-uniform channel with arbitrary cross-section. More specifically, the new model has the following new properties: (i) the arbitrary channel cross-section can be asymmetric with respect to the direction of wave propagation, (ii) the channel cross-section can change appreciably within a wavelength, (iii) the effects of viscosity inside the bottom boundary layer can be considered, and (iv) the three-dimensional flow features can be recovered from the perturbation solutions. Analytical and numerical examples for uniform channels, channels where the cross-sectional geometry changes slowly and channels where the depth and width variation is appreciable within the wavelength scale are discussed to illustrate the validity and capability of the present model. With the consideration of viscous boundary layer effects, the present theory agrees reasonably well with experimental results presented by Chang et al. (J. Fluid Mech., vol. 95, 1979, pp. 401–414) for converging/diverging channels and those of Liu et al. (Coast. Engng, vol. 53, 2006, pp. 181–190) for a uniform channel with a sloping beach. The numerical results for a solitary wave propagating in a channel where the width variation is appreciable within a wavelength are discussed.

Microstructure Evolution of Epitaxial (Ba, Sr) TiO3/ (001) HgO Thin Films

1994 ◽  
Vol 361 ◽  
Author(s):  
V.A. Alyoshin ◽  
E.V. Sviridov ◽  
V.I.M. Hukhortov ◽  
I.H. Zakharchenko ◽  
V.P. Dudkevich
Keyword(s):  
Thin Films ◽  
Cross Section ◽  
Microstructure Evolution ◽  
Three Dimensional ◽  
Gas Pressure ◽  
Smooth Surfaces ◽  
Two Dimensional ◽  
Surface Versus ◽  
Deposition Conditions

ABSTRACTSurface and cross-section relief evolution of ferroelectric epitaxial (Ba,Sr)TiO3 films rf-sputtered on (001) HgO crystal cle-avage surface versus the oxygen worKing gas pressure P and subst-rate temperature T were studied. Specific features of both three-dimensional and two-dimensional epitaxy mechanisms corresponding to various deposition conditions were revealed. Difference between low and high P-T-value 3D epitaxy was established. The deposition of films with mirror-smooth surfaces and perfect interfaces is shown to be possible.

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