Dynamic Interaction Between Two Fluid-Filled Circular Pipelines in Saturated Poroelastic Medium Subjected to Harmonic Waves

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Xue-Qian Fang ◽  
Shao-Pu Yang ◽  
Jin-Xi Liu ◽  
Wen-Jie Feng
Keyword(s):  
Plane Waves ◽  
Closed Form Solution ◽  
Decomposition Theorem ◽  
Expansion Method ◽  
Addition Theorem ◽  
Dynamic Interaction ◽  
Cylindrical Wave ◽  
Form Solution ◽  
Two Fluid ◽  
Saturated Medium

A semi-analytical method is developed to investigate the dynamic interaction of two fluid-filled circular pipelines in a porous elastic fluid-saturated medium subjected to harmonic plane waves. The harmonic equations based on Biot's theory are reduced by Helmholtz decomposition theorem. The potentials in the fluid-saturated medium, in the linings, and inside the pipelines are expressed by wave function expansion method. The addition theorem for cylindrical wave functions is employed to obtain the closed-form solution in the form of infinite series. The hoop stress amplitudes around the pipelines are evaluated and discussed for the representative values of parameters characterizing the model. The effects of the proximity of two pipelines, the geometrical and material properties of linings, and the incident wave frequency on the dynamic stress around the pipelines are examined.

scholarly journals Dynamic Analysis of a Deeply Buried Tunnel Influenced by a Newly-built Adjacent Cavity with a Special Emphasis on the Minimum Seismically Safe Tunnel Distance

2021 ◽  
Author(s):  
Elefterija Zlatanović ◽  
Dragan Č. Lukić ◽  
Vlatko Šešov ◽  
Zoran Bonić
Keyword(s):  
Exact Analytical Solution ◽  
Closed Form Solution ◽  
Decomposition Theorem ◽  
Expansion Method ◽  
Addition Theorem ◽  
Transportation Systems ◽  
Form Solution ◽  
Infinite Length ◽  
Underground Structures ◽  
Plane Sv Waves

Contemporary life streams, more often than ever, impose the necessity for construction of new underground structures in the vicinity of existing tunnels, with an aim to accommodate transportation systems and utility networks. A previously uninvestigated case, in which a newly-constructed tunnel opening is closely positioned behind an existing tunnel, referred to as the tunnel–cavity configuration, has been considered in this study. An exact analytical solution is derived considering a pair of parallel circular cylindrical structures of infinite length, with the horizontal alignment, embedded in a boundless homogeneous, isotropic, elastic medium and excited by time-harmonic plane SV-waves under the plane-strain conditions. The Helmholtz decomposition theorem, the wave functions expansion method, the translational addition theorem for bi-cylindrical coordinates, and the pertinent boundary conditions are jointly employed in order to develop a closed-form solution of the corresponding boundary value problem. The primary goal of the present study is to examine the increase in dynamic stresses at an existing tunnel structure due to the presence of a closely driven unlined cavity, as well as in a localized region around the tunnel (at the position of the cavity in close proximity), under incident SV-waves. A new quantity called dynamic stress alteration factor is introduced and the aspect of the minimum seismically safe distance between the two structures is particularly considered.

Diffraction by a half-plane perpendicular to the distinguished axis of a general gyrotropic medium

1977 ◽  
Vol 55 (4) ◽  
pp. 305-324 ◽  
Author(s):  
S. Przeździecki ◽  
R. A. Hurd
Keyword(s):  
Half Plane ◽  
Fourier Transforms ◽  
Diffraction Problem ◽  
Plane Waves ◽  
Closed Form Solution ◽  
Basic Feature ◽  
Form Solution ◽  
Electromagnetic Plane Wave ◽  
Edge Diffraction ◽  
Special Cases

An exact, closed-form solution is found for the following half-plane diffraction problem: (I) The medium surrounding the half-plane is both electrically and magnetically gyrotropic. (II) The scattering half-plane is perfectly conducting and oriented perpendicular to the distinguished axis of the medium. (III) The incident electromagnetic plane wave propagates in a direction normal to the edge of the half-plane.The formulation of the problem leads to a coupled pair of Wiener–Hopf equations. These had previously been thought insoluble by quadratures, but yield to a newly discovered technique : the Wiener–Hopf–Hilbert method. A basic feature of the problem is its two-mode character i.e. plane waves of both modes are necessary for the spectral representation of the solution. The coupling of these modes is purely due to edge diffraction, there being no reflection coupling. The solution obtained is simple in that the Fourier transforms of the field components are just algebraic functions. Properties of the solution are investigated in some special cases.

scholarly journals Sound Radiation due to Modal Vibrations of a Spherical Source in an Acoustic Quarterspace

2004 ◽  
Vol 11 (5-6) ◽  
pp. 625-635 ◽  
Author(s):  
Seyyed M. Hasheminejad ◽  
Mahdi Azarpeyvand
Keyword(s):  
Acoustic Radiation ◽  
Classical Method ◽  
Spherical Wave ◽  
Closed Form Solution ◽  
Addition Theorem ◽  
Form Solution ◽  
Surface Velocity ◽  
Rigid Boundary ◽  
Radiation Impedance ◽  
Spherical Source

Radiation of sound from a spherical source, vibrating with an arbitrary, axisymmetric, time-harmonic surface velocity, while positioned within an acoustic quarterspace is analyzed in an exact manner. The formulation utilizes the appropriate wave field expansions along with the translational addition theorem for spherical wave functions in combination with the classical method of images to develop a closed-form solution in form of infinite series. The analytical results are illustrated with numerical examples in which the spherical source, vibrating in the pulsating (n= 0) and translational oscillating (n= 1) modes, is positioned near the rigid boundary of a water-filled quarterspace. Subsequently, the basic acoustic field quantities such as the modal acoustic radiation impedance load and the radiation intensity distribution are evaluated for representative values of the parameters characterizing the system.

scholarly journals The Sustainable Characteristic of Bio-Bi-Phase Flow of Peristaltic Transport of MHD Jeffrey Fluid in the Human Body

2018 ◽  
Vol 10 (8) ◽  
pp. 2671 ◽  
Author(s):  
Ahmed Zeeshan ◽  
Nouman Ijaz ◽  
Tehseen Abbas ◽  
Rahmat Ellahi
Keyword(s):  
Volume Fraction ◽  
Closed Form Solution ◽  
Pressure Rise ◽  
Expansion Method ◽  
Form Solution ◽  
Peristaltic Transport ◽  
Jeffrey Fluid ◽  
Physical Parameters ◽  
Phase Flow ◽  
Special Cases

This study deals with the peristaltic transport of non-Newtonian Jeffrey fluid with uniformly distributed identical rigid particles in a rectangular duct. The effects of a magnetohydrodynamics bio-bi-phase flow are taken into account. The governing equations for mass and momentum are simplified using the fact that wavelength is much greater than the amplitude and small Reynolds number. A closed-form solution for velocity is obtained by means of the eigenfunction expansion method whereby pressure rise is numerically calculated. The results are graphically presented to observe the effects of different physical parameters and the suitability of the method. The results for hydrodynamic, Newtonian fluid, and single-phase problems can be respectively obtained by taking the Hartmann number (M = 0), relaxation time (λ1=0), and volume fraction (C = 0) as special cases of this problem.

Pipeline VIV: Analytical Solution, Experiments and Parameter Identification

2009 ◽  
Author(s):  
Sergio B. Cunha ◽  
Cyntia G. C. Matt ◽  
Celso K. Morooka ◽  
Ricardo Franciss ◽  
Raphael I. Tsukada
Keyword(s):  
Closed Form Solution ◽  
Cross Flow ◽  
Form Solution ◽  
Beam Equation ◽  
Small Scale ◽  
Simply Supported ◽  
Fluid Forces ◽  
Fluid Damping ◽  
Flow Oscillations ◽  
Two Fluid

The study presents a closed-form solution for the vibration of a simply-supported beam due to vortex shedding, assuming linear elasticity and considering fluid damping. The in-line and cross-flow fluid forces are coupled to the beam equation as harmonic nonhomogeneous terms. Experimental results of 2 DOF VIV of a flexible small scale pipe in a uniform stream are presented for perpendicular an oblique (at 60 degrees of the translation direction) pipe. The range of relative velocity is from 1 to 10. The performance of two fluid damping models (Venugopal, 1996; Blevins – modified, 1990) is evaluated by comparing their predictions to the measurements of the in-line and cross-flow oscillations. Finally, ranges for in-line and cross-flow force coefficients are proposed and compared to the literature.

scholarly journals New Application of the(G′/G)-Expansion Method for Thin Film Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-6 ◽  
Author(s):  
Wafaa M. Taha ◽  
M. S. M. Noorani ◽  
I. Hashim
Keyword(s):  
Thin Film ◽  
Traveling Wave ◽  
Closed Form Solution ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Form Solution ◽  
Thin Film Equations ◽  
First Time ◽  
Positive Integers ◽  
Good Agreement

The(G′/G)-expansion method is used for the first time to find traveling wave solutions for thin film equations, where it is found that the related balance numbers are not the usual positive integers. The closed-form solution obtained via this method is in good agreement with the previously obtained solutions of other researchers. It is also noted that, for appropriate parameters, new solitary waves solutions are found.

Near-field behaviour of the fundamental elastodynamic solutions for a semi-infinite homogeneous isotropic elastic solid

1991 ◽  
Vol 433 (1887) ◽  
pp. 101-120 ◽  
Keyword(s):  
Near Field ◽  
Plane Waves ◽  
Elastic Solid ◽  
Expansion Method ◽  
Analytic Form ◽  
Fourier Integral ◽  
Cylindrical Wave ◽  
Singular Points ◽  
Scattering Problems ◽  
Natural Coordinate

This paper is concerned with the two-dimensional fields generated by time harmonic compression and shear line sources in a semi-infinite homogeneous isotropic elastic solid. It is well known that these elastodynamic states may easily be expressed as Fourier integral superpositions of plane waves in cartesian coordinates over a continuous spectrum of wavenumbers. The problem addressed here is that of determining the analytic form of these expressions in the neighbourhood of their singular points. The natural coordinate system for the problem is a cylindrical polar system centred at those singular points and thus the Fourier integrals are expanded in terms of cylindrical wave functions. The expansion method presented here is not special to the elasticity problem and has numerous important analytical applications in wave scattering problems in homogeneous and composite bodies.

On a Closed-Form Solution of Prandtl's System of Equations

2013 ◽  
Vol 40 (2) ◽  
pp. 106-114
Author(s):  
J. Venetis ◽  
Aimilios (Preferred name Emilios) Sideridis
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Of Equations

Plane Wave Resonance in the Tire Air Cavity as a Vehicle Interior Noise Source

1995 ◽  
Vol 23 (1) ◽  
pp. 2-10 ◽  
Author(s):  
J. K. Thompson
Keyword(s):  
Closed Form Solution ◽  
Form Solution ◽  
Interior Noise ◽  
Cavity Resonance ◽  
Test Results ◽  
Vehicle Interior ◽  
Air Cavity ◽  
Vehicle Interior Noise ◽  
Wave Resonance ◽  
Resonance Frequencies

Abstract Vehicle interior noise is the result of numerous sources of excitation. One source involving tire pavement interaction is the tire air cavity resonance and the forcing it provides to the vehicle spindle: This paper applies fundamental principles combined with experimental verification to describe the tire cavity resonance. A closed form solution is developed to predict the resonance frequencies from geometric data. Tire test results are used to examine the accuracy of predictions of undeflected and deflected tire resonances. Errors in predicted and actual frequencies are shown to be less than 2%. The nature of the forcing this resonance as it applies to the vehicle spindle is also examined.

Sign in / Sign up

Export Citation Format

Share Document