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.

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 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.

Exact Closed-Form Solution of the Nonlinear Fin Problem With Temperature-Dependent Thermal Conductivity and Heat Transfer Coefficient

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Mahdi Anbarloei ◽  
Elyas Shivanian
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Exact Analytical Solution ◽  
Closed Form Solution ◽  
Form Solution ◽  
Temperature Dependent ◽  
Fin Efficiency ◽  
Temperature Dependent Thermal Conductivity

In the current paper, the nonlinear fin problem with temperature-dependent thermal conductivity and heat transfer coefficient is revisited. In this problem, it has been assumed that the heat transfer coefficient is expressed in a power-law form and the thermal conductivity is a linear function of temperature. It is shown that its governing nonlinear differential equation is exactly solvable. A full discussion and exact analytical solution in the implicit form are given for further physical interpretation and it is proved that three possible cases may occur: there is no solution to the problem, the solution is unique, and the solutions are dual depending on the values of the parameters of the model. Furthermore, we give exact analytical expressions of fin efficiency as a function of thermogeometric fin parameter.

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.

The Overall Elastic Dielectric Properties of Fiber-Strengthened/Weakened Elastomers

2015 ◽  
Vol 82 (11) ◽  
Author(s):  
Victor Lefèvre ◽  
Oscar Lopez-Pamies
Keyword(s):  
Dielectric Properties ◽  
Volume Fraction ◽  
Exact Analytical Solution ◽  
Closed Form Solution ◽  
Dielectric Elastomer ◽  
Form Solution ◽  
Dielectric Elastomers ◽  
Filler Materials ◽  
Elastomer Composites ◽  
Elastic Dielectric

By employing recent results (Lopez-Pamies, O., 2014, “Elastic Dielectric Composites: Theory and Application to Particle-Filled Ideal Dielectrics,” J. Mech. Phys. Solids, 64, p. 6182 and Spinelli, S. A., Lefèvre, V., and Lopez-Pamies, O., “Dielectric Elastomer Composites: A General Closed-Form Solution in the Small-Deformation Limit,” J. Mech. Phys. Solids, 83, pp. 263–284.) on the homogenization problem of dielectric elastomer composites, an approximate solution is generated for the overall elastic dielectric response of elastomers filled with a transversely isotropic distribution of aligned spheroidal particles in the classical limit of small deformations and moderate electric fields. The solution for such a type of dielectric elastomer composites is characterized by 13 (five elastic, two dielectric, and six electrostrictive) effective constants. Explicit formulae are worked out for these constants directly in terms of the elastic dielectric properties of the underlying elastomer and the filler particles, as well as the volume fraction, orientation, and aspect ratio of the particles. As a first application of the solution, with the objective of gaining insight into the effect that the addition of anisotropic fillers can have on the electromechanical properties of elastomers, sample results are presented for the case of elastomers filled with aligned cylindrical fibers. These results are confronted to a separate exact analytical solution for an assemblage of differential coated cylinders (DCC), wherein the fibers are polydisperse in size, and to full-field simulations of dielectric elastomer composites with cylindrical fibers of monodisperse size. These results serve to shed light on the recent experimental findings concerning the dielectric elastomers filled with mechanically stiff fibers. Moreover, they serve to reveal that high-permittivity liquid-like or vacuous fibers—two classes of filler materials yet to be explored experimentally—have the potential to significantly enhance the electrostriction capabilities of dielectric elastomers.

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.

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