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.

Radiation Loading of a Cylindrical Source in a Fluid-Filled Cylindrical Cavity Embedded Within a Fluid-Saturated Poroelastic Medium

2002 ◽  
Vol 69 (5) ◽  
pp. 675-683 ◽  
Author(s):  
S. M. Hasheminejad ◽  
H. Hosseini
Keyword(s):  
Seismic Waves ◽  
Acoustic Radiation ◽  
Surrounding Medium ◽  
Practical Importance ◽  
Closed Form Solution ◽  
Form Solution ◽  
Radiation Impedance ◽  
Harmonic Field ◽  
Cylindrical Source ◽  
Water Saturated

Radiation loading on a vibrating structure is best described through its radiation impedance. In the present work the modal acoustic radiation impedance load on an infinitely long cylindrical source harmonically excited in circumferentially periodic (axially independent) spatial pattern, while positioned concentrically within a fluid cylinder, which is embedded in a fluid-saturated unbounded elastic porous medium, is computed. This configuration, which is a realistic idealization of an acoustic logging tool suspended in a fluid-filled borehole within a permeable surrounding formation (White, J. E., 1983, Underground Sound Application of Seismic Waves, Elsevier, Amsterdam, Fig. 5.29, p. 183), is of practical importance with a multitude of possible applications in seismo-acoustics and noise control engineering. The formulation utilizes the Biot phenomenological model to represent the behavior of the sound in the porous, fluid-saturated, macroscopically homogeneous and isotropic surrounding medium. Employing the appropriate wave-harmonic field expansions and the pertinent boundary conditions for the given boundary configuration, a closed-form solution in the form of an infinite series is developed and the resistive and reactive components of modal radiation impedances are determined. A numerical example for a cylindrical surface excited in vibrational modes of various order, immersed in a water-filled cavity which is embedded within a water-saturated Ridgefield sandstone environment, is presented and several limiting cases are examined. Effects of porosity, frame stiffness, source size, and the interface permeability condition on the impedance values are presented and discussed.

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.

COMPUTATION OF ACOUSTIC FIELD RADIATED BY A SPHERICAL SOURCE NEAR A THERMOVISCOUS FLUID SPHERE

2007 ◽  
Vol 15 (02) ◽  
pp. 159-180
Author(s):  
S. M. HASHEMINEJAD ◽  
A. H. PASDAR
Keyword(s):  
Acoustic Field ◽  
Acoustic Radiation ◽  
Conducting Fluid ◽  
Surface Velocity ◽  
Fluid Sphere ◽  
Spherical Source ◽  
Fluid Medium ◽  
Multiple Precision ◽  
Thermally Conducting ◽  
Thermoviscous Fluid

Acoustic radiation from a spherical source, vibrating with an arbitrary, axisymmetric, time-harmonic surface velocity distribution, while immersed near a thermoviscous fluid sphere suspended in an unbounded viscous thermally conducting fluid medium is computed. The formulation utilizes the appropriate wave field expansions and boundary conditions along with the translational addition theorem for spherical wave functions to develop a closed-form solution in form of infinite series. The prime objective is to investigate the thermoviscous loss effects on acoustic radiation and its associated field quantities. The analytical results are illustrated with a numerical example in which the spherical source, that may vibrate either in a monopole-like or a dipole-like mode, is suspended in a thermoviscous fluid medium near an equal-sized viscous thermally conducting fluid sphere. To avoid numerical difficulties normally arising in process of solving thermoviscous radiation/scattering problems in the frequency range of interest, a basic multiple precision FORTRAN computation package was utilized in developing specialized codes for computing special mathematical functions including spherical Bessel functions of complex argument and performing large complex matrix manipulations on floating point numbers of arbitrarily high precision. The essential acoustic field quantities such as the modal acoustic radiation impedance load on the source, the radiated far-field pressure directivity pattern and the radiated on-axis pressure are evaluated and discussed for representative values of the parameters characterizing the system. Limiting cases are examined and excellent agreements with well known solutions are attained.

scholarly journals Anisotropic Scattering Characteristics of a Radially Multilayered Gyrotropic Sphere

2017 ◽  
Vol 2017 ◽  
pp. 1-8
Author(s):  
Lei Cao ◽  
Yongpin Chen ◽  
Kai Kang
Keyword(s):  
Plane Wave ◽  
Spherical Wave ◽  
Fem Simulation ◽  
Closed Form Solution ◽  
Anisotropic Scattering ◽  
Form Solution ◽  
Scattering Coefficients ◽  
Full Wave ◽  
Spherical Scatterer ◽  
Analytical Expressions

We present a new closed-form solution to the scattering of a monochromatic plane wave by a radially multilayered gyrotropic sphere using the T-matrix method. This approach can be utilized to investigate the interactions of a plane wave and a gyrotropic spherical scatterer of multiple layers with each layer characterized by both permittivity and permeability tensors. Based on the completeness and noncoplanar properties of vector spherical wave functions (VSWFs), analytical expressions of the electromagnetic fields in each gyrotropic layer are first derived. The boundary conditions are then applied on each discontinuous interface to obtain the scattering coefficients. Validations are made by first comparing the radar cross section (RCS) values of a 2-layered gyrotropic sphere with that computed from the full-wave finite element method (FEM) simulation and then reducing the general case to uniaxial case to compare the RCS values with the published results computed by Fourier transform combined with VSWFs method; in both cases good agreements are observed. Several specific cases are fully explored to investigate how the RCS are influenced by the parameters of the multilayered spherical structure. The results show that when both electric and magnetic gyrotropy tensors are considered, the RCS of the multilayered spherical scatterer can be suppressed or enhanced, depending on proper configurations of the material parameters.

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.

A closed-form solution to spherical wave propagation in triaxial stress fields

2020 ◽  
Vol 128 ◽  
pp. 104266
Author(s):  
Hao Xu ◽  
Xing-Guo Yang ◽  
Jian-Hai Zhang ◽  
Jia-Wen Zhou ◽  
Jian Tao ◽  
...  
Keyword(s):  
Wave Propagation ◽  
Closed Form ◽  
Spherical Wave ◽  
Closed Form Solution ◽  
Form Solution ◽  
Triaxial Stress ◽  
Stress Fields

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