Begell House Inc.
International Journal of Fluid Mechanics Research
FMR
2152-5102
28
3
2001
Wave Propagation in Elastic Layer Placed Between Two Different Fluid Media
12
Olga V.
Avramenko
Kirovograd State V. Vinnichenko Pedagogical University, Kirovograd
Igor T.
Selezov
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Zhelyabov St., 8/4, Kyiv, 03680, MSP, Ukraine
Propagation of harmonic waves in a hydroelastic system consisting of the uniform elastic layer between two compressible fluids of different physical properties is investigated. A dispersion equation is derived and analyzed numerically for phase velocities lower than the greater sound velocity of two fluids. The dispersion equation has two real roots close to symmetric and antisymmetric oscillations of the layer loaded by the same fluids from both sides. Limiting case of the same fluids when the problem is splitted into two independent ones, as well as limiting cases of Rayleigh and Stonley waves are considered. The expressions for displacements, shear and normal stresses are obtained. Corresponding wave modes are determined and their properties are analyzed.
Sound Propagation in Human Bronchial Tree. Part I. Theory
17
I. V.
Vovk
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
O. I.
Vovk
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
Analysis of geometric, physical and wave parameters of a bronchial tree and its elements has been conducted. It is shown that in frequency range up to 1000 Hz all geometric parameters of airways (except the length of trachea) are sufficiently smaller than the wavelength of the sound, which propagates inside a bronchial tree. It is established that jump of a section in the point of articulation of adjacent airways can significantly affect the sound propagation in a bronchial tree. At the same time, bifurcation of the airways has almost no impact on this process. Acoustical and mathematical models of the airways (taking into account compliance of their walls) and of parts of articulation between them are stated. Corresponding boundary problems for the Helmholtz equation are solved. Obtained results allowed us to develop an algorithm for general solving for the problem of wave propagation in the bronchial tree.
Sound Propagation in Human Bronchial Tree. Part II. Analysis of Numerical Results
11
O. I.
Vovk
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
I. V.
Vovk
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
V. G.
Basovsky
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
Following the solution algorithm of the problem concerned with propagation of the sound waves in a bronchial tree, developed in the previous paper, the acoustic properties of human bronchial tree are numerically investigated. In particular, the imaginary part of an entry impedance of a bronchial tree is demonstrated to have resonances and antiresonances following one after another. Considerable "peaks" of the real part of an impedance therewith are found on the antiresonance frequencies, while "falls" on the resonances. A comparison between designed and experimental values of an input impedance is conducted and their satisfactory coincidence is shown. Distribution of the sound energy flows in the bronchial tree is studied. It is shown that the energy in the sound propagation process damps rather quickly at the expense of losses in visco-elastic walls of pneumatic paths and re-radiation by walls of the energy in the surrounding biotissue. The essential dependence is proved for phase velocity of the sound inside a bronchial tree both from frequency, and from choice of the initial and the final points of the bronchial tree site, for which this velocity is estimated. It is demonstrated that this speed can be much below and above the sound speed in the free air environment. Possible delay factor of the sound signal at its passing from the onset of trachea's up to the thorax surface is estimated.
Sound Radiation from an Open End of the Wedge-Shaped Waveguide. I. Method of Solution and Numerical Algorithm
15
V. T.
Matsypura
National Engineering University of Ukraine "KPI", Kyiv, Ukraine
The 2D boundary problem arising in the study and analysis of characteristics of sound field radiated from the open end of the wedge-shaped waveguide is presented in the paper. The characteristic feature of the wave-guide geometry is that the end points of the boundary planes are situated on different distances from the top of the wedge. Major attention in this first part of the paper is focused on considering analytic structure of the wave fields and the principal features of solving algorithm. It is shown, that for the considered problems there is an indeterminacy in the form of analytical solution. By doing the analysis of numerical results the indeterminacy can be removed taking into account the minimizing volume of computations involved at their given accuracy.
Sound Radiation from an Open End of the Wedge-Shaped Waveguide. II. Analysis of the Numerical Results
12
V. T.
Matsypura
National Engineering University of Ukraine "KPI", Kyiv, Ukraine
The problem of sound radiation from an open end of a wedge-shaped waveguide is considered. The qualitative data about the structure and the energy characteristics of the sound field are presented. As the initial calculating relationships the formulas from [1] are used. Geometric peculiarity of the waveguides under consideration is that the walls are asymmetric with respect to the apex of the wedge. The additional elongation of one of walls is considered as a screen and is an important element in the mechanism of control over the near and the far field characteristics. Qualitative estimations of the effect of the screen length on an extent of a sound insulation in the zone of acoustical shadow is presented. The data about change of the sound pattern when the parameters of the waveguides are changed illustrate a complex structure of a radiated sound field and a strong dependence of one on the type of normal wave carrying energy to the edge of the wavegiude. Qualitative description of the far field structure is complemented by the data about a concentration factor of the sound energy and the distribution of an energy between the transmitted and reflected waves. It is shown that for any case the elongation of the screen the sound energy concentration can decrease.
Passage of Pressure Pulses through the Finite Elastic Plates
11
L. B.
Lerman
Special Design and Engineering Office of S. P. Timoshenko's Institute of Mechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
The solution of the unsteady acousto-elasticity problem for the finite Timoshenko's plates is presented. The plate is assumed to occupy a part of an acoustically stiff baffle, covering a rectangular wave-guide of arbitrary cross-sectional dimensions (up to infinite extent). Provision is made for consideration of a finite field behind the obstacle. Two possible algorithms of the solution, based on reduction of the problem to various infinite systems of integro-differential equations, are developed. Applicability of the method of reduction to the infinite systems is justified. Several numerical experiments are performed in an effort to estimate both the error, caused by truncation of the infinite systems, and the rate of convergence of the iterative procedure of the solution. Reliability of the computational results is verified by comparison with the experimental data.
Influence of the External Circuit on Bending Vibration of Kinematically Excited Piezoceramic Bimorph Disk
10
Valery
Oliynik
Institute of Hydromechanics of National Academy of Sciences of Ukraine
Within the theory of thin piezoelastic plates the problem on harmonic vibration of the bimorph disk is considered for the case, when its surfaces are coated with electrodes connected to the passive electric circuit. The bimorph's electric loading leads to the change of generated output voltage. It is shown, that when the electric load is of an inductive type, the case for this change can be the essential modification of the bimorph's bending vibration.
Internal Waves Behind a Local Disturbance upon its Weakly Non-Stationary Motion in Stratified Fluid of Finite Depth
13
R. V.
Ol'khovsky
Kyiv Taras Shevchenko National University
O. G.
Stetsenko
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
A method of plotting an asymptotic field of the internal waves behind the local disturbance moving in a weakly non-stationary regime at large values of the Froude number is proposed. The method is based on the use of the locally two-dimensional character of evolution of the internal waves field behind the uniformly moving local disturbance as well as on the use of the geometric optics methods for the expansion of wave rays in horizontally homogeneous mediums. The use of the method is demonstrated in terms of an ovoid body moving in the non-stationary regime in a three-layered stratified medium.
Sound Scattering Caused by the Temperature Inhomogeneities in a Wake Behind the Cylinder
8
A. G.
Rudnitskii
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv
The sound wave scattering caused by temperature discontinuities in a vortex street is researched. The wake-flow structure was induced for a weak-heated and for a heat-insulated cylinder surveyed. The task is solved in Born approximation and in a ray approximation. The expressions linking characteristics of a scattering sound wave with thermodynamic and kinematic flow parameters are obtained.
To Magnetohydrodynamics of Rotating Nonhomogeneous Fluid in Stationary Case
24
V. N.
Saltanov
Kyiv Taras Shevchenko National University
N. V.
Saltanov
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv, Ukraine
The magnetohydrodynamic model of conducting rotatory stratified nonviscous liquid is investigated here in stationary case with the assumption that the magnetic field vector and the speed vector are parallel. Three types of a magnetic field stratification are registered: subalfvenic, alfvenic and superalfvenic. Two ways of reducibility of the three-parametric problem solving linear equations are pointed out. The modified speed vector is expressed in terms of potential complying with the Laplace equation in the first case and the Helmholtz equation in the second case. Two-parametric problem, being based on the symmetry integrals, is reduced to one nonlinear equation in quadratic partial derivatives to establish the modified stream function. This relation generalizes the Yih equation, which is well-known in usual dynamics of nonhomogeneous fluid. A set of situations is pointed when the equation for the modified stream function becomes linear. Magnetohydrodynamic generalization of the well-known in common hydrodynamics Hill vortex is obtained. The exact solutions describing internal waves with finite amplitude in plane and circular layers of magnetized nonhomogeneous fluid are found. An influence of magnetization on dispersion relations is analyzed.
Nonstationary Contact Problems for a Cylinder in Liquid Layer on a Solid Half-Space
15
V. M.
Seimov
Institute of Hydromechanics of National Academy of Sciences of Ukraine, Kyiv
Nonstationary problem for the cylinder interacting with thew layer of compressible liquid and elastic halfspace under dynamic or kinematic loadings is considered. The system of differential equations is solved, which describes the wave processes in liquid layer and elastic halfspace, and the bending vibration of the cylinder. Method of integral transforms (Laplace on time, and Hankel on radial coordinate), method of orthogonal polynomials, method of coordinate functions, and method of collocations are used. In the domain of the Laplace images the problem is reduced to a system of algebraic equations. The Laplace transform inversion is made numerically by means of the Fourier integral. The solutions are obtained for harmonic and nonstationary problems on horizontal and angular vibration of rigid cylinder, and on bending vibration of elastic cylinder. Numerical analysis is made for the case of horizontal vibration of rigid cylinder undergoing the action of horizontal force. The time dependencies of reaction of foundation, displacement and hydrodynamic pressure on the cylinder at nonstationary loading are detected. The dependence of desired functions from the height of liquid layer and mass of the cylinder is established. The considered problems are of interest at studying and calculation of oscillations of a gravitational offshore platforms undergoing the wave, ice, and seismic loading.