scholarly journals Scattering of Elastic Waves by an Inhomogeneous Boundary in the Acoustic Testing of Permanent Joints

2019 ◽  
Vol 10 (4) ◽  
pp. 360-372
Author(s):  
A. R. Baev ◽  
N. V. Levkovich ◽  
A. L. Mayorov ◽  
M. V. Asadchaya
Keyword(s):  
Elastic Waves ◽  
Dimensional Space ◽  
Ultrasonic Method ◽  
Three Dimensional ◽  
Circular Cross Section ◽  
Field Pattern ◽  
Acoustic Beam ◽  
Practical Applications ◽  
Scattering Field ◽  
Scattering Of Elastic Waves

Improving the reliability and testing performance of permanent joints оf different materials made by welding, spraying, gluing, soldering and other methods is an important production task, for which the ultrasonic method is the simplest and most effective. The purpose of this work was to expand the technical possibilities and increase the sensitivity of ultrasonic testing of adhesion defects of materials joints based on the establishment of laws governing the formation of a scattering field of elastic waves from an inhomogeneous boundary in three-dimensional space and issuing recommendations for the development of suggested method.For the first time, in the framework of classical concepts, the scattering fields of elastic waves of an acoustic beam with a circular cross section moving across the boundary of a semi-infinite defect are calculated. It is proposed to use a phase shift between the waves reflected from the indicated surfaces, which varies in the range of π/4–π, as an important parameter of the material joint's defect. It has a significant effect on the field pattern and its angular amplitude extrema — minima and maxima of different orders when the defect boundary is moved relative to the center of the acoustic beam spot.The features of the evolution of the structure of the scattering field are established, which make it possible to identify optimal conditions for the detection of weakly reflective defects in sound. It is shown that it is possible in principle to estimate the defect's area by measuring a change in the amplitude of the primary maximum of the radiation pattern of the scattered waves.Specific examples show the effectiveness of using the proposed method for a number of practical applications.

Multiple Scattering of Elastic Waves by Cubical Lattices of Spheres

2007 ◽  
Author(s):  
Zunping Liu ◽  
Liang-Wu Cai
Keyword(s):  
Multiple Scattering ◽  
Elastic Waves ◽  
Dimensional Space ◽  
Near Field ◽  
Scattering Problem ◽  
Three Dimensional ◽  
Computational System ◽  
Number Of Layers ◽  
Scattering Of Elastic Waves ◽  
Three Dimensional Space

The band gap for elastic waves propagating in a cubical lattice of spherical scatterers is observed through a series of numerical simulations. Along the direction of the incident wave, scatterer arrangements are viewed as comprising layers of scatterers, within which scatterers form a square grid. Starting from one layer and by increasing the number of layers, near-field forward and backward wave propagation spectra are computed as the number of layers increases. In the computations, scatterer polymerization methodology is used. This methodology is based on an analytically exact solution to a general three-dimensional multiple scattering problem obtained by the authors. It can be used to reduce an assemblage of actual scatterers to a lesser number of abstract scatterers. These simulations also demonstrate that the computational system has the capability to simulate multiple scattering of elastic waves in three-dimensional space.

ON THE DOI MODEL FOR THE SUSPENSIONS OF ROD-LIKE MOLECULES IN COMPRESSIBLE FLUIDS

2012 ◽  
Vol 22 (10) ◽  
pp. 1250027 ◽  
Author(s):  
HANTAEK BAE ◽  
KONSTANTINA TRIVISA
Keyword(s):  
Dimensional Space ◽  
Initial Density ◽  
Three Dimensional ◽  
Orientation Distribution ◽  
Polymeric Fluids ◽  
Atmospheric Sciences ◽  
Practical Applications ◽  
Doi Model ◽  
Time Existence ◽  
Three Dimensional Space

Polymeric fluids arise in many practical applications in biotechnology, medicine, chemistry, industrial processes, and atmospheric sciences. In this paper, the Doi model for the suspensions of rod-like molecules in a compressible fluid is investigated. The model under consideration describes the interaction between the orientation of rod-like polymer molecules on the microscopic scale and the macroscopic properties of the fluid in which these molecules are contained. Prescribing arbitrarily the initial density of the fluid, the initial velocity, and the initial orientation distribution in suitable spaces, we establish the global-in-time existence of a weak solution to our model defined on a bounded domain in the three-dimensional space. The proof relies on the construction of an approximate sequence of solutions by introducing appropriate regularization and the establishment of compactness.

The Osculatory Packing of a Three Dimensional Sphere

1973 ◽  
Vol 25 (2) ◽  
pp. 303-322 ◽  
Author(s):  
David W. Boyd
Keyword(s):  
Dimensional Space ◽  
Three Dimensional ◽  
Higher Dimensions ◽  
Dimensional Euclidean Space ◽  
Dimensional Sphere ◽  
Specific Knowledge ◽  
Precise Information ◽  
Practical Applications ◽  
Physical Problems ◽  
Three Dimensional Space

Packings by unequal spheres in three dimensional space have interested many authors. This is to some extent due to the practical applications of such investigations to engineering and physical problems (see, for example, [16; 17; 31]). There are a few general results known concerning complete packings by spheres in N-dimensional Euclidean space, due mainly to Larman [20; 21]. For osculatory packings, although there is a great deal of specific knowledge about the two-dimensional situation, the results for higher dimensions, such as [4], rely on general methods which do not give particularly precise information.

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