scholarly journals A Hybrid Analytical-Numerical Model Based on the Method of Fundamental Solutions for the Analysis of Sound Scattering by Buried Shell Structures

2011 ◽  
Vol 2011 ◽  
pp. 1-22 ◽  
Author(s):  
L. Godinho ◽  
P. Amado-Mendes ◽  
A. Pereira
Keyword(s):  
Sound Propagation ◽  
Elastic Shell ◽  
Fundamental Solutions ◽  
Point Of View ◽  
Analytical Models ◽  
Method Of Fundamental Solutions ◽  
Underwater Sound ◽  
Sound Scattering ◽  
Computational Point ◽  
Propagation Medium

Several numerical and analytical models have been used to study underwater acoustics problems. The most accurate and realistic models are usually based on the solution of the wave equation using a variety of methods. Here, a hybrid numerical-analytical model is proposed to address the problem of underwater sound scattering by an elastic shell structure, which is assumed to be circular and that is buried in a fluid seabed bellow a water waveguide. The interior of the shell is filled with a fluid that may have different properties from the host medium. The analysis is performed by coupling analytical solutions developed both for sound propagation in the waveguide and in the vicinity of the circular hollow pipeline. The coupling between solutions is performed using the method of fundamental solutions. This strategy allows a compact description of the propagation medium while being very accurate and highly efficient from the computational point of view.

An Efficient MFS Formulation for the Analysis of Acoustic Scattering by Periodic Structures

2018 ◽  
Vol 26 (01) ◽  
pp. 1850003 ◽  
Author(s):  
L. Godinho ◽  
P. Amado-Mendes ◽  
A. Pereira ◽  
D. Soares
Keyword(s):  
Periodic Structures ◽  
Acoustic Scattering ◽  
Numerical Approach ◽  
Fundamental Solutions ◽  
Point Of View ◽  
Method Of Fundamental Solutions ◽  
Memory Usage ◽  
Computational Point ◽  
Efficient Memory ◽  
Element Method

The acoustic behavior of periodic structures has been a subject of intense study in recent years. From the computational point of view, these devices have mostly been analyzed using strategies such as the multiple scattering theory (MST) or numerical methods such as the finite element method (FEM). Some recent works propose the use of boundary methods, such as the method of fundamental solutions (MFS) or the boundary element method (BEM). However, the geometry and the large number of scatterers of these devices can lead to very large memory requirements and CPU times, which, particularly in the case of 3D problems, can be prohibitive. Here, a new numerical approach based on a frequency domain MFS formulation is proposed for 3D problems, allowing the analysis of very large problems. In this approach, the periodic character of the devices is used to define a matrix with a block structure, in which repeated blocks are only calculated once. In addition, an adaptive-cross-approximation (ACA) approach is incorporated to allow a more efficient memory usage, reducing the global computational requirements, and allowing the analysis of devices with hundreds of scatterers with a minimal memory usage.

Construction of Dynamic Fundamental Solutions for Piezoelectric Solids

1995 ◽  
Vol 48 (11S) ◽  
pp. S222-S229 ◽  
Author(s):  
Naum Khutoryansky ◽  
Horacio Sosa
Keyword(s):  
Three Dimensional ◽  
Transversely Isotropic ◽  
Fundamental Solutions ◽  
Point Of View ◽  
Integral Representations ◽  
Computational Point ◽  
Plane Wave Decomposition ◽  
Piezoelectric Solid ◽  
Piezoelectric Solids ◽  
Wave Decomposition

Fundamental solutions are derived within the framework of transient dynamic, three-dimensional piezoelectricity. The purpose of the article is to show alternate integral representations for such solutions. Thus, a representation over the unit sphere in accordance to a methodology based on the plane wave decomposition is provided. It is shown, however, that more efficient representations from a computational point of view can be achieved through appropriate coordinate transformations. Hence, representations of the fundamental solutions over surfaces of slowness are provided as novel alternatives to more classical approaches. The computational benefits of these new representations are displayed through a numerical example involving a transversely isotropic piezoelectric solid.

Nonlinear Properties of the Gotland Deep – Baltic Sea

2015 ◽  
Vol 40 (4) ◽  
pp. 595-600 ◽  
Author(s):  
Grażyna Grelowska ◽  
Eugeniusz Kozaczka
Keyword(s):  
Baltic Sea ◽  
Sound Propagation ◽  
Sea Water ◽  
Material Constant ◽  
Point Of View ◽  
Homogeneous Distribution ◽  
Nonlinearity Parameter ◽  
Nonlinear Phenomenon ◽  
Underwater Sound ◽  
Nonlinear Properties

AbstractThe properties of the nonlinear phenomenon in water, including sea water, have been well known for many decades. The feature of the non homogeneous distribution of the speed of sound along the depth of the sea is very interesting from the physical and technical point of view. It is important especially in the observation of underwater area by means of acoustical method (Grelowska et al., 2013; 2014). The observation of the underwater space has been carried out for more than hundred years. In the second half of the twentieth century we observed very intense trend of development of the measuring methods of underwater sound speed. It was done mainly in the linear sound propagation aspect. At the end of 20th century nonlinear devices were invented. Thus, from this point of view, knowledge on the nonlinear properties of the sea water is the matter of interest. The phenomenon of nonlinear distortion of elastic waves, and the same the efficiency of nonlinear transfer of energy from the primary wave to the higher harmonic components depend on properties of the medium, especially on the material constant known as the nonlinearity parameter B/A. The Baltic Sea is a specific reservoir with untypically low salinity and low depth (Grelowska, 2000). In the paper results of investigation of nonlinear properties of the South and the Central Baltic by means of thermodynamic method are presented.

COMBINATORIAL POLYNOMIALLY COMPUTABLE CHARACTERISTICS OF SUBSTITUTIONS AND THEIR PROPERTIES

2020 ◽  
Vol 7 (2) ◽  
pp. 34-41
Author(s):  
VLADIMIR NIKONOV ◽  
◽  
ANTON ZOBOV ◽  
Keyword(s):  
Mathematical Expectation ◽  
Point Of View ◽  
Small Range ◽  
Computational Point ◽  
Wide Range ◽  
Bijective Function ◽  
The Difference ◽  
Element Base ◽  
Selection Of

The construction and selection of a suitable bijective function, that is, substitution, is now becoming an important applied task, particularly for building block encryption systems. Many articles have suggested using different approaches to determining the quality of substitution, but most of them are highly computationally complex. The solution of this problem will significantly expand the range of methods for constructing and analyzing scheme in information protection systems. The purpose of research is to find easily measurable characteristics of substitutions, allowing to evaluate their quality, and also measures of the proximity of a particular substitutions to a random one, or its distance from it. For this purpose, several characteristics were proposed in this work: difference and polynomial, and their mathematical expectation was found, as well as variance for the difference characteristic. This allows us to make a conclusion about its quality by comparing the result of calculating the characteristic for a particular substitution with the calculated mathematical expectation. From a computational point of view, the thesises of the article are of exceptional interest due to the simplicity of the algorithm for quantifying the quality of bijective function substitutions. By its nature, the operation of calculating the difference characteristic carries out a simple summation of integer terms in a fixed and small range. Such an operation, both in the modern and in the prospective element base, is embedded in the logic of a wide range of functional elements, especially when implementing computational actions in the optical range, or on other carriers related to the field of nanotechnology.

scholarly journals Influence of fish backbone model geometrical features on the numerical target strength of swimbladdered fish

2020 ◽  
Author(s):  
I Pérez-Arjona ◽  
L Godinho ◽  
V Espinosa
Keyword(s):  
Atlantic Salmon ◽  
Salmo Salar ◽  
Sparus Aurata ◽  
Fundamental Solutions ◽  
Sea Bream ◽  
Method Of Fundamental Solutions ◽  
Target Strength ◽  
Simplified Models ◽  
Geometrical Features ◽  
Proper Estimation

Abstract The method of fundamental solutions has been applied to evaluate the influence of fish models geometrical features on the target strength (TS) directivity and TS frequency response of swimbladdered fish. Simplified models were considered for two fish species: gilt-head sea bream (Sparus aurata, Linnaeus 1758) and Atlantic salmon (Salmo salar, Linnaeus 1758), and different geometrical details of their morphology were studied, such as backbone presence, and its curvature or the inclusion of vertebrae modulation. Swimbladder shape and tilt, together with the inclusion of backbone (and its realistic curvature) for dorsal measurements were the most important features for proper estimation of mean TS. The estimation of mean TS is considered including the effect of fish tilt, the echosounder frequency, and the fish-to-transducer distance.

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