SOUND PROPAGATION THROUGH STRUCTURAL COMPONENTS UNDER CONDITIONS OF NON-RIGID CONTACT AT THE BOUNDARIES BETWEEN THEM

Akustika ◽  
2021 ◽  
Author(s):  
Konstantin Abbakumov ◽  
Anton Vagin ◽  
Alena Vjuginova
Keyword(s):  
Boundary Conditions ◽  
Inhomogeneous Medium ◽  
Dispersion Equation ◽  
Numerical Solutions ◽  
Sound Propagation ◽  
Structural Components ◽  
Frequency Range ◽  
Problem Statement ◽  
Ultrasonic Measurements ◽  
Rigid Contact

The report considers the problem statement, derivation and solution of the dispersion equation for sound propagation in a layered inhomogeneous medium with oriented fracturing, simulated by the presence of boundary conditions in the "linear slip" approximation. Numerical solutions are obtained and analyzed for the frequency range and values of the parameters of contact breaking, which is relevant in the problems of ultrasonic measurements

Frequency and Time Numerical Solutions of 3D Sound Propagation in Open and Closed Spaces

2000 ◽  
Vol 7 (4) ◽  
pp. 247-261 ◽  
Author(s):  
António Tadeu ◽  
Julieta António ◽  
Luís Godinho
Keyword(s):  
Numerical Solutions ◽  
Sound Propagation ◽  
3D Sound

scholarly journals Numerical Boundary Conditions for Solar Magnetic Hydrodynamic Flows Using the Method of Characteristics

1996 ◽  
Vol 154 ◽  
pp. 149-153
Author(s):  
S. T. Wu ◽  
A. H. Wang ◽  
W. P. Guo
Keyword(s):  
Boundary Conditions ◽  
Method Of Characteristics ◽  
Numerical Solutions ◽  
The Self ◽  
Time Dependent ◽  
Solar Plasma ◽  
The Method Of Characteristics ◽  
Mhd Simulations ◽  
Self Consistent ◽  
Dynamic Structures

AbstractWe discuss the self-consistent time-dependent numerical boundary conditions on the basis of theory of characteristics for magnetohydrodynamics (MHD) simulations of solar plasma flows. The importance of using self-consistent boundary conditions is demonstrated by using an example of modeling coronal dynamic structures. This example demonstrates that the self-consistent boundary conditions assure the correctness of the numerical solutions. Otherwise, erroneous numerical solutions will appear.

scholarly journals Analytical Solution of 1D Advection-Dispersion Equation In Finite Groundwater Reservoir With Spatially Dependent Dispersivity And Two Inputs Sources With Source-Sink Term Impact

2021 ◽  
Author(s):  
Thomas TJOCK-MBAGA ◽  
Patrice Ele Abiama ◽  
Jean Marie Ema'a Ema'a ◽  
Germain Hubert Ben-Bolie
Keyword(s):  
Analytical Solution ◽  
Linear Function ◽  
Dispersion Equation ◽  
Source Term ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Liouville Problem ◽  
Finite Domain ◽  
Advection Dispersion ◽  
Sink Term

Abstract This study derives an analytical solution of a one-dimensional (1D) advection-dispersion equation (ADE) for solute transport with two contaminant sources that takes into account the source term. For a heterogeneous medium, groundwater velocity is considered as a linear function while the dispersion as a nth-power of linear function of space and analytical solutions are obtained for and . The solution in a heterogeneous finite domain with unsteady coefficients is obtained using the Generalized Integral Transform Technique (GITT) with a new regular Sturm-Liouville Problem (SLP). The solutions are validated with the numerical solutions obtained using MATLAB pedpe solver and the existing solution from the proposed solutions. We exanimated the influence of the source term, the heterogeneity parameters and the unsteady coefficient on the solute concentration distribution. The results show that the source term produces a solute build-up while the heterogeneity level decreases the concentration level in the medium. As an illustration, model predictions are used to estimate the time histories of the radiological doses of uranium at different distances from the sources boundary in order to understand the potential radiological impact on the general public.

Travelling peakon and solitary wave solutions of modified Fornberg–Whitham equations with nonhomogeneous boundary conditions

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
İhsan Çelikkaya
Keyword(s):  
Solitary Wave ◽  
Boundary Conditions ◽  
Numerical Solutions ◽  
Test Problems ◽  
Von Neumann ◽  
Nonhomogeneous Boundary ◽  
Whitham Equations ◽  
Fourier Series Method ◽  
Nonhomogeneous Boundary Conditions ◽  
The Stability

Abstract In this study, the numerical solutions of the modified Fornberg–Whitham (mFW) equation, which describes immigration of the solitary wave and peakon waves with discontinuous first derivative at the peak, have been obtained by the collocation finite element method using quintic trigonometric B-spline bases. Although there are solutions of this equation by semi-analytical and analytical methods in the literature, there are very few studies on the solution of the equation by numerical methods. Any linearization technique has not been used while applying the method. The stability analysis of the applied method is examined by the von-Neumann Fourier series method. To show the performance of the method, we have considered three test problems with nonhomogeneous boundary conditions having analytical solutions. The error norms L 2 and L ∞ are calculated to demonstrate the accuracy and efficiency of the presented numerical scheme.

Data-Driven Modeling Techniques to Estimate Dispersion Relations of Structural Components

2018 ◽  
Author(s):  
Vijaya V. N. Sriram Malladi ◽  
Mohammad I. Albakri ◽  
Pablo A. Tarazaga ◽  
Serkan Gugercin
Keyword(s):  
Frequency Response ◽  
Dispersion Relations ◽  
Data Driven ◽  
Response Functions ◽  
Structural Components ◽  
Frequency Range ◽  
Frequency Response Functions ◽  
Material Inhomogeneity ◽  
Modeling Techniques ◽  
Data Driven Modeling

Dispersion relations describe the frequency-dependent nature of elastic waves propagating in structures. Experimental determination of dispersion relations of structural components, such as the floor of a building, can be a tedious task, due to material inhomogeneity, complex boundary conditions, and the physical dimensions of the structure under test. In this work, data-driven modeling techniques are utilized to reconstruct dispersion relations over a predetermined frequency range. The feasibility of this approach is demonstrated on a one-dimensional beam where an exact solution of the dispersion relations is attainable. Frequency response functions of the beam are obtained numerically over the frequency range of 0–50kHz. Data-driven dynamical model, constructed by the vector fitting approach, is then deployed to develop a state-space model based on the simulated frequency response functions at 16 locations along the beam. This model is then utilized to construct dispersion relations of the structure through a series of numerical simulations. The techniques discussed in this paper are especially beneficial to such scenarios where it is neither possible to find analytical solutions to wave equations, nor it is feasible to measure dispersion curves experimentally. In the present work, actual experimental data is left for future work, but the complete framework is presented here.

scholarly journals A Numerical Method for Time-Fractional Reaction-Diffusion and Integro Reaction-Diffusion Equation Based on Quasi-Wavelet

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Sachin Kumar ◽  
Jinde Cao ◽  
Xiaodi Li
Keyword(s):  
Diffusion Equation ◽  
Boundary Conditions ◽  
Numerical Method ◽  
Numerical Solutions ◽  
Exact Analytical Solution ◽  
Research Work ◽  
Reaction Diffusion ◽  
Dirichlet Boundary Conditions ◽  
Reaction Diffusion Equation ◽  
Fractional Reaction

In this research work, we focused on finding the numerical solution of time-fractional reaction-diffusion and another class of integro-differential equation known as the integro reaction-diffusion equation. For this, we developed a numerical scheme with the help of quasi-wavelets. The fractional term in the time direction is approximated by using the Crank–Nicolson scheme. The spatial term and the integral term present in integro reaction-diffusion are discretized and approximated with the help of quasi-wavelets. We study this model with Dirichlet boundary conditions. The discretization of these initial and boundary conditions is done with a different approach by the quasi-wavelet-based numerical method. The validity of this proposed method is tested by taking some numerical examples having an exact analytical solution. The accuracy of this method can be seen by error tables which we have drawn between the exact solution and the approximate solution. The effectiveness and validity can be seen by the graphs of the exact and numerical solutions. We conclude that this method has the desired accuracy and has a distinctive local property.

A Continuous Desingularized Source Distribution Method Describing Wave–Body Interactions of a Large Amplitude Oscillatory Body

2015 ◽  
Vol 137 (2) ◽  
Author(s):  
Aichun Feng ◽  
Zhi-Min Chen ◽  
W. G. Price
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Water Surface ◽  
Numerical Solutions ◽  
Free Water ◽  
Source Distribution ◽  
Surface Boundary ◽  
Distribution Method ◽  
Collocation Points ◽  
Calm Water

A Rankine source method with a continuous desingularized free surface source panel distribution is developed to solve numerically a wave–body interaction problem with nonlinear boundary conditions. A body undergoes forced oscillatory motion in a free water surface and the variation of wetted body surface is captured by a regridding process. Free surface sources are placed in continuous panels, rather than points in isolation, over the calm water surface, with free surface collocation points placed on the calm water surface. Nonlinear kinematic and dynamic free surface boundary conditions along the collocation points on the calm water surface are solved in a time domain simulation based on a Lagrange time dependent formulation. Compared with isolated desingularized source points distribution methods, a significantly reduced number of free surface collocation points with sparse distribution are utilized in the present numerical computation. The numerical scheme of study is shown to be computationally efficient and the accuracy of numerical solutions is compared with traditional numerical methods as well as measurements.

scholarly journals EVALUATION OF SEVERAL NONREFLECTING COMPUTATIONAL BOUNDARY CONDITIONS FOR DUCT ACOUSTICS

1995 ◽  
Vol 03 (04) ◽  
pp. 327-342 ◽  
Author(s):  
WILLIE R. WATSON ◽  
WILLIAM E. ZORUMSKI ◽  
STEVE L. HODGE
Keyword(s):  
Boundary Condition ◽  
Boundary Conditions ◽  
Sound Propagation ◽  
Sparse Matrix ◽  
Nonlocal Boundary Condition ◽  
Nonlocal Boundary ◽  
Substantial Reduction ◽  
Sound Attenuation ◽  
Interior Solution ◽  
Duct Acoustics

Several nonreflecting computational boundary conditions that meet certain criteria and have potential applications to duct acoustics are evaluated for their effectiveness. The same interior solution scheme, grid, and order of approximation are used to evaluate each condition. Sparse matrix solution techniques are applied to solve the matrix equation resulting from the discretization. Modal series solutions for the sound attenuation in an infinite duct are used to evaluate the accuracy of each nonreflecting boundary condition. The evaluations are performed for sound propagation in a softwall duct, for several sources, sound frequencies, and duct lengths. It is shown that a recently developed nonlocal boundary condition leads to sound attenuation predictions considerably more accurate than the local ones considered. Results also show that this condition is more accurate for short ducts. This leads to a substantial reduction in the number of grid points when compared to other nonreflecting conditions.

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