Numerical Analysis Of Wave Propagation Research Articles

An Infinity Tube with an Expansion Chamber for Noise Control in the Ductwork System

This paper proposes a muffler with simple geometry to effectively reduce low-frequency noise in ductwork systems. A muffler named infinity tube with an expansion chamber (ITEC) is developed from the infinity tube (IT). Theoretical and numerical analyses of wave propagation in the ITEC have been conducted in this paper. The transfer matrix method is adopted to predict transmission loss theoretically. The theoretical results are validated by the finite element method simulation. The comparison of the transmission loss between the IT and ITEC illustrates that the ITEC has an advantage in low-frequency noise reduction. The transmission loss results of the ITEC are compared with the Helmholtz resonator system to assess the potential for industrial application. Finally, the geometric parameters of the proposed ITEC on its noise attenuation performance have been analyzed. The proposed ITEC can effectively reduce low-frequency noise, and it is suitable for ductwork systems in constrained spaces.

Numerical analysis of wave propagation and vibration attenuation effects of periodic scattering piles in unsaturated poroviscoelastic ground

ABSTRACT The elastic wave propagation and vibration attenuation zones for periodically scattering piles in unsaturated ground were investigated using Finite-Element Method (FEM) and Bloch periodic theory. The unsaturated ground was modelled by unsaturated poroviscoelastic medium with the weak form governing equations derived from the mass and momentum conservative equations using Galerkin method and Fourier transform. The quadratic polynomial eigenvalue equations for the unsaturated medium were obtained using the Bloch periodic theory, and solved by FEM for the complex eigenvalues to evaluate the band gaps of the pile-soil system. The eigenvalue bands combined with the frequency response function were used to analyse the mitigation effects of piles in unsaturated ground with different soil properties and piles parameters. This research found that the pile-soil system has three propagational waves, in which the shear wave and the slow longitudinal wave carry low-frequency vibrations that undermine the attenuation effects of the piles barrier. The increasing soil saturation degree affects the attenuation effects by reducing the soil modulus and increasing the fluid content. And both of those two mechanisms reduce the frequency of the attenuation zones (AZ), which improves the low-frequency vibration attenuation, and reduces the width of AZ that could reduce the vibration mitigation effects.

Anisotropic guided waves in isotropic metaplate with orthogonal surface perturbation

Analytical solution of elastic wave propagation in anisotropic media is of great interest in various branches of engineering and applied sciences. In this study, a derivation of a generalized elastic wave dispersion equation and its solution is presented for a doubly corrugated metaplate made of isotropic material. The newly formulated dispersion equation resulted the well-known Rayleigh-Lamb (RL) dispersion equations when the surface perturbations were made to zero, resembling a flat plate. However, when the surface perturbation of the isotropic metaplate was non-zero, the solution resulted an anisotropic wave propagation behavior. Helmholtz decomposition of the displacement function with a scalar and three vector potential is the conventional method of finding dispersion equations for Rayleigh-Lamb (RL) wave and Shear Horizontal (SH) waves in isotropic material. However, the presence of orthogonal surface perturbations in isotropic material hinders the use of Helmholtz decomposition. Although the material is isotropic, in this study, the generalized analytical dispersion equations in the metaplate were developed assuming three potential functions first introduced by Buchwald (Buchwald, 1961) for anisotropic materials. Next a logical root-finding algorithm was employed to solve the generalized dispersion equation. A numerical analysis of wave propagation in a flat plate and a corrugated plate was conducted to prove the physics obtained from the analytical solutions. Spatiotemporal displacement data and transformed frequency-wavenumber data are analyzed and verified to show anisotropic wave propagation behavior in orthogonal perturbated waveguide with isotropic material. Finally, comparison of analytical and numerical wave field in passband and bandgap frequencies in a corrugated waveguide are verified.

On the Use of High-Order Shape Functions in the SAFE Method and Their Performance in Wave Propagation Problems

In this research, high-order shape functions commonly used in different finite element implementations are investigated with a special focus on their applicability in the semi-analytical finite element (SAFE) method being applied to wave propagation problems. Hierarchical shape functions (p-version of the finite element method), Lagrange polynomials defined over non-equidistant nodes (spectral element method), and non-uniform rational B-splines (isogeometric analysis) are implemented in an in-house SAFE code, along with different refinement strategies such as h-, p-, and k-refinement. Since the numerical analysis of wave propagation is computationally quite challenging, high-order shape functions and local mesh refinement techniques are required to increase the accuracy of the solution, while at the same time decreasing the computational costs. The obtained results reveal that employing a suitable high-order basis in combination with one of the mentioned mesh refinement techniques has a notable effect on the performance of the SAFE method. This point becomes especially beneficial when dealing with applications in the areas of structural health monitoring or material property identification, where a model problem has to be solved repeatedly.

Analysis of Elastic Pulse Dispersion in Periodically Layered Composite Rods using Wave Finite Element Method

Numerical analysis of wave propagation in composite structures needs large-scale computation which is not feasible in practice. This paper investigates the possibility of applying a wave finite element method (WFEM) to composite structure. The key feature of the WFEM is its capability of accurately analyzing the discontinuities in stress wavefront along with the discontinuities in velocities and strains. In addition, the numerical analysis of the WFEM is unconditionally stable and reduces numerical computation. This paper studies a periodically layered composite rod to analyze the dispersion and propagation of stress waves using the WFEM. The numerical results are compared with other numerical/analytical solutions, paying attention to the accuracy of computing the strong discontinuities in the stress wavefront as well as the dispersion of pulses in a heterogeneous elastic rod. It is shown that the WFEM can be used as an affordable tool for numerically solving wave propagation in composite structures.

Numerical analysis of wave propagation across Solid–Fluid interface with Fluid–Structure interaction in circular tube

Fluid–structure interaction (FSI) and wave propagation in engineering structures can cause severe damage to piping systems or fluid machines, inducing serious accidents. In these phenomena, the mechanism of structural damage depends on the wave propagation across the fluid–solid interface. Previous studies reported that disagreements between the induced pressure value on the solid–fluid movable interface and the value predicted by the classical one-dimensional theory arose from the effects of two-dimensional wave propagation. To address this problem, in this study, a two-dimensional axisymmetric simulation of wave propagation across the solid-fluid interface with FSI was conducted. The simulation was performed using ANSYS Autodyn with a Lagrangian solver for solids and Eulerian solver for water. The results showed that radial wave propagation caused by the dynamic effect of the tube and water's inertia affected the peak pressure on the solid–fluid interface. The peak pressure was attenuated near the tube wall because of the inertial effect of the tube and fluid expansion. By calculating the mean pressure and axial stress to compare the simulated peak pressure with that from one-dimensional acoustic theory, it was indicated that the transition region for transmitted pressure was located immediately after the solid–fluid interface. In this region, the transmitted peak pressure may exceed the value predicted by one-dimensional acoustic theory. The transition region was oriented in the axial direction from the interface. In addition, prediction of the transmitted peak pressure with one-dimensional acoustic theory was suggested via normal wave speed in the unconfined fluid from a safety engineering perspective, although the circumferential stress generated in the tube enclosing fluid can be sufficiently accurately predicted using the same theory with the Korteweg speed.

Numerical analyses of wave propagation over the inner shelf and shoreface of the southern Brazilian coast: from Torres to Mostardas

A plataforma continental interna e a antepraia ao longo do litoral norte e médio do estado do Rio Grande do Sul (RS), Brasil, entre Torres e Mostardas, têm o relevo do fundo homogêneo, mas apresentam variações de inclinação e largura. No setor norte, entre Torres e Pinhal, a plataforma interna é mais larga, enquanto a largura de antepraia é mais estreita. Por outro lado, o oposto ocorre ao Sul de Pinhal. Este trabalho analisa numericamente a propagação de ondas nesta região através do REF/DIF 1, modelo que adota a aproximação parabólica da equação de declive suave. Os diagramas de refração de ondas, baseados em um clima de onda predominante, indicam que o padrão dominante é o divergente para ondas incidentes de 90° a 135°. Análises numéricas das variações de energia de ondas, investigando a influência das variações da largura da plataforma interna e da largura de antepraia, e da fricção com o fundo considerando um coeficiente de atrito fw = 0,01, revelam a pouca influência do atrito com o fundo sobre a transformação das ondas. Adotando-se um coeficiente de atrito fw = 0,2, constata-se, de forma geral, que a influência do aumento da largura da antepraia do sul de Pinhal para o norte no atrito com o fundo é compensada pela influência da diminuição da largura da plataforma continental interna. As análises mostram que os gradientes laterais da energia da onda ao longo da isobatimétrica de 10 m, mesmo considerando as diferenças morfológicas entre os dois setores, são desprezíveis.

A two-step FEM-SEM approach for wave propagation analysis in cable structures

Vibration-based methods are among the most widely studied in structural health monitoring (SHM). It is well known, however, that the low-order modes, characterizing the global dynamic behaviour of structures, are relatively insensitive to local damage. Such local damage may be easier to detect by methods based on wave propagation which involve local high frequency behaviour. The present work considers the numerical analysis of wave propagation in cables. A two-step approach is proposed which allows taking into account the cable sag and the distribution of the axial forces in the wave propagation analysis. In the first step, the static deformation and internal forces are obtained by the finite element method (FEM), taking into account geometric nonlinear effects. In the second step, the results from the static analysis are used to define the initial state of the dynamic analysis which is performed by means of the spectral element method (SEM). The use of the SEM in the second step of the analysis allows for a significant reduction in computational costs as compared to a FE analysis. This methodology is first verified by means of a full FE analysis for a single stretched cable. Next, simulations are made to study the effects of damage in a single stretched cable and a cable-supported truss. The results of the simulations show how damage significantly affects the high frequency response, confirming the potential of wave propagation based methods for SHM.

Wave propagation in the Kolmogorov–Petrovskii–Piskunov problem with delay

The problem of density wave propagation governed by a logistic equation with delay and diffusion (Fisher–Kolmogorov–Petrovskii–Piskunov equation with delay) was studied. To analyze the qualitative behavior of solutions to this equation with periodic boundary conditions in the case of the diffusion parameter tending to zero, the normal form of the problem, i.e., the Ginzburg–Landau equation was constructed near the unit equilibrium. A numerical analysis of wave propagation showed that, for sufficiently small delays, this equation has solutions close to those of the standard Kolmogorov–Petrovskii–Piskunov equation. As the delay parameter increases, a decaying oscillatory component appears in the spatial distribution of the solution and, then, undamped (in time) and slowly propagating (in space) oscillations close to solutions of the corresponding boundary value problem with periodic boundary conditions are observed near the initial perturbation segment.

A numerical Study on In-plane Wave Propagation in Mooring Cables

This study presents the results of a numerical analysis of wave propagation in a mooring cable, focusing on structural waves that form and propagate in mooring cables. For mooring cables, there exists another source of nonlinearity besides the hydrodynamic effect and geometric stiffening effect, that is the seabed interaction. To study the wave propagation in mooring cables including these nonlinearities, a numerical analysis is carried out in this paper. Herein the partial differential equations describing the dynamics of the submerged mooring cable formulated in Lagrangian reference frame are used and they are further solved using space-time finite difference method. In particular, the in-plane wave propagation in a typical mooring cable partly grounded on the seabed is studied. Numerical results for the cable under fairlead excitations are presented. The characteristics of the wave propagation from the fairlead to the seabed anchor and wave reflection at the seabed touching down point are discussed.

Spatially inhomogeneous structures in the solution of Fisher-Kolmogorov equation with delay

We consider the problem of density wave propagation in a logistic equation with delay and diffusion (Fisher-Kolmogorov equation with delay). A Ginzburg-Landau equation was constructed in order to study the qualitative behavior of the solution near the equilibrium state. The numerical analysis of wave propagation shows that for a sufficiently small delay this equation has a solution similar to the solution of a classical Fisher-Kolmogorov equation. The delay increasing leads to existence of the oscillatory component in spatial distribution of solutions. A further increase of delay leads to destruction of the traveling wave. That is expressed in the fact that undamped spatio-temporal fluctuations exist in a neighborhood of the initial perturbation. These fluctuations are close to the solution of the corresponding boundary value problem with periodic boundary conditions. Finally, when the delay is sufficiently large we observe intensive spatio-temporal fluctuations in the whole area of wave propagation.

Dynamical Properties of the Fisher–Kolmogorov–Petrovskii–Piscounov Equation with Deviation of the Spatial Variable

We consider the problem of density wave propagation of a logistic equation with deviation of the spatial variable and diffusion (Fisher-Kolmogorov equation with deviation of the spatial variable). A Ginzburg–Landau equation was constructed in order to study the qualitative behavior of the solution near the equilibrium state. We analyzed the profile of the wave equation and found conditions for the appearance of oscillatory regimes. The numerical analysis of wave propagation shows that for a suficiently small spatial deviation this equation has a solution similar to the solution of the classical Fisher–Kolmogorov equation. The spatial deviation increasing leads to the existence of the oscillatory component in the spatial distribution of solutions. A further increase of the spatial deviation leads to destruction of the traveling wave. That is expressed in the fact that undamped spatio-temporal fluctuations exist in a neighborhood of the initial perturbation. These fluctuations are close to the solution of the corresponding boundary value problem with periodic boundary conditions. Finally, when the spatial deviation is suficiently large we observe intensive spatio-temporal fluctuations in the whole area of wave propagation.

Fisher–Kolmogorov–Petrovskii–Piscounov Equation with Delay

We considered the problem of density wave propagation in a logistic equation with delay and diffusion (Fisher–Kolmogorov equation with delay). It was constructed a Ginzburg–Landau equation in order to study the qualitative behavior of the solution near the equilibrium state. The numerical analysis of wave propagation shows that for a sufficiently small delay this equation has a solution similar to the solution of a classical Fisher–Kolmogorov equation. The delay increasing leads to existence of the oscillatory component in spatial distribution of solutions. A further increase of delay leads to the destruction of the traveling wave. That is expressed in the fact that undamped spatio-temporal fluctuations exist in a neighborhood of the initial perturbation. These fluctuations are close to the solution of the corresponding boundary value problem with periodic boundary conditions. Finally, when the delay is sufficiently large we observe intensive spatio-temporal fluctuations in the whole area of wave propagation.

Numerical analysis of wave propagation in fluid‐filled deformable tubes

AbstractThe theory of Biot describing wave propagation in fluid saturated porous media is a good effective approximation of a wave induced in a fluid‐filled deformable tube. Nonetheless, it has been found that Biot's theory has shortcomings in predicting the fast P‐wave velocities and the amount of intrinsic attenuation. These problems arises when complex mechanical interactions of the solid phase and the fluid phase in the micro‐scale are not taken into account. In contrast, the approach proposed by Bernabe does take into account micro‐scopic interaction between phases and therefore poses an interesting alternative to Biot's theory. A Wave propagating in a deformable tube saturated with a viscous fluid is a simplified model of a porous material, and therefore the study of this geometry is of great interest. By using this geometry, the results of analytical and numerical results have an easier interpretation and therefore can be compared straightforward. Using a Finite Difference viscoelastic wave propagation code, the transient response was simulated. The wave source was modified with different characteristic frequencies in order to gain information of the dispersion relation. It was found that the P‐wave velocities of the simulations at sub‐critical frequencies closely match those of Bernabe's solution, but at over‐critical frequencies they come closer to Biot's solution. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Wave propagation and localisation in a softening two-phase medium

Within the framework of the generalised theory of heterogeneous media, the complete set of equations is derived for a three-dimensional fluid-saturated porous medium. Subsequently, stability and dispersion analyses are carried out for an infinite one-dimensional continuum that has been deforming homogeneously prior to the application of the perturbation. For common values of the stiffness, the porosity and the mass densities, the two-phase medium is found to remain stable when the solid is elastic. When an elastoplastic or an elasticity-based damage model is adopted for the solid constituent, loss of stability occurs at the peak in the uniaxial stress–strain relation for the solid constituent, which is identical to a single-phase medium. From the dispersion analysis it appears that a dispersive wave is obtained, but that the internal length scale associated with it vanishes in the short wavelength limit, at least for the assumptions made regarding the constitutive behaviour of the solid and of the fluid. This result leads to the conclusion that, upon the introduction of softening, localisation in a zero width will occur and no regularisation will be present. This conclusion is corroborated by the results of numerical analyses of wave propagation in a finite one-dimensional bar.

A posteriori evaluation of wave reflection for adaptive analysis of wave propagation in unbounded domains

An adaptive analysis procedure is proposed as a new paradigm with enhanced efficiency and reliability for numerical analysis of wave propagation in unbounded domains. In the context of one-dimensional wave propagation, a local solution procedure is designed based on the method of characteristics for a posteriori evaluation of reflected waves. It is shown that the strain associated with the reflected wave exhibit excellent correlation with the order of the absorbing boundary condition employed, and thus can effectively be used as an error estimator. A simple adaptive analysis algorithm is designed to demonstrate the use of the error estimator in adaptively adjusting the order of the absorbing boundary condition to control, within predetermined tolerance, spurious wave reflection from the boundary of truncation. This leads to the use of an optimal-order absorbing boundary condition that results in solutions of desired accuracy.

PROPAGATION OF ELECTROMAGNETIC WAVES ALONG AN ANNULAR PLASMA COLUMN

Historically, surface wave sustained microwave plasmas were almost exclusively generated and investigated in a standard configuration of an elongated cylinder. One of the new configurations, proposed more recently, is Duo-plasmaline [1]. There, the plasma is located outside a cylindrical dielectric vessel, adjacent to its wall, and forms a structure of a ring shaped cross-section. An axially located cylindrical conductor corresponds to the outer metallic cylinder surrounding plasma in the standard configuration. We report results of a numerical analysis of wave propagation in such annular structures in a wide range of plasma parameters. We show that two different waves may propagate, each related to one of the two boundary surfaces of the plasma. The waves can be clearly distinguished in the domain of large electron densities. Presented are calculated complex propagation coefficients of waves and radial distributions of the electromagnetic field. Asymptotic cases are defined and analyzed.

Numerical analysis of wave propagation through assemblies of elliptical particles

Wave propagation in granular materials is numerically studied using discrete element simulation. Primary interest is concerned with linking material microstructure with wave propagational behaviors for materials composed of elliptical particles. The discrete element (DEM) scheme uses a nonlinear hysteretic contact law which accounts for differences related to the radius of curvature at the interparticle point of contact. Modeling results yield information on wave speed and amplitude attenuation on two-dimensional, meso-domain model systems of both regular and random assemblies. Particulate models were numerically generated using a biasing scheme whereby partial control of particular fabric measures could be achieved. Three specific fabric measures which were used to characterize the granular material models include branch, contact normal and orienation vectors . DEM simulation results indicated that wave speed and attenuation generally correlated with vector distributions of these fabric variables. A power law relation was proposed between wave speed/attenuation and three averaged projected fabric variables based on orientation, contact normal and branch vectors. Predictions from this specific relation correlated reasonably well with DEM results.

Determination of the inhomogeneous structure of a medium from its plane wave reflection response, part I: A numerical analysis of the direct problem

A numerical analysis of wave propagation in one dimensional inhomogeneous media is presented in this paper, the first (Part I) of two companion papers. The aim is to provide a natural and physical basis for the solution of the inverse scattering problem in one dimension. The paper includes (i) a discussion of some aspects of the numerical solution of the direct problem, (ii) typical results of calculation and (iii) a comparison between exact solutions and forward scattering approximation (FSA) solutions of the direct problem. It is shown that the FSA allows accurate calculations of the reflected wave and thus constitutes a sound basis for the solution of the inverse problem treated in Part II.

Wave-Envelope Technique for Wave Propagation in Nonuniform Ducts

The method of variation of parameters is used to analyze wave propagation in variable area, plane ducts with no mean flow. The method has an explicit representation of the fast axial variation of the acoustic modes, and numerical integration is required only for the slower axial variations of the mode amplitudes and phases. Results are presented which demonstrate the numerical advantages of the method. Comparison of the results with those of a small perturbation theory are given. The relationship between this method and the method of weighted- residuals is discussed. 7 among others. Each approach has unique characteristics and advantages, as well as obvious limitations, either of a numerical or physical nature. For example, no tests have been made to establish the range of geometry variations for which the multiple-scale solutions remain valid; direct numerical analyses require small step sizes and large computation times for high frequencies and high-order modes because of the rapid axial and transverse oscillations; and weighted-residual analysis7 also requires a numerical integration over each axial oscillation of the signal although the transverse variations of high-order modes present no difficulty. The computation of these axial variations has been sim- plified in a direct numerical analysis of wave propagation in constant-area ducts by using an estimate of the harmonic axial variations of the fundamental mode.8 This procedure was reportedly advantageous even with estimates that were only moderately accurate. In the work reported here, acoustic propagation in variable- area ducts without mean flow is analyzed by the method of variation of parameters 9 in a manner that incorporates features of several previous investigations. To facilitate the study of high-order modes and multimodal interactions, the acoustic disturbance is represented as a superposition of parallel-duct eigenf unctions. Moreover, the fast axial variation is given explicitly, and numerical integration is required only for the slower axial variations of the amplitudes and the phases of the modes. We have borrowed the term 'wave-envelope method' as a description of this aspect of the method, although in most respects it bears little resemblance to the procedure used by Baumeister.8 Finally, the representation of the acoustic wave is required to satisfy an integrability constraint derived from the wave equation; this feature is similar to that used in the multiple-scale analysis by Nayfeh and Telionis,3 but does not have the small per- turbation limitation.