Free Wave Propagation Research Articles

Neural networks as a diagnosing tool for industrial level measurement through non-contacting radar type and support to the decision for its better application

Abstract: The aim of this study was to develop an analysis tool based on artificial neural networks (ANN) to detect level measurement problems with free wave propagation radars. The trend of using this type of radar has been growing in the last ten years mainly because of its easy installation on the top of tanks and reservoirs, and for its low rate maintenance comparing to other level measurement technologies. For the experiments, a Rosemount radar was used and the training of the neural network was based on the data from the software Radar Master. Therefore, some network topologies in different scenarios were tested and it was possible to demonstrate the efficiency of the ANN with accuracy rate between 94.44 to 100% for the first experiment with networks using 10, 20 or 50 neurons in the hidden layer. This technique was applied in a real industrial application, a sugar and ethanol mill, and accuracy rate was about 87,0 to 96,1%. This methodology can be applied to asset management software for diagnosis report or troubleshooting which would increase the level measurement reliability and plant safety.

A hybrid wave-mode formulation for the vibro-acoustic analysis of 2D periodic structures

In the framework of vibrational analysis of 2D periodic waveguides, Floquet–Bloch theorem is widely applied for the determination of wave dispersion characteristics. In this context, the Wave Finite Element Method (WFEM) combines Periodic Structure Theory (PST) with standard FE packages, enabling wave dispersion analysis of waveguides involving structurally realistic unit-cells. For such applications, the computational efficiency of the WFEM depends on the choice of the formulation and can lead to numerical issues, worsen by extensive computational cost. This paper presents a coupled wave-mode approach for the determination of wave dispersion characteristics in structurally advanced periodic structures. It combines two scales of model order reduction. At the unit-cell׳s scale, Component Mode Synthesis (CMS) provides the displacement field associated with local resonances of the periodic structure, while the free wave propagation is considered using a spectral problem projection on a reduced set of shape functions associated with propagating waves, thus providing considerable reduction of the computational cost. An application is provided for a bi-directionally stiffened panel and the influence of reduction parameters is discussed, as well as the robustness of the numerical results.

A lightweight vibro-acoustic metamaterial demonstrator: Numerical and experimental investigation

In recent years metamaterials gained a lot of attention due to their superior noise and vibration insulation properties, be it at least in some targeted and tuneable frequency ranges, referred to as stopbands. These are frequency zones for which free wave propagation is prevented throughout the metamaterial, resulting in frequency zones of pronounced wave attenuation. Metamaterials are achieved due to addition of an, often periodic, grid of resonant structures to a host material or structure. The interaction between resonant inclusions and host structure can lead to a performance which is superior to the ones of any of the constituent materials. A key element in this concept is that waves can be affected by incorporating structural resonant elements of sub-wavelength sizes, i.e. features that are actually smaller than the wavelength of the waves to be affected. This paves the way towards compact and light vibro-acoustic solutions in the lower frequency ranges. This paper discusses the numerical design and experimental validation of acoustic insulation based on the concept of metamaterials: a hollow core periodic sandwich structure with added local resonant structures. In order to investigate the sensitivity to specific parameters in the metamaterial design and the robustness of the design, a set of variations on the nominal design are investigated. The stop bands are numerically predicted through unit cell modelling after which a full vibro-acoustic finite element model is applied to predict the insertion loss of the demonstrator. The results of these analyses are compared with measurements; both indicate that this metamaterials concept can be applied to combine light weight, compact volume and good acoustic behaviour.

Trajectory Analysis of the Mechanism for Westward Propagation of Rossby Waves

Abstract An analysis of Rossby wave dynamics in two and three dimensions is carried from the point of view of a reference frame propagating with the zonal phase speed of the wave. Since trajectories and streamlines coincide in this reference frame, the mechanism for (westward) propagation of free waves has a different interpretation than in a reference frame fixed to the ground. In the wave reference frame, propagating free-wave solutions are possible only when parcels approach from the west. When parcels approach from the east, potential vorticity cannot be conserved along trajectories.

Off-axis angular spectrum method with variable sampling interval

We proposed a novel off-axis angular spectrum method (ASM) for simulating free space wave propagation with a large shifted destination plane. The off-axis numerical simulation took wave propagation between a parallel source and a destination plane, but a destination plane was shifted from a source plane. The shifted angular spectrum method was proposed for diffraction simulation with a shifted destination plane and satisfied the Nyquist condition for sampling by limiting a bandwidth of a propagation field to avoid an aliasing error due to under sampling. However, the effective sampling number of the shifted ASM decreased when the shifted distance of the destination plane was large which caused a numerical error in the diffraction simulation. To compensate for the decrease of an effective sampling number for the large shifted destination plane, we used a variable sampling interval in a Fourier space to maintain the same effective sampling number independent of the shifted distance of the destination plane. As a result, our proposed off-axis ASM with a variable sampling interval can produce simulation results with high accuracy for nearly every shifted distance of a destination plane when an off-axis angle is less than 75°. We compared the performances of the off-axis ASM using the Chirp Z transform and non-uniform FFT for implementing a variable spatial frequency in a Fourier space.

Gradual time reversal in thermo- and photo-acoustic tomography within a resonant cavity

Thermo- and photo-acoustic tomography require reconstructing initial acoustic pressure in a body from time series of pressure measured on a surface surrounding the body. For the classical case of free space wave propagation, various reconstruction techniques are well known. However, some novel measurement schemes place the object of interest between reflecting walls that form a de facto resonant cavity. In this case, known methods (including the popular time reversal algorithm) cannot be used. The inverse problem involving reflecting walls can be solved by the gradual time reversal method we propose here. It consists in solving back in time on the interval the initial/boundary value problem for the wave equation, with the Dirichlet boundary data multiplied by a smooth cutoff function. If T is sufficiently large one obtains a good approximation to the initial pressure; in the limit of large T such an approximation converges (under certain conditions) to the exact solution.

Dynamic analysis of functionally graded nanocomposite cylinders reinforced by wavy carbon nanotube under an impact load

This work mainly reports on the effects of the aspect ratio and waviness index of carbon nanotubes (CNTs) on the free vibration and stress wave propagation of functionally graded (FG) nanocomposite cylinders that are reinforced by wavy single-walled carbon nanotubes based on a mesh-free method. In this simulation, an axisymmetric model is used, three linear types of FG distributions of wavy CNTs along the radial direction of the cylinder are considered and their results are compared with the results of a uniform distribution. The material properties are estimated by a micromechanical model. In the mesh-free analysis, moving least squares shape functions are used for approximation of the displacement field in the weak form of motion equation and the transformation method was used for the imposition of essential boundary conditions. Also, the effects of volume fraction and distribution pattern of wavy CNTs and cylinder thickness are investigated on the natural frequency and stress wave propagation of carbon nanotube reinforced composite (CNTRC) cylinders subjected to an impact load. It is observed that waviness has a significant effect on the dynamic behavior of the CNTRC cylinders.

Excitation and propagation of shear horizontal waves in a piezoelectric layer imperfectly bonded to a metal or elastic substrate

The performance of shear horizontal waves excited by an external voltage imposed on the surface of a transversely isotropic piezoelectric sensitive layer imperfectly bonded to a metal or elastic substrate is investigated. The phase velocity, electromechanical coupling factor, temperature coefficient of delay, mass loading sensitivity, and displacement distribution along the thickness direction for the propagation of free waves, resonance frequency, and displacement signal and input admittance for the forced vibration are considered. Numerically, the SH wave speed smaller than Bleustein–Gulyaev wave velocity of a piezoelectric layer can be achieved for electrically open and shorted conditions when the interface is imperfect, which is totally different from the case of perfect interface. The imperfect interface evidently improves the energy transformation ratio, temperature stability, and mass sensitivity of the composite structure. The viscoelastic damping parameter has no relationship with resonance frequencies, and it only decreases the amplitudes of displacement signal and input admittance. The outcome is widely applicable and can be used to design high-performance surface acoustic wave devices.

A reduced formulation for the free-wave propagation analysis in composite structures

This paper presents an improved numerical strategy for the broadband analysis of wave propagation in composite or complex cross-sectional waveguides using the wave finite element method (WFE). Numerical analysis of such structures require highly discretized finite element models and leads to extensive computations. The proposed formulation relies on a projection of the cross-sectional transfer matrices on a reduced set of shape functions associated to propagating waves. Dispersion curves are then predicted only using a reduced number of eigenvectors. The performances and stability of this method are evaluated using the wavenumbers and wave shapes. Validations are provided for a sandwich composite beam and a cylindrical elasto-acoustic waveguide.

Propagation of Free Torsional Waves in a Non Homogeneous Magneto visco Elastic Slab with a Cylindrical Hole

The aim of the present paper is to investigate the propagation of free torsional waves in a non-homogeneous magneto-visco-elastic slab with a cylindrical hole and obtain frequency equation. The shear modulus meu and the density rho of the slab are assumed to vary as some power of the radial distance.

Effects of Underground Cavities on the Frequency Spectrum of Seismic Shear Waves

A numerical method is proposed to study the scattering of seismic shear waves induced by the presence of underground cavities in homogeneous soils. The method is based on the superposition of two solutions: the solution of the free-wave propagation problem in a uniform half-space, easily determined analytically, and the solution of the wave scattering problem due to the cave presence, evaluated numerically by means of an ad hoc code implemented by using the ANSYS Parametric Design Language. In the two-dimensional setting, this technique is applied to the case of a single cave, placed at a certain depth from the ground level. The frequency spectrum of the seismic shear oscillation on the ground surface is determined for different dimensions and depths of the cave and compared with the spectrum registered without caves. The influence of the cave dimensions and depth on the spectrum amplification is analyzed and discussed.

Ostéotomies métatarsiennes distales percutanées : suivi rétrospectif de 50 cas

Modeling the propagation of nonlinear free surface waves is a challenging task but inevitable in studying nearshore wave propagation processes. More recently, meshless methods are emerging as potential tools for studying water wave related problems, in particular when there is a flow separation. In this study, smoothed particle hydrodynamics (SPH) has been shown to be useful to study the propagation of nonlinear water waves generated in a numerical flume. The problems considered address various aspects associated with long time simulation and highly nonlinear waves such as bore formation and wave breaking. An explicit dynamic free surface boundary condition has been imposed in the SPH model for steady long time simulation. A correction has been prescribed for the mass of the ghost particles at the geometric singular zones for the present application. The developed model is validated with FEM based simulation and other meshless methods. The split-up of a single solitary wave as it crosses continental shelf is simulated by the present method.

SPH Simulation of shallow water wavepropagation

Modeling the propagation of nonlinear free surface waves is a challenging task but inevitable in studying nearshore wave propagation processes. More recently, meshless methods are emerging as potential tools for studying water wave related problems, in particular when there is a flow separation. In this study, smoothed particle hydrodynamics (SPH) has been shown to be useful to study the propagation of nonlinear water waves generated in a numerical flume. The problems considered address various aspects associated with long time simulation and highly nonlinear waves such as bore formation and wave breaking. An explicit dynamic free surface boundary condition has been imposed in the SPH model for steady long time simulation. A correction has been prescribed for the mass of the ghost particles at the geometric singular zones for the present application. The developed model is validated with FEM based simulation and other meshless methods. The split-up of a single solitary wave as it crosses continental shelf is simulated by the present method.

Surface waves guided by topography in an anisotropic elastic half-space

We consider the propagation of free surface waves on an elastic half-space that has a localized geometric inhomogeneity perpendicular to the direction of wave propagation (such waves are known as topography-guided surface waves). Our aim is to investigate how such a weak inhomogeneity modifies the surface-wave speed slightly. We first recover previously known results for isotropic materials and then present additional results for a generally anisotropic elastic half-space assuming only one plane of material symmetry. It is shown that a topography-guided surface wave in the present context may or may not propagate depending on a number of factors. In particular, they cannot propagate if the original two-dimensional surface wave on a flat half-space is supersonic with respect to the speed of anti-plane shear waves. For the case when a topography-guided surface wave may exist, the existence and computation of wave speed correction is reduced to the solution of a simple eigenvalue problem whose properties are previously well understood. As a by-product of our analysis, we deduce that there exists at least one topography-guided surface wave on an isotropic elastic half-space, and that it is unique when the geometric inhomogeneity has sufficiently small amplitude.

Shock wave impact simulation of a vehicle occupant using fluid/structure/dynamics interactions

Ground vehicles subjected to blast can result in vehicle movements and occupant injuries. The engineering mechanisms involved in such blasts include fluid dynamics, solid dynamics, and multi-body dynamics. This paper describes a parallel computer simulation methodology that can be applied to couple the structural deformation prediction of a ground vehicle system and the associated occupant kinematics during a blast event. Generic box and dummy models were used in the demonstration of this newly-developed methodology. The generic system structure consists of an outer cube representing a vehicle armor structure, and a dummy representing a crew member in a ground vehicle. Simulation results for different cases include free air blast wave propagation, blast on a metal plate and over a hemispherical dome, and blast wave interaction with a vehicle and its occupant inside.

Free-wave propagation relationships of second-order and fourth-order periodic systems

This talk develops an analytical expression for the determinant of two diagonally-indexed, full matrices when they are zero. These matrices originate from second- and fourth-order periodic system theory. The partial differential equations of these systems are solved using a series solution and are converted into closed-form analytical expressions. The denominators of these expressions are zero when free-wave propagation is present, and these denominators are equated to the determinants of the system matrices derived from a second analytical method. This process develops a relationship between frequency and wavenumber that is explicit for free-wave propagation in these systems. Two examples are included to illustrate this relationship.

Dynamics of rotating composite beams: A comparative study between CNT reinforced polymer composite beams and laminated composite beams using spectral finite elements

This paper presents a spectral finite element formulation for uniform and tapered rotating CNT embedded polymer composite beams. The exact solution to the governing differential equation of a rotating Euler–Bernoulli beam with maximum centrifugal force is used as an interpolating function for the spectral element formulation. Free vibration and wave propagation analysis is carried out using the formulated spectral element. The present study shows the substantial effect of volume fraction and L/D ratio of CNTs in a beam on the natural frequency, impulse response and wave propagation characteristics of the rotating beam. It is found that the CNTs embedded in the matrix can make the rotating beam non-dispersive in nature at higher rotation speeds. Embedded CNTs can significantly alter the dynamics of polymer-nanocomposite beams. The results are also compared with those obtained for carbon fiber reinforced laminated composite rotating beams. It is observed that CNT reinforced rotating beams are superior in performance compared to laminated composite rotating beams.

Dynamic analysis of functionally graded nanocomposite cylinders reinforced by carbon nanotube by a mesh-free method

In this paper, dynamic analysis of nanocomposite cylinders reinforced by single-walled carbon nanotubes (SWCNTs) subjected to an impact load was carried out by a mesh-free method. Free vibration and stress wave propagation analysis of carbon nanotube reinforced composite (CNTRC) cylinders are presented. In this simulation, an axisymmetric model is used. Four types of distributions of the aligned carbon nanotubes (CNTs) are considered; uniform and three kinds of functionally graded (FG) distributions along the radial direction of cylinder. Material properties are estimated by a micro mechanical model. In the mesh-free analysis, moving least squares (MLSs) shape functions are used for approximation of displacement field in the weak form of motion equation and the transformation method was used for the imposition of essential boundary conditions. Effects of the kind of distribution and volume fractions of carbon nanotubes and cylinder thickness on the natural frequencies and stress wave propagation of CNTRC cylinders are investigated. Results obtained for this analysis were compared with FEM and previous published work and good agreement was seen between them.

On the problem of radial vibrations in non-homogeneity isotropic cylinder under influence of initial stress and magnetic field

In the present work, the effects of initial stress, magnetic field and non-homogeneity on wave propagation of free harmonic waves in isotropic material are discussed. The one-dimensional equation of elastodynamic is solved in terms of radial displacement and different cases of the boundary conditions for the hollow cylinder are considered. The determination is concerned with the eigenvalues of the natural frequencies of the radial vibrations for different boundary conditions in the case of harmonic vibrations. Numerical results are given and illustrated graphically for each case considered. Comparisons are made with the results in the absence of initial stress, magnetic field and non-homogeneity.

Formation of a wave on an ice-sheet above the dipole, moving in a fluid

Theory of wave motions of a fluid with an ice-sheet was developed due to the necessity of solving of a number of problems of marine and land physics. The main attention in these investigations was focused on propagation and interaction of free waves, and also on appearance of waves under action of different loadings on the ice-sheet. From the other side, the problems dealing with waves on the fluid surface, free from the ice due to motion in the mass of the fluid of rigid bodies, has the known solutions. In this connection, it seems natural to disserminate the formulation and methods of such problems to the case of the fluid with the ice-sheet. In the present note we describe the character of formation of waves from the singularity, localized in the fluid of infinite depth beneath the ice-sheet. We use the example of the dipole, which models a cylinder in the infinite mass of the fluid. The character of the formation does not depend on the type of singularity. The ice-sheet is considered as a thin elastic plate of a constant width, floating on the water surface.