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Allen T. Chwang - One of the best experts on this subject based on the ideXlab platform.

  • Scattering of surface waves by a semi-infinite floating Elastic Plate
    Physics of Fluids, 2001
    Co-Authors: Trilochan Sahoo, Allen T. Chwang
    Abstract:

    A new inner product is developed based on the Fourier analysis to study the scattering of surface waves by a floating semi-infinite Elastic Plate in a two-dimensional water domain of finite depth. The eigenfunctions for the Plate-covered region are orthogonal with respect to this new inner product. The problem is studied for various wave and geometrical conditions. Especially, the influence of different edge conditions on the hydrodynamic behavior is investigated and compared. The edge conditions considered in the present study involve (i) a free edge, (ii) a simply supported edge, and (iii) a built-in edge. The hydrodynamic performance of an Elastic Plate is characterized for various conditions in terms of wave reflection and transmission, Plate deflection, and surface strain. It is observed that the hydrodynamic behavior depends on the wave conditions, the geometrical settings, and the edge conditions. The built-in edge condition induces the maximum wave reflection and the minimum wave transmission. The free edge condition leads to the maximum Plate deflection.

  • scattering of surface waves by a semi infinite floating Elastic Plate
    Physics of Fluids, 2001
    Co-Authors: Trilochan Sahoo, Allen T. Chwang
    Abstract:

    A new inner product is developed based on the Fourier analysis to study the scattering of surface waves by a floating semi-infinite Elastic Plate in a two-dimensional water domain of finite depth. The eigenfunctions for the Plate-covered region are orthogonal with respect to this new inner product. The problem is studied for various wave and geometrical conditions. Especially, the influence of different edge conditions on the hydrodynamic behavior is investigated and compared. The edge conditions considered in the present study involve (i) a free edge, (ii) a simply supported edge, and (iii) a built-in edge. The hydrodynamic performance of an Elastic Plate is characterized for various conditions in terms of wave reflection and transmission, Plate deflection, and surface strain. It is observed that the hydrodynamic behavior depends on the wave conditions, the geometrical settings, and the edge conditions. The built-in edge condition induces the maximum wave reflection and the minimum wave transmission. The...

Xiafu Lv - One of the best experts on this subject based on the ideXlab platform.

  • experimental verification of cumulative growth effect of second harmonics of lamb wave propagation in an Elastic Plate
    Applied Physics Letters, 2005
    Co-Authors: Mingxi Deng, Ping Wang, Xiafu Lv
    Abstract:

    Wedge transducers are used to generate and detect the primary (fundamental) waves and second harmonics of Lamb wave propagation on the surface of an Elastic Plate. The amplitudes of the primary waves and the second harmonics on the Plate surface are measured for different separations of the transmitting and receiving wedge transducers. In the immediate vicinity of a driving frequency at which the primary and the double-frequency Lamb waves have the same phase velocities, the quantitative relationships of the second-harmonic amplitudes on propagation distance are analyzed. It is experimentally verified that the second harmonics of primary Lamb waves have a cumulative growth effect with propagation distance.

  • experimental observation of cumulative second harmonic generation of lamb wave propagation in an Elastic Plate
    Journal of Physics D, 2005
    Co-Authors: Mingxi Deng, Ping Wang, Xiafu Lv
    Abstract:

    The experimental observation of cumulative second-harmonic generation of the primary (fundamental) Lamb-wave propagation is reported in this paper. Using the dispersion relations for Lamb waves and the modal expansion analysis approach for waveguide excitation, a straightforward model has been presented for analysing the physical process of generation of the time-domain pulses of the second harmonics by the fundamental time-domain pulses of the primary Lamb-wave propagation. The physical meaning of the integrated amplitudes, both of the fundamental waves and the second harmonics, is clearly illustrated. Wedge transducers are used to generate and detect the fundamental waves and the second harmonics of the Lamb-wave propagation on the surface of an Elastic Plate. The clear second-harmonic signals can be observed near the frequency at which Lamb waves have a strong nonlinearity. The amplitudes of the fundamental waves and the second harmonics of the Lamb-wave propagation on the Plate surface are measured for different separations between the transmitting and receiving wedge transducers. In the immediate vicinity of a driving frequency at which the fundamental and the double-frequency Lamb waves have the same phase velocities, the quantitative relationships between the second-harmonic amplitudes and propagation distance are analysed. It is observed that the second harmonics of primary Lamb waves grow with propagation distance.

Murray S Korman - One of the best experts on this subject based on the ideXlab platform.

  • nonlinear tuning curve and two tone tests using glass beads vibrating over clamped Elastic Plate
    Proceedings of Meetings on Acoustics, 2018
    Co-Authors: Emily V Santos, Murray S Korman
    Abstract:

    A soil Plate oscillator (SPO) apparatus consists of two circular flanges sandwiching and clamping a thin circular Elastic Plate. The apparatus can model the acoustic landmine detection problem. Uniform spherical glass beads – representing a nonlinear mesoscopic Elastic material – are supported at the bottom by the acrylic Plate (4.5 inch diam, 1/8 inch thick) and stiff cylindrical sidewalls of the upper flange. A magnetic disk centered and fastened below the Plate is driven by an AC coil placed below the magnet. Nonlinear tuning curves of the magnet’s acceleration are measured by driving the coil with a swept sinusoidal signal applied to a constant current amplifier. In two-tone tests, air-borne sound from 3 inch diameter speakers drive the bead column surface at closely spaced frequencies near the fundamental resonance. Nonlinearly generated combination frequency tones are compared for each of the bead diameter experiments.

  • classroom demonstration of nonlinear tuning curve vibration and two tone tests using a column of glass beads vibrating over a clamped Elastic Plate
    Journal of the Acoustical Society of America, 2018
    Co-Authors: Emily V Santos, Murray S Korman
    Abstract:

    A soil Plate oscillator (SPO) apparatus consists of two circular flanges sandwiching and clamping a thin circular Elastic Plate. The apparatus can model the acoustic landmine detection problem. Here, uniform spherical glass beads—representing a nonlinear mesoscopic Elastic material—are supported at the bottom by the acrylic Plate (4.5 inch diam, 1/8 inch thick) and stiff cylindrical sidewalls of the upper flange. A magnetic disk centered and fastened below the Plate is driven by an AC coil placed below the magnet. Nonlinear tuning curves of the magnet’s acceleration are measured by driving the coil with a swept sinusoidal signal applied to a constant current amplifier. Ten (separate) tuning curve experiments are performed using a fixed column of 350 grams of beads using 1,2,3,…,10 mm diameter beads. The backbone curves (peak acceleration vs. corresponding resonant frequency) exhibit a linear region with comparable slopes, while the detailed curvature vs. bead diameter reveals more structure. A bilinear hy...

  • classroom demonstration of acoustic landmine detection using a clamped soil Plate oscillator
    Journal of the Acoustical Society of America, 2018
    Co-Authors: Jenna M Cartron, Murray S Korman
    Abstract:

    In landmine detection some mines (constructed out of plastic) are difficult to detect using ground penetrating radar. In acoustic landmine detection, one can detect a vibration profile across the surface of the soil (sand) due to the interaction between the soil column and the Elastic top Plate. Table top classroom demonstrations can bring to life idealized field experiments. The soil Plate oscillator (SPO) apparatus models an idealization of an acoustic landmine detection experiment. The clamped circular Elastic Plate models the top Plate of a plastic buried mine while the soil column supported by the Elastic Plate models the burial depth. An amplified sinusoidal chirp from a sweep spectrum analyzer drives an AC coil placed below a small magnet attached to the underside of the clamped Plate—causing vibration. A laser Doppler vibrometer measured the rms particle velocity at 13 scan locations across the 4.5 inch diameter soil surface in sweeps between 50 Hz and 850 Hz. Results show a fundamental mode shape...

  • demonstration of nonlinear tuning curve vibration of granular medium supported by a clamped circular Elastic Plate using a soil Plate oscillator
    Journal of the Acoustical Society of America, 2017
    Co-Authors: Emily V Santos, Murray S Korman
    Abstract:

    A demonstration will be conducted in order to show how a soil Plate oscillator (SPO) filled with granular material will create a nonlinear system due to shifting peaks in a tuning curve with incremental increases in the swept drive amplitude. An SPO has two flanges clamping an Elastic Plate which supports a circular column of granular material. The Plate (with a magnet and accelerometer fastened to the underside) is driven below by an amplified swept sinusoidal current applied to an AC coil. Past results have used masonry sand, granular edible uncooked materials, and glass beads in order to study the nonlinear tuning curve response near a resonance with (1) a fixed soil column while changing drive amplitude and (2) mass loading of a soil column versus the resonant frequency response of the system at a fixed drive amplitude. When the experiments are performed at a fixed drive but with a changing mass layer the resonant frequency increases then decreases with increased added mass due to an increase in flexu...

  • nonlinear behavior of different sized granular bead media on a vibrating clamped circular Elastic Plate
    Journal of the Acoustical Society of America, 2017
    Co-Authors: Claire E Haas, Murray S Korman
    Abstract:

    This experiment uses a soil Plate oscillator (SPO), or a circular acrylic (Elastic) Plate clamped into place using flanges, to study the nonlinear oscillatory behavior of a column of granular media (with selected diameters) that is supported by the Plate. Secured on the underside of the Plate's center is a rare earth magnet that is driven by an AC coil which is controlled by an amplified swept sinusoidal chirp. An accelerometer is fastened to the magnet and a spectrum analyzer measures the Plate's acceleration versus frequency. In separate measurements of nonlinear tuning curve response, the Plate is loaded with 350 grams of spherical soda lime beads of diameters 2, 3, 4, 5, 6, 7, and 10 mm. The driver current is changed in 40 evenly spaced increments, holding other parameters fixed, during each sweep. A study of the backbone curve (rms acceleration a(f) peak versus frequency f) for each bead diameter exhibits a frequency “softening” vs. amplitude—similar to the nonlinear mesoscopic Elasticity observed in...

Michael H Meylan - One of the best experts on this subject based on the ideXlab platform.

  • water wave scattering and energy dissipation by a floating porous Elastic Plate in three dimensions
    Wave Motion, 2017
    Co-Authors: Michael H Meylan, Luke G Bennetts, Malte A Peter
    Abstract:

    Abstract An eigenfunction-matching method is developed for the problem of linear water-wave scattering by a circular floating porous Elastic Plate, and a coupled boundary-element and finite-element method is developed for the problem in which the Plate is of arbitrary shape. The methods are shown to produce the same solutions for a circular Plate, and their convergence properties are established. The impact of porosity on the far field (the wave field away from the Plate) is investigated using integral representations for the Bessel and Hankel functions. It is shown that wave-energy dissipation due to porosity initially increases as the Plate becomes more porous, but reaches a maximum and then slowly decreases as the porosity increases further.

  • the wiener hopf and residue calculus solutions for a submerged semi infinite Elastic Plate
    Journal of Engineering Mathematics, 2012
    Co-Authors: Timothy D Williams, Michael H Meylan
    Abstract:

    We present a solution for the interaction of normally incident linear waves with a submerged Elastic Plate of semi-infinite extent, where the water has finite depth. While the problem has been solved previously by the eigenfunction-matching method, the present study shows that this problem is also amenable to the more analytical, and extremely efficient, Wiener–Hopf (WH) and residue calculus (RC) methods. We also show that the WH and RC solutions are actually equivalent for problems of this type, a result which applies to many other problems in linear wave theory. (e.g., the much-studied floating Elastic Plate scattering problem, or acoustic wave propagation in a duct where one wall has an abrupt change in properties.) We present numerical results and a detailed convergence study, and discuss as well the scattering by a submerged rigid dock, particularly the radiation condition beneath the dock.

  • an Elastic Plate model for wave attenuation and ice floe breaking in the marginal ice zone
    Journal of Geophysical Research, 2008
    Co-Authors: Alison L Kohout, Michael H Meylan
    Abstract:

    [1] We present a model for wave attenuation in the marginal ice zone (MIZ) based on a two-dimensional (one horizontal and one vertical dimension) multiple floating Elastic Plate solution in the frequency domain, which is solved exactly using a matched eigenfunction expansion. The only physical parameters that enter the model are length, mass, and Elastic stiffness (of which, the latter two depend primarily on thickness) of the ice floes. The model neglects all nonlinear effects as well as floe collisions or ice creep and is therefore most applicable to floes which are large compared to the thickness and to wave conditions which are not extreme. The solution for a given arrangement of floes is fully coherent, and the results are therefore dependent on the exact geometry. We firstly show that this dependence can be removed by averaging over a distribution of floe lengths (we choose the Rayleigh distribution). We then show that after this averaging, the attenuation coefficient is a function of floe number and independent of floe length, provided the floe lengths are sufficiently large. The model predicts an exponential decay of energy, just as is shown experimentally. This enables us to provide explicit values for the attenuation coefficient, as a function of the average floe thickness and wave period. We compare our theoretical predictions of the wave attenuation with measured data and other scattering models. The limited data allows us to conclude that our model is applicable to large floes for short to medium wave periods (6 to 15 seconds). We also derive a floe breaking model, based on our wave attenuation model, which indicates that we are under-predicting the attenuation coefficients at long periods.

Celine Grandmont - One of the best experts on this subject based on the ideXlab platform.

  • Existence of weak solutions for the unsteady interaction of a viscous fluid with an Elastic Plate
    2012
    Co-Authors: Celine Grandmont
    Abstract:

    We consider a three–dimensional viscous incompressible fluid governed by the Navier–Stokes equations, interacting with an Elastic Plate located on one part of the fluid boundary. We do not neglect the deformation of the fluid domain which consequently depends on the displacement of the structure. The purpose of this work is to study the solutions of this unsteady fluid–structure interaction problem, as the coefficient modeling the viscoElasticity (resp. the rotatory inertia) of the Plate tends to zero. As a consequence, we obtain the existence of at least one weak solution for the limit problem (Navier–Stokes equation coupled with a Plate in flexion) as long as the structure does not touch the bottom of the fluid cavity. 1 Introduction. Many physical phenomena deal with a fluid interacting with a moving or deformable structure. This kind of problems have a lot of important applications, for instance in areolasticity, biomechanics, hydroElasticity, sedimentation... From the mathematical point of view they have been studied extensivell

  • Existence of Weak Solutions for the Unsteady Interaction of a Viscous Fluid with an Elastic Plate
    SIAM Journal on Mathematical Analysis SIAM Journal of Mathematical Analysis, 2008
    Co-Authors: Celine Grandmont
    Abstract:

    We consider a three--dimensional viscous incompressible fluid governed by the Navier--Stokes equations, interacting with an Elastic Plate located on one part of the fluid boundary. We do not neglect the deformation of the fluid domain which consequently depends on the displacement of the structure. The purpose of this work is to study the solutions of this unsteady fluid--structure interaction problem, as the coefficient modeling the viscoElasticity (resp. the rotatory inertia) of the Plate tends to zero. As a consequence, we obtain the existence of at least one weak solution for the limit problem (Navier--Stokes equation coupled with a Plate in flexion) as long as the structure does not touch the bottom of the fluid cavity.

  • existence of weak solutions for the unsteady interaction of a viscous fluid with an Elastic Plate
    Journal of Mathematical Fluid Mechanics, 2005
    Co-Authors: Antonin Chambolle, Benoit Desjardins, Maria J Esteban, Celine Grandmont
    Abstract:

    The purpose of this work is to study the existence of solutions for an unsteady fluid-structure interaction problem. We consider a three-dimensional viscous incompressible fluid governed by the Navier–Stokes equations, interacting with a flexible Elastic Plate located on one part of the fluid boundary. The fluid domain evolves according to the structure’s displacement, itself resulting from the fluid force. We prove the existence of at least one weak solution as long as the structure does not touch the fixed part of the fluid boundary. The same result holds also for a two-dimensional fluid interacting with a one-dimensional membrane.