ABSTRACT
Coupled-mode equations governing the amplitudes of the higher-order symmetric Lamb modes S1 and S2 with the antisymmetric mode A2 in an infinite elastic plate with sinusoidal surface corrugation over a finite length are obtained via multiple-scales analysis. This phenomenon of threemode coupling is observed when the wavenumbers k(s1) and k(s2) of the symmetric modes and k(A2) of the antisymmetric mode satisfy the simultaneous resonance conditions k(s1) - k(A2) = k(w) and k(A2) - k(s2) = k(w), where k(w) is the wavenumber of the sinusoidal corrugation. Near resonance, the coupled amplitude equations are solved exactly as an initial-value problem and it is seen that the modes are transmitted through the grating without reflection. Complete conversion from the symmetric modes into the antisymmetric mode is observed at periodic intervals along the grating when the resonance conditions are exactly satisfied. The effect of detuning away from resonance also shows propagation without reflection with periodic energy exchange. In the latter case, the modes couple without complete conversion. This phenomenon of mode conversion is confirmed by the results of an experiment on an aluminum plate with a triangular grating excited with the S2 symmetric mode at 2.7 MHz.
ABSTRACT
Guided waves propagation in immersed plates with irregular surfaces has potential application to detection and assessment of the extent, depth and pattern of the irregularity. The complexity of the problem, due to the large number of involved parameters, has limited the number of existing studies. The simplest case of irregularities of practical interest is the two-dimensional corrosion profile. Even this case is in general so complex, that one can extract several amplitude dominant periodic surfaces only by using a Fourier spectrum of the surface. Guided waves in plates, with one or both free surfaces having periodic perturbations of different shapes, have been presented in specialized literature. In this paper is studied the propagation of Lamb waves in an aluminum plate with a periodic grooved surface on only one side and immersed in water. The interaction between an incident Lamb wave and the grating gives rise to retro-converted waves. Preliminary numerical simulation by the finite element method is performed in order to obtain key parameters for the experiments. It is shown that retro-converted waves radiating into the water are detectable although their amplitudes are small. The phonon relation is verified for the leaky Lamb modes. The damping coefficients of the leaky Lamb modes in the grooved immersed plate are evaluated.
Subject(s)
Aluminum/chemistry , Models, Chemical , Scattering, Radiation , Sound , Computer Simulation , Materials Testing , Surface PropertiesABSTRACT
In this paper, guided ultrasonic wave propagation is analyzed in an elastic plate with sinusoidal surface corrugations. The corrugated area acts as a finite-length grating which corresponds to a 1-D phononic crystal (PC). The multiple-scale perturbation technique is used to derive coupled-mode equations describing the amplitudes of interacting modes. These equations are solved exactly for the two-point boundary-value problem of the PC. The study involves the coupling of the incident symmetric Lamb wave S(0) to the reflected antisymmetric Lamb wave A(0). The influences of the depth of corrugation and length of the PC are studied. Theoretical results are compared with experimental measurements.
ABSTRACT
This paper deals with the analysis of the guided evanescent waves in stopbands of a 1D phononic crystal (PC). A new numerical implementation is shown in order to get the complex values of the wavenumbers in a frequency range where a gap occurs. The considered phononic system is an aluminum plate with a one-dimensional sinusoidal grating. For this structure a mode-gap (mini stopband) occurs at low frequency: it involves the two fundamental Lamb modes A(0) and S(0). The numerical study is performed by using a finite element method (ATILA code). The experiments deal with a finite length grating and evanescent waves are characterized at the vicinity of the mini stopband.
ABSTRACT
The aim of this work is to propose a method to determine the elastic parameters and the thickness of a thin epoxy film located inside a 3-layer aluminum/epoxy/aluminum structure, based on ultrasonic measurements. This study is conducted at low frequencies, to allow the vibration of the whole structure. First, the direct problem is addressed. The sensitivity of the vibration modes to the parameters of interest is studied to select the most sensitive one for a given parameter to be determined. Second, the identification of the parameters with the selected modes is obtained by a minimization of the characteristic equation. This process is applied to experimental data: the longitudinal and shear wave velocities and the thickness of the epoxy film are obtained within a 3% error range.
ABSTRACT
When a Lamb wave propagates on a plate engraved by a periodic grating, it may exhibit attenuation. This attenuation is related to a coupling of this incident mode with other propagating modes. As the propagation takes place in a periodic medium, the dispersion curves of the modes are of interest because they exhibit passbands and stopbands related to the geometry of the waveguide. The goal of this work is to quantitatively establish the relation between the value of the attenuation of the propagating waves and the width of the forbidden bands appearing inside the Brillouin zone. This study is performed by using a finite element method (ATILA code).
ABSTRACT
A new 4D space-time-wave number-frequency representation Z(x,t,k,f) is introduced. The Z(x,t,k,f) representation is used for processing 2D space-time signal collection issued from wave propagation along a 1D medium. This representation is an extension along the time dimension of the space-wave number-frequency representation. The Z(x,t,k,f) representation is obtained by short time-space 2D Fourier transforming the space-time collection. The Z(x,t,k,f) representation allows the characterization transient aspects of wave generation and propagation in both space and time dimensions. The Z(x,t,k,f) representation is used to experimentally investigate Lamb wave generation and propagation around a cylindrical shell (relative thickness is equal to 0.03) surrounded by water and excited by a pulse (0.1 micros duration with 1-5 MHz transducers). Three kinds of fluids have been used inside the shell: air, water, propanol. In all the cases, the Z(x,t,k,f) analysis clearly identify the reflected field on the insonified side of the shell and it allows the measurement of the local reflection coefficients R(x,t,k,f). The generation and the propagation of Lamb waves are also quantified. For the liquid filled shells, the multiple internal reflections are revealed by Z(x,t,k,f) analysis: the local transmission coefficients T(x,t,k,f) are also measured. When local matching conditions allows Lamb wave generation, the multiple regeneration of Lamb wave is observed. Based on these results, a link is establish toward the theoretical results obtained by steady state approach and Sommerfeld-Watson transform.
ABSTRACT
The evolution of the experimental frequency width of symmetric modes of an aluminum plate is studied as a function of the angle of incidence below the first critical angle. It is found that the frequency width predicted by resonant scattering theory, corrected for the directivity of emitter and receiver, generally explains the experimental frequency width well. However, large discrepancies remain for the frequency width of the S1 mode at angles of incidence larger than 9 degrees. It is demonstrated that these are caused by not taking into account the complex nature of the slowness of the plate mode. This suggests that there is a need for a theory that models the interaction of a beam of ultrasound, bounded in space and time, with an elastic plate.
