In this paper, we numerically and experimentally demonstrate the existence of complete band gaps and resonances in a plate with a periodic stubbed surface. Numerical results show that a complete band gap forms as the stub height reaches about three times the plate thickness. In the experiment, we used a pulsed laser to generate broadband elastic waves and used optical devices as well as point piezoelectric transducers to detect wave signals. The results show that the numerical predictions are in very good agreement with those measured experimentally. Remarkable resonances on the top surface of the stubs are found and discussed.

Evidence of complete band gap and resonances in a plate with periodic stubbed surface

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Recent research advances in the dynamic behavior of shells: 1989–2000, Part 2: Homogeneous shells

This paper presents a study of the velocity of the propagation of energy in guided waves in plates. The motivation of the work comes from the practical observation that the conventional approach to predicting the velocities of pulses or wave packets, that is, the simple group velocity calculation, breaks down when the guided waves are attenuative. The conventional approach is therefore not valid for guided waves in absorbing materials or for leaky waves. The paper presents a theoretical derivation of an expression to predict the energy velocity of guided waves in an isotropic plate, based on the integration of the Poynting energy vectors. When applied to modes with no attenuation, it is shown analytically from this expression that the energy velocity is always identical to the group velocity. On the other hand, when applied to attenuative modes, numerical integration of the expression to yield the true energy velocity shows that this can differ quite significantly from the group velocity. Experimental validation of the expression is achieved by measuring the velocity of wave packets in an absorbing plate, under such conditions when the energy velocity differs substantially from the group velocity. Excellent agreement is found between the predictions and the measurements. The paper also shows the Poynting vectors in the various model studies, and some interesting phenomena relating to their directions.

Guided waves energy velocity in absorbing and non-absorbing plates

Analysis of adhesively bonded repairs in composites: Damage detection and prognosis

The study of the normal diffusion of an ultrasonic plane wave by cylinders and plates imbedded in the water shows resonances which are the natural modes of vibration. When a natural mode of an elastic target is excited, the energy which is stored during the forced excitation is emitted after the end of the forced excitation. The observation of backscattered spectra obtained by the Resonance Isolation and Identification Method (RIIM) from an aluminum cylinder shows supplementary resonances. The directivity pattern of the transducer is the cause of these supplementary resonances. The behavior of these resonances is analogous to the resonances of the plate. This leads us to study the natural modes of the cylinder. All the resonances which are experimentally detected may be considered as normal modes of the target. The results obtained on plates and cylinders have a common point: the generation of a guided wave by the excitation of a resonance.

Resonances of plates and cylinders: Guided waves

The propagation of Lamb waves in a plate with an engraved periodic grating is addressed in this article. Mode conversions and reflections are analyzed. In the first part the conversion modes are explained by the existence of a resonance condition between the Lamb-wave wavenumbers and the fundamental and harmonic spatial periods of the grating. These phenomena are experimentally and numerically highlighted for a metallic waveguide with a rectangular grating. The second part focuses on the pseudo-Lamb wave dispersion curves in a periodic waveguide. The periodicity implies that the Lamb waves dispersion curves fold back at the edge of the Brillouin zone. Several stop bands appear: classical band gaps at the boundary of the Brillouin zone and mini-stop-bands inside the Brillouin zone. For the ministop band, dispersion curves cross and a possible coupling occurs between the modes. Finally, conversions or the existence of gaps are linked with the Power Spectral Density of the grating profile.

Ultrasonic guided waves on a periodical grating: Coupled modes in the first Brillouin zone

In this paper the propagation of Lamb waves in an aluminium plate with a periodic grating containing triangular grooves is studied. Numerical simulations (FEM) are performed. A single incident mode is excited on a flat area and the interaction with the periodic grating is studied. Reflected converted waves are observed when the incident Lamb wave passes through the grating. At the entrance of the periodic grating, a phonon relation is written between the incident signal, the converted mode, and the phonon related to the grating. An experimental verification of the phonon relation is carried out.

Propagation of Lamb waves in a plate with a periodic grating: Interpretation by phonon

Interaction of Lamb waves on bonded composite plates with defects

In this paper, the authors deal with theoretical and experimental studies about the acoustic scattering by an elastic solid cylinder immersed in water, at oblique incidence. Comparisons are made between the calculated form function and measured scattered pressure for incidence angles varying from 0° to 30°, in the normalized frequency range 0–30. The behavior of the resonances when the incidence angle increases is shown and the connection between helical surface waves propagation and resonance is explained, using the contributions of the resonance scattering theory and the Sommerfeld–Watson transformation. More accurately, resonances are due to the phase matching of circumnavigating helical surface waves, and a refraction effect is found to take place between the incident and the helical surface wave direction of propagation, which clearly explains the resonance shift with respect to incidence angle variations. Guided waves appear at oblique incidence with a polarization primarily transverse at small inci...

Jean-Louis Izbicki

Papers

Resonances of plates and cylinders: Guided waves

Ultrasonic guided waves on a periodical grating: Coupled modes in the first Brillouin zone

Propagation of Lamb waves in a plate with a periodic grating: Interpretation by phonon

Interaction of Lamb waves on bonded composite plates with defects

Relation between surface helical waves and elastic cylinder resonances