Numerical analysis of wave propagating in a periodic layered structure

2022 ◽  
Author(s):  
Takaaki Fukuchi ◽  
Naoki Mori ◽  
Takahiro Hayashi
Keyword(s):  
Plane Wave ◽  
Thin Plate ◽  
Layered Structure ◽  
Lamb Waves ◽  
Sound Field ◽  
Noise Removal ◽  
Wave Mode ◽  
Sound Fields ◽  
Tuning Frequency ◽  
Periodic Layered Structure

Abstract Controlling sound fields is a key technology for noise removal, acoustic lenses, energy harvesting, etc. This study investigated the control of sound field by a periodic layered structure. At first, we formulated the wave propagation in a periodic layered structure and proved that the wave fields constructed by the periodic boundary conditions are limited to plane wave modes with discretely different propagation directions. Numerical calculations clarified that the desired plane wave mode can be obtained in the transmitted wave through an intermediate thin-plate stacked region in a periodic layered structure, in which Lamb waves travel in each plate at different phase velocities and create phase difference at the exit of the intermediate thin-plate region. Further numerical investigations revealed that tuning frequency and length of the thin-plate region provides wave field more dominantly with a single wanted plane wave mode.

Suppressing Technique of the Antisymmetric Mode by the Superposition of Lamb Waves Generated by Two Laser Beams in a Thin Plate

2006 ◽  
Vol 321-323 ◽  
pp. 103-107
Author(s):  
Seung Seok Lee ◽  
Sang Whoe Dho
Keyword(s):  
Thin Plate ◽  
Opposite Direction ◽  
Lamb Wave ◽  
Lamb Waves ◽  
Wave Mode ◽  
Laser Beams ◽  
Symmetric Mode ◽  
Antisymmetric Mode

We present a suppressing technique of the antisymmetric mode by superposition of Lamb waves generated by two laser beams in a thin plate. Two Lamb waves of the same frequency propagating from the opposite direction simultaneously arrive at the point of measurement and are superposed to compose one Lamb wave. The amplitude of the superposed Lamb wave depends on the distance between two laser beams. The suppressing of antisymmetric Lamb wave mode is accomplished by selecting the distance between two beams which simultaneously satisfies the condition of the anti-node(maximum) for the symmetric mode and the minimum for the antisymmetric mode. By this method, the antisymmetric Lamb wave mode is suppressed to the degree of 1.4% of the amplitude measured at zero distance between two beams.

scholarly journals Partial Energy Transfer Model of Lamb Waves Scattering in Materially Isotropic Waveguides

2021 ◽  
Vol 11 (10) ◽  
pp. 4508
Author(s):  
Pavel Šofer ◽  
Michal Šofer ◽  
Marek Raček ◽  
Dawid Cekus ◽  
Paweł Kwiatoń
Keyword(s):  
Energy Transfer ◽  
Lamb Waves ◽  
Hybrid Approach ◽  
Wave Mode ◽  
Transfer Model ◽  
Material Interface ◽  
Modal Expansion ◽  
Scattering Coefficients ◽  
Expansion Technique ◽  
Partial Energy

The scattering phenomena of the fundamental antisymmetric Lamb wave mode with a horizontal notch enabling the partial energy transfer (PET) option is addressed in this paper. The PET functionality for a given waveguide is realized using the material interface. The energy scattering coefficients are identified using two methods, namely, a hybrid approach, which utilizes the finite element method (FEM) and the general orthogonality relation, and the semi-analytical approach, which combines the modal expansion technique with the orthogonal property of Lamb waves. Using the stress and displacement continuity conditions on the present (sub)waveguide interfaces, one can explicitly derive the global scattering matrix, which allows detailed analysis of the scattering process across the considered interfaces. Both methods are then adopted on a simple representation of a surface breaking crack in the form of a vertical notch, of which a certain section enables not only the reflection of the incident energy, but also its nonzero transfer. The presented results show very good conformity between both utilized approaches, thus leading to further development of an alternative technique.

Notice of Removal: Zero TCF resonator based on S0 Lamb wave mode in AlN thin plate films

2017 ◽  
Author(s):  
Mohammed Moutaouekkil ◽  
Abdelkrim Talbi ◽  
Omar Elmazria ◽  
El Houssaine El Boudouti ◽  
Philippe Pernod ◽  
...  
Keyword(s):  
Thin Plate ◽  
Lamb Wave ◽  
Wave Mode

Noncontact Evaluation of Defects in Thin Plate With Multimodes Lamb’s Waves and Wavelet Transform

2002 ◽  
Author(s):  
Morimasa Murase ◽  
Koichiro Kawashima
Keyword(s):  
Group Velocity ◽  
Thin Plate ◽  
Wavelet Transformation ◽  
Velocity Dispersion ◽  
Lamb Waves ◽  
Group Velocity Dispersion ◽  
Dispersion Curves ◽  
Contact Method ◽  
Intact Specimen ◽  
Time Frequency

Multimode’s Lamb waves in aluminum plates with various defects were excited by a Q-switched Nd:YAG laser. The Lamb waves past through the defects were received a laser interferometer. The received signals of the Lamb waves are processed by the wavelet transformation. The wavelet transformation is generally shown on the time-frequency domain. By dividing a propagation distance by the time, the group velocities are identified. In this way, group velocity dispersion maps of multimode’s Lamb waves are constructed with the received temporal signals. By changing the shape of the mother wavelet, Gabor function, we can identify the dispersion curves of the higher mode Lamb waves. The group velocity dispersion maps of a intact specimen agree well on theoretical dispersion curves of S0, A0, S1, A1, S2, A2, and A3 modes. The difference between the dispersion maps of the intact specimen and that with defects clearly visualizes the existence of defects. This non-contact method is effective for inspecting various defects in thin plate structures.

Silicon Pillars as Resonators in an Acoustical Metamaterial

2014 ◽  
Author(s):  
Bernard Bonello ◽  
Rémi Marchal ◽  
Rayisa Moiseyenko ◽  
Yan Pennec ◽  
Bahram Djafari-Rouhani ◽  
...  
Keyword(s):  
Thin Plate ◽  
Lamb Waves ◽  
Mass Density ◽  
Resonant Mode ◽  
Ultrasonic Technique ◽  
Frequency Range ◽  
Negative Mass ◽  
Laser Ultrasonic ◽  
Compressional Mode ◽  
Bending Modes

We have investigated the propagation of Lamb waves in structures made of either an isolated resonant pillar or a set of pillars arranged in a line on a thin plate. The resonators as well as the plate are made of silicon. FEM computations show that two bending modes and one compressional mode are unambiguously identified in the frequency range of interest (0–10 MHz). We used a laser ultrasonic technique to map both the amplitude and the phase of the normal displacements on top of the pillars and at the surface of the sample. When the frequency is tuned to a resonant mode, either compressional or bending, the pillars vibrate 180° out-of-phase with respect to the Lamb waves, resulting in a negative modulus or negative mass density respectively.

scholarly journals Numerical Simulation of Nonlinear Lamb Waves Used in a Thin Plate for Detecting Buried Micro-Cracks

Sensors ◽  
2014 ◽  
Vol 14 (5) ◽  
pp. 8528-8546 ◽  
Author(s):  
Xiang Wan ◽  
Qing Zhang ◽  
Guanghua Xu ◽  
Peter Tse
Keyword(s):  
Numerical Simulation ◽  
Thin Plate ◽  
Lamb Waves ◽  
Micro Cracks

Recurrent relationships for reflection coefficients of electromagnetic wave potential representation modes in manylayered spherical environment excitation problem

2021 ◽  
Author(s):  
S.A. Colichev ◽  
N.S. Camalova
Keyword(s):  
Plane Wave ◽  
Layered Structure ◽  
Recurrence Relations ◽  
Scattering Problem ◽  
Reflection Coefficients ◽  
Total Field ◽  
Spherical Shells ◽  
Field Source ◽  
Modes Of Representation ◽  
Simple Physical Model

In theoretical assessments of the electrodynamic characteristics of multilayer screens of electromagnetic waves, the concept of the input impedance of a wave on the surface of the screen is used [1]. In [2], an approach was proposed that is not based on this characteristic, and direct recurrence relations were obtained both for the reflection coefficient of a plane wave from a multilayer screen and for the coefficient of transmission of such a wave through this screen. In [3], this approach was applied to solving problems of excitation of a layered medium by localized sources. In this paper, we generalize the approach to the case of a multilayer medium with another simple layer geometry (with interface in the form of concentric spherical shells). The solution of excitation problems is based on the representation of the Hertz potentials of waves of electric (magnetic) types in the form of series in spherical harmonics. Each harmonic defines the angular distribution of radially converging and diverging modes of the representation of potentials in layers free from external sources. The recurrence relations for the reflection coefficients of convergent (diverging) modes of representation when sequentially adding interfaces are a consequence of the boundary conditions. One of the equivalent forms of these relations is derived from the condition for the existence of a nontrivial solution of a system of linear equations for the amplitudes of converging (diverging) modes in adjacent layers. The other is based on a simple physical model of the process of interaction of a converging (diverging) mode in a layer with a layered structure, which it covers (which covers it). For a field source inside one of the layers, one can determine the representation of potentials that this source would excite in an infinite medium with permeabilities similar to a layer. The amplitudes of the modes of representation of this «primary» field and the reflection coefficients of the modes of representation from structures at the internal and external boundaries of the layer, found from recurrence relations, determine the amplitudes of the modes of the total field of the layer incident on these boundaries. To determine the amplitudes of the modes of representation of the potentials of the fields in the remaining layers, recurrence relations can also be used, in a certain sense inverse to the recurrence relations for reflection coefficients. If a layered structure is excited by a plane wave (scattering problem), the total field potentials (of the electric and magnetic types) are the sum of radially converging modes in the potentials describing the incident plane wave and radially diverging modes formed by the reflection of these converging mod from structure. With the proposed approach, the complexity of solving the excitation problems of the considered layered structure remains almost unchanged with an increase in the number of layers. In essence, only the number of repetition cycles of the obtained recurrence relations increases. The proposed approach is conceptually simple, the final recurrence relations are physically transparent. The work does not represent the full facilities of the approach. Within the framework of this approach, recurrence relations for the permeability coefficients of multilayer spherical shells of the structure under consideration, recurrence relations during its layer-by-layer formation or formation from several multilayer shells can be found.

Quantifying Non-Linearity in Early Decay Curves of Measured and Computer-Modeled Room Impulse Responses of a Highly Non-Diffuse Room Exhibiting Flutter Echo

2020 ◽  
Author(s):  
Heather L. Lai ◽  
Brian Hamilton
Keyword(s):  
Linear Regression ◽  
Computer Modeling ◽  
Impulse Response ◽  
Decay Curve ◽  
Sound Field ◽  
Energy Decay ◽  
Room Acoustics ◽  
Reverberation Time ◽  
Sound Fields ◽  
Regression Curves

Abstract This paper investigates the use of two room acoustics metrics designed to evaluate the degree to which the linearity assumptions of the energy density curves are valid. The study focuses on measured and computer-modeled energy density curves derived from the room impulse response of a space exhibiting a highly non-diffuse sound field due to flutter echo. In conjunction with acoustical remediation, room impulse response measurements were taken before and after the installation of the acoustical panels. A very dramatic decrease in the reverberation time was experienced due to the addition of the acoustical panels. The two non-linearity metrics used in this study are the non-linearity parameter and the curvature. These metrics are calculated from the energy decay curves computed per octave band, based on the definitions presented in ISO 3382-2. The non-linearity parameter quantifies the deviation of the EDC from a straight line fit used to generated T20 and T30 reverberation times. Where the reverberation times are calculated based on a linear regression of the data relating to either −5 to −25 dB for T20 or −5 to −35 dB for T30 reverberation time calculations. This deviation is quantified using the correlation coefficient between the energy decay curve and the linear regression for the specified data. In order to graphically demonstrate these non-linearity metrics, the energy decay curves are plotted along with the linear regression curves for the T20 and T30 reverberation time for both the measured data and two different room acoustics computer-modeling techniques, geometric acoustics modeling and finite-difference wave-based modeling. The intent of plotting these curves together is to demonstrate the relationship between these metrics and the energy decay curve, and to evaluate their use for quantifying degree of non-linearity in non-diffuse sound fields. Observations of these graphical representations are used to evaluate the accuracy of reverberation time estimations in non-diffuse environments, and to evaluate the use of these non-linearity parameters for comparison of different computer-modeling techniques or room configurations. Using these techniques, the non-linearity parameter based on both T20 and T30 linear regression curves and the curvature parameter were calculated over 250–4000 Hz octave bands for the measured and computer-modeled room impulse response curves at two different locations and two different room configurations. Observations of these calculated results are used to evaluate the consistency of these metrics, and the application of these metrics to quantifying the degree of non-linearity of the energy decay curve derived from a non-diffuse sound field. These calculated values are also used to evaluate the differences in the degree of diffusivity between the measured and computer-modeled room impulse response. Acoustical computer modeling is often based on geometrical acoustics using ray-tracing and image-source algorithms, however, in non-diffuse sound fields, wave based methods are often able to better model the characteristic sound wave patterns that are developed. It is of interest to study whether these improvements in the wave based computer-modeling are also reflected in the non-linearity parameter calculations. The results showed that these metrics provide an effective criteria for identifying non-linearity in the energy decay curve, however for highly non-diffuse sound fields, the resulting values were found to be very sensitive to fluctuations in the energy decay curves and therefore, contain inconsistencies due to these differences.

Sign in / Sign up

Export Citation Format

Share Document