A simple mass oscillator metasurface design with linear phase shift

2022 ◽  
Author(s):  
Wei Wang ◽  
Chengming Xuan ◽  
Weikai Xu ◽  
Zhe Yang ◽  
Jie Li
Keyword(s):  
Phase Shift ◽  
Forced Vibration ◽  
Flexural Wave ◽  
Linear Phase ◽  
Flexural Waves ◽  
Broad Application ◽  
Beam Focusing ◽  
Application Potential ◽  
Simple Mass ◽  
Structure Configuration

Abstract In this paper, a simple mass oscillator metasurface is designed, which can regulate the phase shift of flexural wave covering 0-2π by adjusting the number of mass oscillators on the connecting bar. Based on the forced vibration theory, there is a simple approximately linear relationship between the number and phase shift of mass oscillators, which can more intuitively and accurately predict the phase of different number of mass oscillators, and then realize the metasurface design of mass oscillators with different requirements. Therefore, arbitrary regulation of flexural waves, such as abnormal refraction, beam focusing, and self-acceleration, can be realized by reasonably arranging the number of mass oscillators. The results show that the proposed metasurface can be greatly simplified both in the establishment of phase shift relation and in the fabrication of structure configuration, and will have broad application potential in the engineering field.

Fast and slow interaction of elastic waves with platonic clusters

2011 ◽  
Vol 467 (2136) ◽  
pp. 3509-3529 ◽  
Author(s):  
Michael H. Meylan ◽  
Ross C. McPhedran
Keyword(s):  
Elastic Waves ◽  
Early Time ◽  
Approximate Solutions ◽  
Wave Profile ◽  
Flexural Wave ◽  
Flexural Waves ◽  
Analytical Extension ◽  
Scattering Of Elastic Waves ◽  
Classical Models ◽  
The Time Domain

We study the scattering of elastic waves by platonic clusters in the time domain, both for plane wave excitations and for a specified initial wave profile. We show that we can use an analytical extension of our problem to calculate scattering frequencies of the solution. These allow us to calculate approximate solutions that give the flexural wave profile accurately in and around the cluster for large times. We also discuss the early-time behaviour of flexural waves in terms of the classical models of Sommerfeld and Brillouin.

scholarly journals Elastic properties of floating sea ice from air-coupled flexural waves

2021 ◽  
Author(s):  
Rowan Romeyn ◽  
Alfred Hanssen ◽  
Bent Ole Ruud ◽  
Tor Arne Johansen
Keyword(s):  
Sea Ice ◽  
Elastic Properties ◽  
Ice Sheets ◽  
Ice Sheet ◽  
Flexural Wave ◽  
Ice Thickness ◽  
Linear Filter ◽  
Flexural Stiffness ◽  
Flexural Waves ◽  
Impulsive Source

Abstract. Air-coupled flexural waves appear as wave trains of constant frequency that arrive in advance of the direct air-wave from an impulsive source travelling over a floating ice sheet. The frequency of these waves varies with the flexural stiffness of the ice sheet, which is controlled by a combination of thickness and elastic properties. We develop a theoretical framework to understand these waves, utilizing modern numerical and Fourier methods to give a simpler and more accessible description than the pioneering, yet unwieldly analytical efforts of the 1950's. Our favoured dynamical model can be understood in terms of linear filter theory and is closely related to models used to describe the flexural waves produced by moving vehicles on floating plates. We find that air-coupled flexural waves are a robust feature of floating ice-sheets excited by impulsive sources over a large range of thicknesses, and we present a simple closed-form estimator for the ice thickness. Our study is focussed on first-year sea ice of ~20–80 cm thickness in Van Mijenfjorden, Svalbard, that was investigated through active source seismic experiments over four field campaigns in 2013, 2016, 2017 and 2018. The air-coupled flexural frequencies for sea-ice in this thickness range are ~60–240 Hz. While air-coupled flexural waves for thick sea-ice have received little attention, the higher frequencies associated with thin ice on fresh water lakes and rivers are well known to the ice-skating community and have been reported in popular media. Estimation of ice physical properties, following the approach we present, may allow improved surface wave modelling and wavefield subtraction in reflection seismic studies where flexural wave noise is undesirable. On the other hand, air-coupled flexural waves may also permit non-destructive continuous monitoring of ice thickness and flexural stiffness using simple, relatively inexpensive microphones located in the vicinity of the desired measurement location, either above the ice-sheet or along the shoreline. In this case, naturally forming cracks in the ice may be an appropriate impulsive source capable of exciting flexural waves in floating ice sheets in a passive monitoring context.

Quaternion-based anisotropic inversion for flexural waves in horizontal transverse isotropic formations with unmatched sources: A synthetic example

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. A69-A74 ◽  
Author(s):  
Fuqiang Zeng ◽  
Wenzheng Yue ◽  
Chao Li
Keyword(s):  
Structural Information ◽  
Amplitude Ratio ◽  
Flexural Wave ◽  
Data Sets ◽  
Flexural Waves ◽  
P Waves ◽  
Source Type ◽  
Transverse Isotropic ◽  
Sonic Logging ◽  
Incident Waves

The anisotropy of elastic waves has been widely used to obtain structural information on formations in geosciences research. Flexural wave splitting is generally applied to evaluate anisotropy with geophysical inversion methods. Cross-dipole sonic logging has been widely used for anisotropic inversions in horizontal transverse isotropic formations. Traditional methods assume that fast and slow flexural waves are similar in shape and are not dispersive and that the radiation characteristics of the two orthogonal dipole sources are identical. The two above assumptions cannot be satisfied in field conditions. Therefore, the methods used in anisotropy inversion based on these assumptions will lead to inaccurate results. The introduction of the amplitude ratio (AR), the ratio of slow to fast flexural waves, which is not dependent on the source type, can eliminate the wave-shape assumption. Two data sets from orthogonally oriented receivers can be constructed as a quaternion array. Fast and slow flexural waves are the two main incident waves, and other arrivals such as P-waves can be taken as noise. The AR and a quaternion multiple signal classification algorithm are used to demonstrate how to improve the anisotropic inversion and avoid these assumptions. Compared with the traditional method, the new method presents better inversion results for the synthetic example with two different sources. We have determined that the inversion residual from the new objective function can be used to indicate the inversion quality.

scholarly journals Creating the Coupled Band Gaps in Piezoelectric Composite Plates by Interconnected Electric Impedance

Materials ◽  
2018 ◽  
Vol 11 (9) ◽  
pp. 1656 ◽  
Author(s):  
Lin Li ◽  
Zhou Jiang ◽  
Yu Fan ◽  
Jun Li
Keyword(s):  
Band Gap ◽  
Piezoelectric Materials ◽  
Composite Plates ◽  
Forced Response ◽  
Band Gaps ◽  
Piezoelectric Composite ◽  
Flexural Wave ◽  
Response Analysis ◽  
Flexural Waves ◽  
Single Wave

In this paper, we investigate the coupled band gaps created by the locking phenomenon between the electric and flexural waves in piezoelectric composite plates. To do that, the distributed piezoelectric materials should be interconnected via a ‘global’ electric network rather than the respective ‘local’ impedance. Once the uncoupled electric wave has the same wavelength and opposite group velocity as the uncoupled flexural wave, the desired coupled band gap emerges. The Wave Finite Element Method (WFEM) is used to investigate the evolution of the coupled band gap with respect to propagation direction and electric parameters. Further, the bandwidth and directionality of the coupled band gap are compared with the LR and Bragg gaps. An indicator termed ratio of single wave (RSW) is proposed to determine the effective band gap for a given deformation (electric, flexural, etc.). The features of the coupled band gap are validated by a forced response analysis. We show that the coupled band gap, despite directional, can be much wider than the LR gap with the same overall inductance. This might lead to an alternative to adaptively create band gaps.

scholarly journals Numerical study of the effect of cement defects on flexural-wave logging

Geophysics ◽  
2019 ◽  
Vol 84 (4) ◽  
pp. D171-D177
Author(s):  
Ruolong Song ◽  
Hefeng Dong ◽  
Xueshan Bao
Keyword(s):  
Group Velocity ◽  
Numerical Study ◽  
Staggered Grid ◽  
Flexural Wave ◽  
Burial Depth ◽  
Flexural Waves ◽  
Wave Technique ◽  
Bond Evaluation ◽  
Pulse Echo ◽  
Leaky Lamb Wave

Cement-bond evaluation is needed for new wells and plug and abandonment activities. The ultrasonic leaky Lamb-wave (also called the flexural-wave) technique, in combination with the pulse-echo technique, has been widely used for cement-quality evaluation. Using a 2D time-domain staggered-grid stress-velocity finite-difference methodology, we have numerically investigated the attenuation and group velocity of flexural waves, and the scattering from defects, in the presence of a water-filled void in the cement annulus. The position, length, thickness, and burial depth of a defect are considered. The numerical study suggests that the combination of the attenuation and group velocity of the flexural wave allows for a discrimination between solids and liquids. The scattering from voids can be used to indicate the existence of a hidden defect, which cannot be detected by using the attenuation and group velocity if it is located larger than 5 mm away from the casing. The void signatures can even be used to characterize the geometry of the defect for neat cement. The numerical results provide improved understanding of flexural-wave logging results.

The Hanging Column as a Dynamic Vibration Absorber

2018 ◽  
Vol 18 (07) ◽  
pp. 1871008 ◽  
Author(s):  
C. Y. Wang
Keyword(s):  
Forced Vibration ◽  
Vibration Absorber ◽  
Initial Value ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
Spring System ◽  
Simple Mass ◽  
Mass Spring ◽  
First Time

A simple mass–spring system with an attached hanging column is investigated. The problem is formulated and the frequencies obtained with an efficient initial value method. Under forced vibration, the amplitude of the mass may be greatly reduced by adding a hanging column. The possibility of using such a hanging column as a dynamic vibration absorber is shown for the first time.

Pulsed Control of Thermoacoustic Instabilities: Analysis and Experiment

2009 ◽  
Vol 131 (4) ◽  
Author(s):  
J. Matthew Carson ◽  
William T. Baumann ◽  
William R. Saunders
Keyword(s):  
Phase Shift ◽  
Limit Cycle ◽  
Fourier Component ◽  
Linear Phase ◽  
Cycle Frequency ◽  
Thermoacoustic Instabilities ◽  
Control Authority ◽  
Subharmonic Frequency ◽  
Cycling Behavior ◽  
Instability Frequency

Thermoacoustic instabilities in combustors have been suppressed using phase-shift algorithms pulsing an on-off actuator at the limit cycle frequency (flc) or at the subharmonics of flc. It has been suggested that control at a subharmonic rate may extend the actuator lifetime and possibly require less actuator bandwidth. This paper examines the mechanism of subharmonic control in order to clarify the principles of operation and subsequently identify potential advantages for combustion control. Theoretical and experimental arguments show that there must be a Fourier component of the subharmonic control signal at flc in order to stabilize the limit cycling behavior. It is also demonstrated that the magnitude of that Fourier component must be equivalent to the signal magnitude for a linear phase-shift controller that operates directly at flc. The concept of variable-subharmonic control is introduced whereby the actuator is pulsed at the instability frequency to initially stabilize the system and then is pulsed at a subharmonic frequency to maintain stability. These results imply that an actuator used for subharmonic control cannot be effective unless its bandwidth spans the instability frequency. The advantage of reduced cycling may still be realized but will require higher control authority to produce the same effect as an actuator pulsed at the instability frequency.

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