scholarly journals Scattering Reduction and Resonant Trapping of Flexural Waves: Two Rings to Rule Them

2021 ◽  
Vol 11 (10) ◽  
pp. 4462
Author(s):  
Alexander B. Movchan ◽  
Ross C. McPhedran ◽  
Giorgio Carta
Keyword(s):  
Thin Plate ◽  
High Frequency ◽  
Finite Element Models ◽  
Vibration Modes ◽  
Elastic Plates ◽  
Flexural Waves ◽  
Double Ring ◽  
Elastic Thin Plate ◽  
Equivalent Mass ◽  
Single Mass

In this paper, we discuss two problems concerning scattering and localisation of flexural waves in structured elastic plates. Firstly, we compare the scattering amplitudes of waves in a thin plate, generated by a point source, due to a single mass and to a large number of smaller masses, having the same equivalent mass and located around a circle. We show that in the second case, the scattering can be reduced, in particular in the medium- and high-frequency regimes. Secondly, we develop a homogenised model for a double-ring cluster of spring-mass resonators, connected to an elastic thin plate. We determine the conditions for which the plate exhibits vibration modes trapped between the two rings. Further, we show that the frequencies of the localised modes can be tuned by varying the geometry of the two rings and the characteristics of the resonators. The analytical results are corroborated by numerical simulations performed with independent finite element models.

scholarly journals Development of a Fish-Like Robot with a Continuous and High Frequency Snap-Through Buckling Mechanism Using a Triangular Cam

2021 ◽  
Vol 33 (2) ◽  
pp. 400-409
Author(s):  
Daisuke Nakanishi ◽  
Shoya Kobayashi ◽  
Kiichi Obara ◽  
Shotaro Matsumura ◽  
Yuichiro Sueoka ◽  
...  
Keyword(s):  
Thin Plate ◽  
Swimming Speed ◽  
High Frequency ◽  
Single Peak ◽  
Driving Mechanism ◽  
Drive Mechanism ◽  
Elastic Thin Plate ◽  
The Relationship

This study focuses on the high maneuverability of fish in water to design a fish-like robot via snap-through buckling. The aim of this study is to improve swimming speed by increasing the frequency at which snap-through buckling occurs. Here, we propose a novel drive mechanism using a triangular cam that can continuously generate snap-through buckling at a high frequency. In addition, we developed a fish-like robot via the proposed mechanism and analyzed the influence of the frequency of snap-through buckling on swimming speed. The results obtained indicate that swimming speed is improved and that the relationship between frequency and swimming speed exhibits a single peak. In other words, the swimming speed is reduced when the frequency is significantly increased. We also determined that swimming speed was improved using a wide elastic thin plate as the driving mechanism.

Diffraction of flexural waves by cracks in orthotropic thin elastic plates. Part II. Far field analysis

2007 ◽  
Vol 463 (2082) ◽  
pp. 1615-1638 ◽  
Author(s):  
Ian Thompson ◽  
I.David Abrahams
Keyword(s):  
Thin Plate ◽  
Scattered Field ◽  
Asymptotic Approximation ◽  
Principal Direction ◽  
Field Analysis ◽  
Flexural Wave ◽  
Far Field ◽  
Elastic Plates ◽  
Flexural Waves ◽  
Thin Elastic Plates

The scattered field arising from diffraction of a plane flexural wave by a semi-infinite crack in an orthotropic Kirchhoff thin plate is analysed. The crack is aligned with a principal direction of the material, so that two of the plate's three planes of symmetry are preserved. An asymptotic approximation is derived via the method of steepest descents, and explicit expressions are given for the most significant contributions. The effects of anisotropy upon the scattered field are made clear, and numerical results are presented for several typical engineering materials.

scholarly journals Numerical solution of acoustic scattering by finite perforated elastic plates

2016 ◽  
Vol 472 (2188) ◽  
pp. 20150767 ◽  
Author(s):  
A. V. G. Cavalieri ◽  
W. R. Wolf ◽  
J. W. Jaworski
Keyword(s):  
Boundary Conditions ◽  
Acoustic Scattering ◽  
Free Edge ◽  
Solution Procedure ◽  
Sound Level ◽  
Vibration Modes ◽  
Elastic Plates ◽  
Beneficial Effects ◽  
Plate Length ◽  
Radiated Sound

We present a numerical method to compute the acoustic field scattered by finite perforated elastic plates. A boundary element method is developed to solve the Helmholtz equation subjected to boundary conditions related to the plate vibration. These boundary conditions are recast in terms of the vibration modes of the plate and its porosity, which enables a direct solution procedure. A parametric study is performed for a two-dimensional problem whereby a cantilevered perforated elastic plate scatters sound from a point quadrupole near the free edge. Both elasticity and porosity tend to diminish the scattered sound, in agreement with previous work considering semi-infinite plates. Finite elastic plates are shown to reduce acoustic scattering when excited at high Helmholtz numbers k 0 based on the plate length. However, at low k 0 , finite elastic plates produce only modest reductions or, in cases related to structural resonance, an increase to the scattered sound level relative to the rigid case. Porosity, on the other hand, is shown to be more effective in reducing the radiated sound for low k 0 . The combined beneficial effects of elasticity and porosity are shown to be effective in reducing the scattered sound for a broader range of k 0 for perforated elastic plates.

Time Varying Control of a Bladed Disk Assembly Using Shaft Based Actuation

1999 ◽  
Author(s):  
György Szász ◽  
George T. Flowers
Keyword(s):  
High Frequency ◽  
Thrust Bearing ◽  
Vibration Modes ◽  
Thrust Bearings ◽  
Bladed Disk ◽  
Time Period ◽  
Bladed Disk Assembly ◽  
Linearized Model ◽  
Original Domain ◽  
Time Periodic

Abstract A study of bladed-disk vibration control using magnetic bearings is presented. A key issue is a method for achieving practical controllability for such a system. For a tuned or symmetrically mistuned bladed disk assembly, several vibration modes are coupled only to the axial dynamics. Magnetic thrust bearings generally lack sufficient bandwidth to control even moderately high frequency vibration. A simplified model is developed and used to identify controllable vibration modes. A control strategy based upon deliberately mistuning in a non-symmetric manner is developed. The method presented does not require a thrust bearing for complete controllability of a bladed disk assembly via hub based actuators. However, since the linearized model for such a system has time periodic coefficients, an advanced time period controller is required. Controlling time periodic systems is a significant engineering challenge. One innovative approach that seems to be especially promising involves application of the Lyapunov Floquet (LF) transformation to eliminate time periodic terms from the system state matrices. Traditional control design techniques are then applied and the resulting gains transformed back to the original domain. Some simulation results are presented and discussed to illustrate the method.

Sign in / Sign up

Export Citation Format

Share Document