“Knocked Over!”: A visual demonstration of time reversal focusing using bending waves in a thin plate

Sarah M. Young; Christopher Heaton; Brian E. Anderson

doi:10.1121/1.4950186

Design of a Variable Thickness Plate to Focus Bending Waves

ASME 2012 Noise Control and Acoustics Division Conference ◽

10.1115/ncad2012-1330 ◽

2012 ◽

Cited By ~ 3

Author(s):

Noah H. Schiller ◽

Sz-Chin Steven Lin ◽

Randolph H. Cabell ◽

Tony Jun Huang

Keyword(s):

Numerical Simulations ◽

Thin Plate ◽

Traveling Waves ◽

Variable Thickness ◽

Focal Point ◽

Frequency Range ◽

Additional Energy ◽

Broad Frequency Range ◽

Bending Waves ◽

Energy Dissipated

This paper describes the design of a thin plate whose thickness is tailored in order to focus bending waves to a desired location on the plate. Focusing is achieved by smoothly varying the thickness of the plate to create a type of lens, which focuses structure-borne energy. Damping treatment can then be positioned at the focal point to efficiently dissipate energy with a minimum amount of treatment. Numerical simulations of both bounded and unbounded plates show that the design is effective over a broad frequency range, focusing traveling waves to the same region of the plate regardless of frequency. This paper also quantifies the additional energy dissipated by local damping treatment installed on a variable thickness plate relative to a uniform plate.

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Incorporating Compressional and Shear Wave Types Into Fuzzy Structure Models for Plates

Volume 3B: 15th Biennial Conference on Mechanical Vibration and Noise — Acoustics, Vibrations, and Rotating Machines ◽

10.1115/detc1995-0413 ◽

1995 ◽

Author(s):

Judith L. Rochat ◽

Victor W. Sparrow

Keyword(s):

Thin Plate ◽

Shear Waves ◽

Wave Theory ◽

Structure Theory ◽

Detailed Knowledge ◽

Bending Waves ◽

Incident Plane ◽

Dependent Mass ◽

Mass Spring ◽

Bending Wave

Abstract Although realistic complex structures are usually difficult to model theoretically, fuzzy structure theory enables one to produce such a model without a detailed knowledge of the entire structure. Using the theory established by Pierce et al. [A. D. Pierce, V. W. Sparrow, and D. A. Russell, J. Vib. Acoust. (to be published), also ASME 93-WA/NCA-17.] regarding fundamental structural-acoustic idealizations for structures with imprecisely known or fuzzy internals, the effects that fuzzy attachments have on different wave types in a primary (or master) structure are examined in this paper. In the theory by Pierce et al., the primary structure that undergoes vibrations is a thin plate mounted in an infinite baffle. On one side of the plate are fuzzy attachments, represented as an array of attached mass-spring-dashpot systems, which are excited by an incident plane pulse. This known theory explains the effects of these attachments on bending waves in the plate. In this paper, the theory is extended to isolated compressional and shear waves in a plate. While studying this new problem, it is discovered that coupling effects occur when the plate and attachment properties are not uniform in the direction perpendicular to the wave propagation. Hence, unlike the bending wave theory which models a finite thin plate with point attached oscillators, the new wave type theory uses a thin plate infinite in one direction with line attached oscillators also infinite in the same direction. For both the compressional and shear waves, it is found that the fuzzy attachments add an apparent frequency dependent mass and damping to the plate. These results are similar to those for the bending wave theory.

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Propagation of bending waves in a thin plate with an ensemble of randomly located holes of non-canonical form

Prykladni Problemy Mekhaniky i Matematyky ◽

10.15407/apmm2020.18.144-149 ◽

2020 ◽

Vol 18 (0) ◽

Author(s):

Ya. I. Kunets' ◽

V. V. Matus ◽

V. O. Mishchenko ◽

V. V. Porokhovs'kyi

Keyword(s):

Thin Plate ◽

Canonical Form ◽

Bending Waves

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The energetics of cylindrical bending waves in a thin plate

Journal of Sound and Vibration ◽

10.1016/j.jsv.2004.01.028 ◽

2005 ◽

Vol 279 (1-2) ◽

pp. 513-518 ◽

Cited By ~ 3

Author(s):

R.H. Lande ◽

R.S. Langley

Keyword(s):

Thin Plate ◽

Cylindrical Bending ◽

Bending Waves

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Shock Reduction Technique on Thin Plate Structure by Wave Refraction Using an Elastic Patch

Shock and Vibration ◽

10.1155/2021/6836899 ◽

2021 ◽

Vol 2021 ◽

pp. 1-14

Author(s):

Dae-Hyun Hwang ◽

Jae-Hung Han

Keyword(s):

Thin Plate ◽

Reduction Method ◽

Reduction Technique ◽

Target Area ◽

Structural Stiffness ◽

Wave Refraction ◽

Bending Waves ◽

Shock Response ◽

Different Shapes ◽

The Waves

In general, bending waves transfer the largest portion of shock energy in a plate-like structure. This study proposes a new shock reduction method using an elastic patch designed to defocus the bending waves through the refraction of the waves so that it is possible to effectively reduce the propagating shock for a certain target area. Elastic patches of three different shapes were considered. The shock reduction performance of these patches was analytically, numerically, and experimentally investigated and compared. All results consistently showed that attached patches can effectively reduce passing waves for areas behind patches. Therefore, utilizing the proposed methods, we can reduce the transient shock response at certain target areas of various practical structures without degradation of structural stiffness or strength simply by bonding with an elastic patch.

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Platonic Scattering Cancellation for Bending Waves in a Thin Plate

Scientific Reports ◽

10.1038/srep04644 ◽

2014 ◽

Vol 4 (1) ◽

Cited By ~ 21

Author(s):

M. Farhat ◽

P.-Y. Chen ◽

H. Bağcı ◽

S. Enoch ◽

S. Guenneau ◽

...

Keyword(s):

Thin Plate ◽

Bending Waves

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Physical and social environmental imagery: A visual demonstration

PsycEXTRA Dataset ◽

10.1037/e611312012-431 ◽

1972 ◽

Author(s):

Bernard Perloff ◽

David Greenberg ◽

Roger Webster ◽

Ted Smith ◽

Gary Greenberg

Keyword(s):

Visual Demonstration ◽

Social Environmental

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Validation of a Belt Model for Prediction of Hub Forces from a Rolling Tire4

Tire Science and Technology ◽

10.2346/1.3130984 ◽

2009 ◽

Vol 37 (2) ◽

pp. 62-102 ◽

Cited By ~ 3

Author(s):

C. Lecomte ◽

W. R. Graham ◽

D. J. O’Boy

Keyword(s):

Internal Pressure ◽

Equations Of Motion ◽

Three Dimensional ◽

Prediction Method ◽

Analytical Models ◽

Beam Model ◽

Impedance Boundary ◽

Bending Waves ◽

Tire Rotation ◽

Three Dimensional Models

Abstract An integrated model is under development which will be able to predict the interior noise due to the vibrations of a rolling tire structurally transmitted to the hub of a vehicle. Here, the tire belt model used as part of this prediction method is first briefly presented and discussed, and it is then compared to other models available in the literature. This component will be linked to the tread blocks through normal and tangential forces and to the sidewalls through impedance boundary conditions. The tire belt is modeled as an orthotropic cylindrical ring of negligible thickness with rotational effects, internal pressure, and prestresses included. The associated equations of motion are derived by a variational approach and are investigated for both unforced and forced motions. The model supports extensional and bending waves, which are believed to be the important features to correctly predict the hub forces in the midfrequency (50–500 Hz) range of interest. The predicted waves and forced responses of a benchmark structure are compared to the predictions of several alternative analytical models: two three dimensional models that can support multiple isotropic layers, one of these models include curvature and the other one is flat; a one-dimensional beam model which does not consider axial variations; and several shell models. Finally, the effects of internal pressure, prestress, curvature, and tire rotation on free waves are discussed.

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