Torsional vibrations of circular elastic plates with thickness steps

Kang, Minkyu; Huang, Rui; Knowles, Terence J.

doi:10.1109/tuffc.2006.1593373

Cited by 11 publications

(9 citation statements)

References 28 publications

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“…These 2D equations yield the exact solutions for zeroth-and first-order torsional modes in uniform plates without any correction factors [23].…”

Section: Torsional Vibrations Of Stepped Platesmentioning

confidence: 95%

“…The remainder of this paper focuses on the circumferential motion, corresponding to torsional modes in the elastic plates [23]. The uncoupling of torsional modes from flexural modes allows pure in-plane motion of the resonator, which is advantageous for applications requiring immersion in or in contact with liquids [12].…”

Section: Two-dimensional Plate Equationsmentioning

confidence: 99%

“…1(a), we develop an approximate method to analyze the torsional vibrations by coupling two uniform plates of different thicknesses for the inner and outer regions through a mixed boundary condition at the junction [23]. By setting b to be a constant (i.e., 0…”

Section: Torsional Vibrations Of Stepped Platesmentioning

confidence: 99%

“…Based on the series expansion of the displacement and the integral definition of the 2D tractions, an approximation of the mixed boundary condition is given by [23] In addition, a traction-free condition at the outer edge (r = a) requires that…”

Section: Torsional Vibrations Of Stepped Platesmentioning

confidence: 99%

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Trapped torsional vibrations in elastic plates

Knowles¹,

Kang

Huang

2005

Applied Physics Letters

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Abstract-We have observed that torsional vibrations can be trapped in elastic plates with circular regions of slightly thicker steps or with smooth convex contoured surfaces. An electromagnetic acoustic transducer (EMAT) was used to generate oscillatory surface traction. The resonant frequencies and Q-values were measured. It was found that these trapped torsional modes have Q-values exceeding 100,000 with pure inplane motion, which is of practical importance for acoustic sensor applications.In this paper, a set of approximate two-dimensional equations is developed to study vibrations in axisymmetrically contoured or stepped elastic plates. By assuming circumferentially independent motion, the first-order equations are decoupled into four groups, with torsional modes uncoupled from flexural and extensional modes. Analytical solutions for torsional modes are obtained for stepped and linearly contoured circular plates. It is found that the firstorder torsional modes can be trapped in an infinite plate with a stepped or contoured region if critical conditions for the geometrical parameters are met. The analytical results are compared to experiments and finite element analyses with good agreements. I. INTRODUCTIONMechanical resonators with energy trapping typically have low losses and hence high quality factors, and are therefore sensitive to surface loading. An example of this is the thickness-shear mode quartz crystal microbalance (QCM), which has found broad applications as detectors for mass deposition, for chemical and biochemical absorption, and for liquid phase sensing [1][2][3]. Energy trapping in QCM is usually achieved by confining thickness-shear mode vibrations under a thin-film electrode deposited on part of crystal surface, which eliminates crystal edges and mounting structures as sources of energy loss. The quartz plate can be regarded as an acoustic waveguide, with the electrode acting as a mass load. The mass reduces the cut-off frequency and results in a frequency band, within which at least one trapped resonance exists [4,5]. To eliminate undesirable overtones, the upper limit of the ratio between the electrode size and the quartz thickness is set by Bechmann's number, as given by Mindlin and Lee [6] and others [7][8][9].

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“…These 2D equations yield the exact solutions for zeroth-and first-order torsional modes in uniform plates without any correction factors [23].…”

Section: Torsional Vibrations Of Stepped Platesmentioning

confidence: 95%

Section: Two-dimensional Plate Equationsmentioning

confidence: 99%

Section: Torsional Vibrations Of Stepped Platesmentioning

confidence: 99%

Section: Torsional Vibrations Of Stepped Platesmentioning

confidence: 99%

See 2 more Smart Citations

Trapped torsional vibrations in elastic plates

Knowles¹,

Kang

Huang

2005

Applied Physics Letters

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“…Consequently, no compressional waves are generated in the adjacent liquid, and the sensor response can be related to the liquid properties without concerning the liquid thickness. Previously we have demonstrated that energy-trapping torsional-mode vibrations can be excited in elastic plates by using an electromagnetic acoustic transducer (EMAT) [10,11]. In this paper, experiments are conducted to study effect of liquid thickness on the torsional-mode resonators, in comparison with thickness-shear mode.…”

Section: Introductionmentioning

confidence: 99%

Energy-Trapping Torsional-Mode Resonators for Liquid Sensing

Kang

Huang

Knowles³

2006

2006 IEEE International Frequency Control Symposium and Exposition

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Abstract-Thickness-shear mode quartz crystal microbalance (QCM) has been widely used as liquid-phase sensors, such as viscometers and bio-detectors. However, due to coupling between the in-plane shear motion and the out-of-plane flexure, when used in contact with or immersed in a liquid, the out-of-plane motion generates compressional waves in the liquid that reflect off the liquid surface and return to the crystal. This interference effect causes depth-sensitive perturbations in the sensor response, often undesirable. In this study, we show that torsional-mode resonators may be used for liquid sensing without the depth effect. Samples in form of stepped plates, circular decals, and convex contoured faces are machined in elastic plates (e.g., cast aluminum, stainless steel, and brass). A non-contact electromagnetic acoustic transducer (EMAT) was employed to drive torsional-mode vibrations. Efficient energy trapping was observed for first-order torsional modes, leading to high quality factors. When placed in contact with water, the resonance frequency of the torsional mode was found to be independent of the water depth, in contrast to depth-dependent frequency oscillation for the thickness-shear mode. Finite element analyses are conducted to understand the torsional-mode vibrations as well as the effect of material anisotropy.

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A Comparison of Gear Mesh Stiffness Modeling Strategies

Meagher

Kong

et al. 2011

Conference Proceedings of the Society for Experimental Mechanics Series

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Torsional vibrations of circular elastic plates with thickness steps

Cited by 11 publications

References 28 publications

Trapped torsional vibrations in elastic plates

Trapped torsional vibrations in elastic plates

Energy-Trapping Torsional-Mode Resonators for Liquid Sensing

A Comparison of Gear Mesh Stiffness Modeling Strategies

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