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Research Papers

Finite Element Analysis of Thermoelastic Damping in Contour-Mode Vibrations of Micro- and Nanoscale Ring, Disk, and Elliptical Plate Resonators

[+] Author and Article Information
Yun-Bo Yi

Department of Mechanical and Materials Engineering, University of Denver, Denver, CO 80208yyi2@du.edu

J. Vib. Acoust 132(4), 041015 (Jul 15, 2010) (7 pages) doi:10.1115/1.4001506 History: Received June 16, 2009; Revised March 25, 2010; Published July 15, 2010; Online July 15, 2010

Thermoelastic damping in contour-mode in-plane vibrations of rings, disks, and elliptical plates is investigated on various size scales, using a reduced finite element formulation. The Fourier scheme is applied to the axisymmetric geometries including circular rings and disks, and is found to be remarkably efficient in searching solutions. The numerical accuracy is further improved by the implementation of quadratic interpolation functions. The computational results are validated by comparing with the commercial software packages as well as the existing analytical solutions in literature. For resonators of elliptical shapes, the dominant frequency has a weak dependence on the geometric aspect ratio γ, whereas the effect of γ on the quality factor (Q value) is much stronger and the peak Q value of the leading mode consistently occurs in the vicinity of γ=1.42.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

Convergence test for the resonant frequency of flexural-mode vibrations of simply supported beams using both linear and nonlinear elements

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Figure 4

Comparison of the quality factor between the finite element model and the LR solution for the flexural-mode vibrations of simply supported beams

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Figure 5

Convergence test for the resonant frequency of the contour-mode vibrations of circular disks using both linear and nonlinear Fourier elements (r=43 nm, m=2)

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Figure 6

Convergence test for the quality factor of the contour-mode vibrations of circular disks using both linear and nonlinear Fourier elements (r=43 nm, m=2)

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Figure 7

Frequency of the leading mode of contour-mode vibration of circular disks as a function of disk radius

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Figure 8

Quality factor of the leading mode of contour-mode vibration of circular disks as a function of disk radius

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Figure 9

Frequency of the contour-mode vibration of circular ring as a function of Ri/Ro

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Figure 10

Quality factor of the contour-mode vibration of circular ring as a function of Ri/Ro

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Figure 11

Two-dimensional plane stress finite element model for the contour-mode vibration of circular plates: (a) free mesh, (b) lattice mesh, and (c) the dominant eigenmode

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Figure 12

Frequency as a function of geometric aspect ratio in the contour-mode vibration of elliptical plate resonators

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Figure 13

Quality factor as a function of geometric aspect ratio in the contour-mode vibration of elliptical plate resonators

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Figure 14

Dominant mode patterns in the contour-mode vibration of elliptical plate resonator of aspect ratio 1.42

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Figure 2

Convergence test for the quality factor of flexural-mode vibrations of simply supported beams using both linear and nonlinear elements

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Figure 3

Comparison of the resonant frequency (as a function of beam thickness) between the finite element model and the LR solution for the flexural-mode vibrations of simply supported beams

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