Eigenvalue Solution of Thermoelastic Damping in Beam Resonators Using a Finite Element Analysis

[+] Author and Article Information
Yun-Bo Yi1

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

Mohammad A. Matin

Department of Engineering,  University of Denver, Denver, CO 80208


Corresponding author.

J. Vib. Acoust 129(4), 478-483 (Feb 23, 2007) (6 pages) doi:10.1115/1.2748472 History: Received June 14, 2006; Revised February 23, 2007

A finite element formulation is developed for solving the problem related to thermoelastic damping in beam resonator systems. The perturbation analysis on the governing equations of heat conduction, thermoleasticity, and dynamic motion leads to a linear eigenvalue equation for the exponential growth rate of temperature, displacement, and velocity. The numerical solutions for a simply supported beam have been obtained and shown in agreement with the analytical solutions found in the literature. Parametric studies on a variety of geometrical and material properties demonstrate their effects on the frequency and the quality factor of resonance. The finite element formulation presented in this work has advantages over the existing analytical approaches in that the method can be easily extended to general geometries without extensive computations associated with the numerical iterations and the analytical expressions of the solution under various boundary conditions.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 8

Frequency (엯) and quality factor (*) of vibration as functions of Young’s modulus

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Figure 1

Comparison of the finite element solution and exact solution for frequency of a simply supported thin beam. The theoretical solution corresponds to the undamped natural frequency.

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Figure 2

Convergence test showing the quality factor (*) and frequency (엯) as functions of element number

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Figure 3

Comparison of the normalized quality factor with the existing analytical solutions

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Figure 4

Frequency (엯) and quality factor (*) of vibration as functions of beam aspect ratio

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Figure 5

Frequency (엯) and quality factor (*) of vibration as functions of temperature

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Figure 6

Frequency (엯) and quality factor (*) of vibration as functions of thermal diffusivity

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Figure 7

Frequency (엯) and quality factor (*) of vibration as functions of Poisson’s ratio



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