Journal Article10.1109/JMEMS.2008.916316
Theory of Thermoelastic Damping in Micromechanical Resonators With Two-Dimensional Heat Conduction
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TL;DR: In this paper, an exact theory for TED with 2-dimensional heat conduction was presented, which enables a detailed evaluation of the accuracy of the quasi-1-D theories for low-loss vacuum-operated micro-and nanomechanical resonators used in microelectro- mechanical systems.
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Abstract: Analysis of thermoelastic damping (TED) is an important component of the design of low-loss vacuum-operated micro- and nanomechanical resonators used in microelectro- mechanical systems (MEMS). The quasi-1-D theories developed by Zener in 1937, and subsequently improved by Lifshitz and Roukes in 2000, are now widely used in MEMS design. This paper presents an exact theory for TED with 2-D heat conduction that enables a detailed evaluation of the accuracy of the quasi-1-D theories. A Green's function method is used to solve the 2-D heat- conduction equation, and an expression for TED is derived in the form of an infinite series. The effects of beam geometry, length-to- thickness aspect ratio, natural frequency, flexural mode shapes, and structural boundary conditions on TED are investigated for the representative case of single-crystal silicon microbeam resonators. The errors in the exact quasi-1-D theory range from 2% to 80% depending upon the aspect ratio and the mode shape. Implications for the use of the quasi-1-D and 2-D theories in MEMS design are discussed. [2007-0199].
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Citations
Thermoelastic Damping in Micro- and Nano-Mechanical Systems.
Ron Lifshitz,Michael L. Roukes +1 more
- 01 Mar 2000
Abstract: The importance of thermoelastic damping as a fundamental dissipation mechanism for small-scale mechanical resonators is evaluated in light of recent efforts to design high-Q micrometer- and nanometer-scale electromechanical systems. The equations of linear thermoelasticity are used to give a simple derivation for thermoelastic damping of small flexural vibrations in thin beams. It is shown that Zener’s well-known approximation by a Lorentzian with a single thermal relaxation time slightly deviates from the exact expression.
681
Micromachined Resonators: A Review
TL;DR: A review of the remarkable progress that has been made during the past few decades in design, modeling, and fabrication of micromachined resonators with references to the most influential contributions in the field for those interested in a deeper understanding of the material.
204
Thermoelastic damping in micro-scale circular plate resonators
Yuxin Sun,Yuxin Sun,Masumi Saka +2 more
TL;DR: In this paper, the governing equations of coupled thermoelastic problems are established for out-of-plane vibration of a circular plate and the analytical expression for thermo-elastic damping is obtained.
167
High Quality Factor Resonant MEMS Accelerometer With Continuous Thermal Compensation
TL;DR: In this paper, the authors report a new silicon Microelectromechanical systems (MEMS) accelerometer based on differential frequency modulation (FM) with experimentally demonstrated thermal compensation over a dynamic temperature environment and the Allan deviation of bias.
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Thermoelastic damping in rectangular and circular microplate resonators
Pu Li,Yuming Fang,Rufu Hu +2 more
TL;DR: In this article, the authors presented an analytical model for the TED in the fully clamped and simply supported rectangular microplates by calculating the energy dissipated per cycle of vibration over the volume of the microplate.
125
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Thermoelastic damping in micro- and nanomechanical systems
Ron Lifshitz,Michael L. Roukes +1 more
TL;DR: In this paper, the importance of thermoelastic damping as a fundamental dissipation mechanism for small-scale mechanical resonators is evaluated in light of recent efforts to design high-Q micrometer-and nanometer-scale electromechanical systems.
Internal friction in solids. i. theory of internal friction in reeds
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