Thermoelastic damping of the axisymmetric vibration of circular plate resonators

Thermoelastic damping is recognized as a significant loss mechanism at room temperature in micro-scale circular plate resonators. In this paper, the governing equations of coupled thermoelastic problems are established for axisymmetric out-of-plane vibration of circular plate. Then the analytical expression for thermoelastic damping is obtained. The effects of environmental temperature, plate dimensions and boundary conditions on the thermoelastic damping are studied.

[1]  V. T. Srikar,et al.  Thermoelastic damping in fine-grained polysilicon flexural beam resonators , 2002 .

[2]  C. Quate,et al.  Atomic resolution with an atomic force microscope using piezoresistive detection , 1993 .

[3]  J. Butler,et al.  Loss due to transverse thermoelastic currents in microscale resonators , 2004 .

[4]  T. Roszhart The effect of thermoelastic internal friction on the Q of micromachined silicon resonators , 1990, IEEE 4th Technical Digest on Solid-State Sensor and Actuator Workshop.

[5]  Parpia,et al.  Low temperature mechanical properties of boron-doped silicon. , 1992, Physical review letters.

[6]  Peter Vettiger,et al.  Temperature dependence of the force sensitivity of silicon cantilevers , 2004 .

[7]  H. Ziegler,et al.  Digital sensor for IR radiation , 1983 .

[8]  C. Zener INTERNAL FRICTION IN SOLIDS. I. THEORY OF INTERNAL FRICTION IN REEDS , 1937 .

[9]  S. Galliou,et al.  Analysis of the infrared sensitivity of a quartz resonator application as a thermal sensor , 1994, 1994 Proceedings of IEEE Ultrasonics Symposium.

[10]  D. Fang,et al.  Thermoelastic damping in micro-beam resonators , 2006 .

[11]  Stewart McWilliam,et al.  Thermoelastic damping of the in-plane vibration of thin silicon rings , 2006 .

[12]  John R. Vig,et al.  Uncooled IR imaging array based on quartz microresonators , 1996 .

[13]  M. Roukes,et al.  Thermoelastic damping in micro- and nanomechanical systems , 1999, cond-mat/9909271.

[14]  A. Akhiezer,et al.  QUANTUM ELECTRODYNAMICS. , 1965 .

[15]  Qing Jiang,et al.  Analysis of the Air-damping Effect on a Micromachined Beam Resonator , 2003 .

[16]  J. David Zook,et al.  Optically excited self-resonant microbeams , 1996 .

[17]  N. C. MacDonald,et al.  Dissipation measurements of vacuum-operated single-crystal silicon microresonators , 1995 .

[18]  C. Zener INTERNAL FRICTION IN SOLIDS II. GENERAL THEORY OF THERMOELASTIC INTERNAL FRICTION , 1938 .

[19]  D. Greywall,et al.  Theory of amplifier-noise evasion in an oscillator employing a nonlinear resonator. , 1995, Physical review. A, Atomic, molecular, and optical physics.

[20]  G. Bao,et al.  A heat transfer analysis for quartz microresonator IR sensors , 1998 .

[21]  J. K. Gimzewski,et al.  Photothermal spectroscopy with femtojoule sensitivity using a micromechanical device , 1994, Nature.

[22]  C. Zener,et al.  Internal Friction in Solids III. Experimental Demonstration of Thermoelastic Internal Friction , 1938 .

[23]  Michael L. Roukes,et al.  Energy dissipation in suspended micromechanical resonators at low temperatures , 2000 .

[24]  H. Hosaka,et al.  DAMPING CHARACTERISTICS OF BEAM-SHAPED MICRO-OSCILLATORS , 1995 .

[25]  M. Roukes,et al.  Fabrication of high frequency nanometer scale mechanical resonators from bulk Si crystals , 1996 .

[26]  Inspec Properties of silicon , 1988 .

[27]  B. S. Berry Precise Investigation of the Theory of Damping by Transverse Thermal Currents , 1955 .

[28]  Chi-Hung Huang,et al.  Transverse vibration analysis and measurement for the piezoceramic annular plate with different boundary conditions , 2005 .

[29]  D. Fang,et al.  ADVANCES IN THERMOELASTIC DAMPING IN MICRO- AND NANO-MECHANICAL RESONATORS: A REVIEW , 2007 .

[30]  Harold G. Craighead,et al.  Measurement of nanomechanical resonant structures in single-crystal silicon , 1998 .