Thermoelastic damping in fluid-conveying microresonators

Abstract As an inherent energy dissipation mechanism, the thermoelastic damping (TED) imposes an upper limit on the quality factors of microresonators. On the basis of Hamilton principle, the governing equation of solid–liquid-thermal coupling vibration of fluid-conveying microresonator is deduced. For different thermal boundary conditions, the analytical expressions of TED are separately derived by solving the heat diffusion equation of the thermal flow across the fluid-conveying microbeam. The results show that the liquid in the hollow microbeam has significant impact on TED. The natural frequency decreases with the increase of the flow velocity or axial pressure. However, both for the two proposed fluid-conveying models, TED increase with the increase of the flow velocity or axial pressure. The peak value of TED of the proposed models is larger than the hollow beam, but smaller than the solid beam. As a function of channel geometry, beam properties and flow velocity, the second peak is about to occur for the fluid-conveying beam. In addition, different from the results of the hollow beam and the low flow velocity models, the peak value of TED in the high flow velocity model increases monotonously with the increasing ratio of channel width to channel height due to the great area of heat convection between the inner channel and the fluid.

[1]  M. Younis,et al.  The dynamic response of electrostatically driven resonators under mechanical shock , 2010 .

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

[3]  Thomas Brooke Benjamin,et al.  Dynamics of a system of articulated pipes conveying fluid - II. Experiments , 1961, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[4]  A. Mioduchowski,et al.  Thermoelastic dissipation of hollow micromechanical resonators , 2010 .

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

[6]  Lin Wang,et al.  Size-dependent vibration characteristics of fluid-conveying microtubes , 2010 .

[7]  Christoph Gerber,et al.  Development of Robust and Standardized Cantilever Sensors Based on Biotin/Neutravidin Coupling for Antibody Detection , 2013, Sensors.

[8]  Ali H. Nayfeh,et al.  Modeling and simulations of thermoelastic damping in microplates , 2004 .

[9]  Reza Abdolvand,et al.  Quality factor in trench-refilled polysilicon beam resonators , 2006, Journal of Microelectromechanical Systems.

[10]  Lin Wang,et al.  The thermal effect on vibration and instability of carbon nanotubes conveying fluid , 2008 .

[11]  N. Quirke,et al.  Fluid flow in carbon nanotubes and nanopipes. , 2007, Nature nanotechnology.

[12]  N. Najafi,et al.  Dynamic and kinematic viscosity measurements with a resonating microtube , 2009 .

[13]  Seizo Morita,et al.  Atomic force microscopy as a tool for atom manipulation. , 2009, Nature nanotechnology.

[14]  S. Manalis,et al.  Weighing of biomolecules, single cells and single nanoparticles in fluid , 2007, Nature.

[15]  C. Ru Thermoelastic dissipation of nanowire resonators with surface stress , 2009 .

[16]  Z. Nourmohammadi,et al.  Thermoelastic Damping in Layered Microresonators: Critical Frequencies, Peak Values, and Rule of Mixture , 2013, Journal of Microelectromechanical Systems.

[17]  L. Ke,et al.  Flow-induced vibration and instability of embedded double-walled carbon nanotubes based on a modified couple stress theory , 2011 .

[18]  Michael P. Païdoussis,et al.  Dynamics of microscale pipes containing internal fluid flow: Damping, frequency shift, and stability , 2010 .

[19]  R. Kolahchi,et al.  NONLINEAR STRAIN GRADIENT THEORY BASED VIBRATION AND INSTABILITY OF BORON NITRIDE MICRO-TUBES CONVEYING FERROFLUID , 2014 .

[20]  U. Kurzweg Enhanced heat conduction in oscillating viscous flows within parallel-plate channels , 1985, Journal of Fluid Mechanics.

[21]  S. Prabhakar,et al.  Thermoelastic Damping in Hollow and Slotted Microresonators , 2009, Journal of Microelectromechanical Systems.

[22]  G. Meng,et al.  Thermoelastic Damping in the Size-Dependent Microplate Resonators Based on Modified Couple Stress Theory , 2015, Journal of Microelectromechanical Systems.

[23]  Lin Wang,et al.  A reappraisal of the computational modelling of carbon nanotubes conveying viscous fluid , 2009 .

[24]  Sairam Prabhakar,et al.  Thermoelastic damping in bilayered micromechanical beam resonators , 2007 .

[25]  M. I. Younis,et al.  Dynamics of MEMS Arches of Flexible Supports , 2013, Journal of Microelectromechanical Systems.

[26]  P. Enoksson,et al.  A silicon straight tube fluid density sensor , 2007 .

[27]  Thomas Brooke Benjamin,et al.  Dynamics of a system of articulated pipes conveying fluid - I.Theory , 1961, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences.

[28]  Peter Enoksson,et al.  A silicon resonant sensor structure for Coriolis mass-flow measurements , 1997 .

[29]  C. Wang,et al.  Buckling analysis of micro- and nano-rods/tubes based on nonlocal Timoshenko beam theory , 2006 .

[30]  S. Kitipornchai,et al.  Nonlinear free vibration of embedded double-walled carbon nanotubes based on nonlocal Timoshenko beam theory , 2009 .

[31]  Srikar Vengallatore,et al.  Analysis of thermoelastic damping in laminated composite micromechanical beam resonators , 2005 .

[32]  Woo-Tae Park,et al.  Impact of geometry on thermoelastic dissipation in micromechanical resonant beams , 2006, Journal of Microelectromechanical Systems.

[33]  Siavash Pourkamali,et al.  A finite element analysis of thermoelastic damping in vented MEMS beam resonators , 2013 .

[34]  M. Païdoussis Fluid-Structure Interactions: Slender Structures and Axial Flow , 2014 .

[35]  Guang Meng,et al.  Thermoelastic damping in optical waveguide resonators with the bolometric effect. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.