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Mathematical Modeling of Thermal Effects in Steady State Dynamics of Microresonators Using Lorentzian Function: Part 1 — Thermal Damping

[+] Author Affiliations
G. Nakhaie Jazar, M. Mahinfalah, M. R. Aagaah, N. Mahmoudian

North Dakota State University

A. Khazaei

Newcomb & Boyd Consulting

M. H. Alimi

Department of Public Works and Planning

Paper No. IMECE2005-81837, pp. 1093-1102; 10 pages
doi:10.1115/IMECE2005-81837
From:
  • ASME 2005 International Mechanical Engineering Congress and Exposition
  • Design Engineering, Parts A and B
  • Orlando, Florida, USA, November 5 – 11, 2005
  • Conference Sponsors: Design Engineering Division
  • ISBN: 0-7918-4215-0 | eISBN: 0-7918-3769-6
  • Copyright © 2005 by ASME

abstract

Mathematical modeling of thermal effects on steady state dynamics of microresonators, utilizing an analytical approach is studied. Thermal phenomena has two distinct effects, which in this report are called, thermal damping and temperature relaxation. In this part of a two-part report we investigate the thermal damping and its effects on microresonator dynamics. To do this, first the reduced order mathematical model of the system is introduced as a forced mass-spring-damper system, and then a linearized model of electric actuated microbeam resonator is employed. The effect of thermal damping is modeled as an increase in damping rate, utilizing a Lorentzian function of excitation frequency. The steady state frequency-amplitude dependency of the system will be derived utilizing averaging perturbation method. The developed analytic equation describing the frequency response of the system around resonance can be utilized to explain the dynamics of the system, as well as design of dynamic parameters. However, we have focused on exploration of thermal damping.

Copyright © 2005 by ASME

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