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Mathematical Modeling of Thermal Effects in Steady State Dynamics of Microresonators Using Lorentzian Function: Part 2 — Temperature Relaxation

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

North Dakota State University

A. Khazaei

Newcomb & Boyd Consulting

M. H. Alimi

Department of Public Works & Planning

Paper No. IMECE2005-81882, pp. 1133-1142; 10 pages
  • 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


Thermal phenomena have two distinct effects, which are called, in this report, “thermal damping” and “temperature relaxation”. In this second part of a two-part report we (only) model and investigate the temperature relaxation and its effects on microresonator dynamics. A reduced order mathematical model of the system is introduced as a mass-spring-damper system actuated by a linearized electrostatic force. Temperature relaxation is the thermal stiffness softening and is modeled as a decrease in stiffness rate, utilizing a Lorentzian function of excitation frequency. The steady state frequency-amplitude dependency of the system will be derived utilizing averaging perturbation method. Analytic equation describing the frequency response of the system near resonance which can be utilized to explain the dynamics of the system, as well as design of involved dynamic parameters is developed.

Copyright © 2005 by ASME



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