Mathematical Modeling of Thermal Effects in Steady State Dynamics of Microresonators Using Lorentzian Function: Part 2 - Temperature Relaxation
نویسنده
چکیده
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.
منابع مشابه
Mathematical Modeling of Thermal Effects in Steady State Dynamics of Microresonators Using Lorentzian Function: Part 1 - Thermal Damping
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 or...
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