Abstract
We study the dynamics of a resonantly driven nonlinear resonator (primary) that is nonlinearly coupled to a non-resonantly driven linear resonator (secondary) with a relatively short decay time. Due to its short relaxation time, the secondary resonator adiabatically tracks the primary resonator and modifies its response. Our model, which is motivated by experimental studies on the interaction between nano- and micro-resonators, is relatively simple and can be analyzed analytically and numerically to show that the driven response of the primary resonator can be enhanced significantly due to the interaction with the secondary resonator. Such an arrangement may pave the way for systematic control of driven responses and signal amplification in engineering applications involving nano- and micro-electro-mechanical-systems.
Highlights
We study the dynamics of a resonantly driven nonlinear resonator that is nonlinearly coupled to a non-resonantly driven linear resonator with a relatively short decay time
Our model, which is motivated by experimental studies on the interaction between nano- and microresonators, is relatively simple and can be analyzed analytically and numerically to show that the driven response of the primary resonator can be enhanced significantly due to the interaction with the secondary resonator
Such an arrangement may pave the way for systematic control of driven responses and signal amplification in engineering applications involving nano- and micro-electro-mechanical-systems
Summary
Signal amplification of driven resonators is essential in engineering applications involving nano- and microelectro-mechanical-systems (N/MEMS). Resonator q1 is driven resonantly by an excitation F1 cos(ωF1 t + θ) and oscillates around its stable equilibrium q1 = 0 with a large amplitude and nonlinear restoring forces that stem from a potential U (q1). Where the dot symbol denotes a time derivative, the prime symbol denotes a differentiation of a function with respect to its single variable, and −2Γkqk models the linear friction force experienced by resonator k (k = 1, 2) Both resonators are lightly damped (Γk/ωk ≪ 1), and the secondary resonator decays much faster than the primary resonator (Γ2/Γ1 ≫ 1). The functional L[q1, t] is the driven response (by the external excitation and the primary resonator) of the secondary, and M (t) is the response of the secondary resonator to its initial state
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