Nonlinear Dynamics of an Electrically Driven Impact Microactuator

Abstract

We study the dynamics of an electrostatically driven impact microactuator. Impact between moving elements of the microactuator is modeled using the coefficient of restitution. Friction between the microactuator and its supporting substrate is modeled using the Amonton-Coulomb law. We consider the bifurcations under changes in the driving voltage and frequency. Grazing bifurcations introduce discontinuous transitions between different motions. It is also found that impacts dramatically change the characteristics of the frequency-response curve. Finally, we discuss the evolution of incomplete chatter to complete chatter, that is, sticking.

Asymptotic approximation of an ionic model for cardiac restitution

“…Piecewise smooth dynamical systems may exhibit various discontinuity-induced bifurcations, such as grazing bifurcations in systems with discontinuous changes in states [7,19,20] and border-collision bifurcations in piecewise continuous maps [5,16,21]. To explore the possibility for discontinuous bifurcations, we first examine the type of discontinuities in the mapping.…”

“…At the start of phase 2 of the (n + 1) st action potential (19) and at the end of this phase (20) Proof: As noted above, h term ≈ h min (C n ) defines the end of phase 2: i.e., the point at which h has decayed so much that the inward current can no longer balance the outward current. This verifies (20).…”

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“…The most promising driving and controlling candidate seems to be electrostatic actuator, but there are still some major problems. For example, rather high operating voltage and inherent non-linearity [13,14] remain to be solved for this kind of actuator. Moreover, even if the above mentioned actuators can satisfy certain requirements for particular application, they cannot fulfill the direct conversion of RF or microwave energy into kinetic energy.…”

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“…For example, a micromachined impact actuator (known as Mita's actuator) driven by electric forces was developed to produce a precise displacement [1]. A later theoretical study unveils the complex dynamics of Mita's actuator and provides a guideline for designing it [2,3]. Another example is the atomic force microscopy (AFM) operating in the tapping mode.…”