KEYWORDS: Switches, Switching, Capacitance, Modulation, Control systems, Signal processing, Digital signal processing, Aerospace engineering, Piezoelectric driven mechanisms
Piezoelectric-based state switching selectively switches between available stiffness states. Some state switching methods require switching from a high- to low-stiffness state at points in the vibration cycle of non-zero strain, resulting in a rapid dissipation of the stored piezoelectric voltage, and a corresponding rapid variation in the system stiffness. This manner of switching induces high-frequency, large-amplitude mechanical transients that are unavoidable and is analogous to an impact, where increasing the switch duration reduces the range of modes excited. Recent develops show that controlling the duration of the voltage dissipation by means of a resistor in the shunt circuit significantly reduces these induced transients; however, incorporating a resistor in the shunt can introduce damping which may be undesirable, depending on the application. As such, this paper numerically investigates an alternate method of controlling the duration of the switch via a variable capacitance shunt.
Piezoelectric-based, semi-active vibration reduction approaches have been studied for over a decade due to their potential in controlling vibration over a large frequency range. Previous studies have relied on a discrete model when switching between the stiffness states of the system. In such a modeling approach, the energy dissipation of the stored potential energy and the transient dynamics, in general, are not well understood. In this paper, a switching model is presented using a variable capacitance in the attached shunt circuit. When the switch duration is small in comparison to the period of vibration, the vibration reduction performance approaches that of the discrete model with an instantaneous switch, whereas longer switch durations lead to less vibration reduction. An energy analysis is then performed that results in the appearance of an energy dissipation term due to the varying capacitance in the shunt circuit.
Performance of piezoelectric-based, semi-active vibration reduction approaches has been studied extensively in the past decade. Originally analyzed with single-degree-of-freedom systems, these approaches have been extended to multi-mode vibration reduction. However, the accompanying analysis typically assumes well-separated modes, which is often not the case for plate structures. Because the semi-active approaches induce a shift in the structural resonance frequency (at least temporarily), targeting a specific mode for vibration reduction can actually lead to additional vibration in an adjacent mode. This paper presents an analysis using a simplified model of a two-degree-of-freedom mass-spring-damper system with lightly-coupled masses to achieve two closely-spaced modes. This investigation is especially applicable to the resonance frequency detuning approach previously proposed to reduce vibrations caused by transient excitation in turbomachinery blades where regions of high modal density exist. More generally, this paper addresses these effects of stiffness state switches in frequency ranges containing regions of high modal density and subject to frequency sweep excitation. Of the approaches analyzed, synchronized switch damping on an inductor offers the greatest vibration reduction performance, whereas resonance frequency detuning and state switching each yield similar performance. Additionally, as the relative distance between resonance peaks decreases, the performance for the vibration reduction methods approaches that of a single-degree-of-freedom system; however, there are distances between these resonant peaks that diminish vibration reduction potential.
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