Garrett K. Lopp

Switch Triggers for Optimal Vibration Reduction Via Resonance Frequency Detuning

Resonance frequency detuning (RFD) is a piezoelectric-based vibration reduction approach that applies to systems experiencing transient excitation through a system resonance. Particularly, this vibration reduction technique can be applied to turbomachinery experiencing changes in rotation speed, such as on spool-up and spool-down. This technique relies on the inclusion of piezoelectric material and manipulation of its electrical boundary conditions, which control the stiffness of the piezoelectric material—the open-circuit condition corresponds to the high stiffness state of the material and the short-circuit condition corresponds to the low stiffness state. When placed in a region of high strain, the altered stiffness of the piezoelectric material causes a global stiffness change in the system. Resonance frequency detuning takes advantage of this effect by switching from the opento the short-circuit stiffness state as the excitation approaches resonance, subsequently detuning the structure from the excitation and reducing the vibratory response. Although other piezoelectric vibration techniques exist that allow for a greater reduction of the response (spanning the range from passive to active approaches), these techniques suffer drawbacks when applied to systems with tight size and power requirements, such as a turbomachinery environment. Resonance frequency detuning simplifies these approaches by relaxing some of these requirements by creating a large broadband vibration reduction approach with limited power, circuitry, and signal processing requirements. For this approach, the peak response dynamics are

Optimal Resonance Frequency Detuning Switch Trigger Determination Using Measurable Response Characteristics

For systems experiencing transient vibration associated with passage through resonance, resonance frequency detuning (RFD) offers a source of vibration reduction by altering the stiffness state of the structure as the swept excitation frequency approaches any resonance frequency. The peak response dynamics and overall maximum amplitude reduction is governed by the sweep rate, modal damping ratio, electromechanical coupling coefficient, and the point at which this stiffness switch occurs, and the optimal switch trigger has been established when all system information is readily available. This study investigates a method of determining the optimal switch trigger using only the open-circuit piezoelectric voltage time response. For the purposes of simulation, a curve fit is employed and a subsequent optimal trigger control law is extracted. This empirical control law agrees well with and produces comparable response to that of the optimal control determined using perfect and complete knowledge of the system.

A continuous switching model for piezoelectric state switching methods

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.

Switch Triggers for Optimal Vibration Reduction via Resonance Frequency Detuning

For systems subjected to linear frequency sweep excitation, piezoelectric-based resonance frequency detuning provides vibration reduction by altering the stiffness state of the material as it passes through resonance. This vibration reduction technique applies to turbomachinery experiencing changes in rotation speed, for example on spool-up and spool-down. The peak response dynamics are determined by the system’s sweep rate, modal damping ratio, electromechanical coupling coefficient, and, most importantly, the frequency at which the stiffness state is altered. An analytical approach is employed to solve the nondimensional single degree of freedom equation of motion and is scaled to incorporate the altered system frequency following the stiffness state switch. This paper provides an extensive study over a range of sweep rates, damping ratios, and electromechanical coupling coefficients to determine the optimal frequency switch trigger that minimizes the response envelope. This switch trigger is primarily a function of the electromechanical coupling coefficient and the phase of vibration at which the switch occurs. As the coupling coefficient increases, the switch trigger decreases and is approximately linear with the square of this coupling coefficient. Furthermore, as with other state-switching techniques, the optimal frequency switch occurs when the phase of vibration is at the point of maximum displacement, or peak strain energy.© 2014 ASME

A Method for Canceling Force Transducer Mass and Inertia Effects

Experimental modal analysis via shaker testing introduces errors in the measured structural response that can be attributed to the force transducer assembly fixed on the vibrating structure. Previous studies developed transducer mass-cancellation techniques for systems with translational degrees of freedom; however, studies addressing this problem when rotations cannot be neglected are sparse. In situations where rotations cannot be neglected, the apparent mass of the transducer is dependent on its geometry and is not the same in all directions. This paper investigates a method for correcting the measured system response that is contaminated with the effects of the attached force transducer mass and inertia. Experimental modal substructuring facilitated estimations of the translational and rotational mode shapes at the transducer connection point, thus enabling removal of an analytical transducer model from the measured test structure resulting in the corrected response. A numerical analysis showed the feasibility of the proposed approach in estimating the correct modal frequencies and forced response. To provide further validation, an experimental analysis showed the proposed approach applied to results obtained from a shaker test more accurately reflected results obtained from a hammer test.

Experimental Demonstration of a Tunable Acoustoelastic System

Acoustoelastic coupling occurs when a hollow structure’s in-vacuo mode aligns with an acoustic mode of the internal cavity. The impact of this coupling on the total dynamic response of the structure can be quite severe depending on the similarity of the modal frequencies and shapes. Typically, acoustoelastic coupling is not a design feature, but rather an unfortunate result that must be remedied as modal tests are often used to correlate or validate finite element models of the uncoupled structure. Here, however, a test structure is intentionally designed such that multiple structural and acoustic modes are well-aligned, resulting in a coupled system that allows for an experimental investigation. Coupling in the system is first identified using a measure termed the magnification factor and the structural-acoustic interaction for a target mode is then measured. Modifications to the system demonstrate the dependency of the coupling with respect to changes in the mode shape and frequency proximity. This includes an investigation of several practical techniques used to decouple the system by altering the internal acoustic cavity, as well as the structure itself. Furthermore, acoustic absorption material effectively decoupled the structure while structural modifications, in their current form, proved unsuccessful. The most effective acoustic absorption method consisted of randomly distributing typical household paper towels in the acoustic cavity; a method that introduces negligible mass to the structural system with the additional advantages of being inexpensive and readily available.

Vibration Reduction of Mistuned Bladed Disks via Piezoelectric-Based Resonance Frequency Detuning

Recent trends in turbomachinery blade technology have led to increased use of monolithically constructed bladed disks (blisks). Although offering a wealth of performance benefits, this construction removes the blade-attachment interface present in the conventional design, thus unintentionally removing a source of friction-based damping needed to counteract large vibrations during resonance passages. This issue is further exacerbated in the presence of blade mistuning that arises from small imperfections from otherwise identical blades and are unavoidable as they originate from manufacturing tolerances and operational wear over the lifespan of the engine. Mistuning is known to induce vibration localization with large vibration amplitudes that render blades susceptible to failure induced by high-cycle fatigue. The resonance frequency detuning (RFD) method reduces vibration associated with resonance crossings by selectively altering the blades structural response. This method utilizes the variable stiffness properties of piezoelectric materials to switch between available stiffness states at some optimal time as the excitation frequency sweeps through a resonance. For a single-degree-of-freedom (SDOF) system, RFD performance is well defined. This research provides the framework to extend RFD to more realistic applications when the SDOF assumption breaks down, such as in cases of blade mistuning. Mistuning is inherently random; thus, a Monte Carlo analysis performed on a computationally cheap lumpedparameter model provides insight into RFD performance for various test parameters. Application

On the transient dynamics of piezoelectric-based, state-switched systems

This letter reports on the induced mechanical transients for piezoelectric-based, state-switching approaches utilizing both experimental tests and a numerical model that more accurately captures the dynamics associated with a switch between stiffness states. Currently, switching models instantaneously dissipate the stored piezoelectric voltage, resulting in a discrete change in effective stiffness states and a discontinuity in the system dynamics during the switching event. The proposed model allows for a rapid but continuous voltage dissipation and the corresponding variation between stiffness states, as one sees in physical implementations. This rapid variation in system stiffness when switching at a point of non-zero strain leads to high-frequency, large-amplitude transients in the system acceleration response. Utilizing a fundamental piezoelectric bimorph, a comparison between the numerical and experimental results reveals that these mechanical transients are much stronger than originally anticipated and masked by measurement hardware limitations, thus highlighting the significance of an appropriate system model governing the switch dynamics. Such a model enables designers to analyze systems that incorporate piezoelectric-based state switching with greater accuracy to ensure that these transients do not degrade the intended performance. Finally, if the switching does create unacceptable transients, controlling the duration of voltage dissipation enables control over the frequency content and peak amplitudes associated with the switch-induced acceleration transients.This letter reports on the induced mechanical transients for piezoelectric-based, state-switching approaches utilizing both experimental tests and a numerical model that more accurately captures the dynamics associated with a switch between stiffness states. Currently, switching models instantaneously dissipate the stored piezoelectric voltage, resulting in a discrete change in effective stiffness states and a discontinuity in the system dynamics during the switching event. The proposed model allows for a rapid but continuous voltage dissipation and the corresponding variation between stiffness states, as one sees in physical implementations. This rapid variation in system stiffness when switching at a point of non-zero strain leads to high-frequency, large-amplitude transients in the system acceleration response. Utilizing a fundamental piezoelectric bimorph, a comparison between the numerical and experimental results reveals that these mechanical transients are much stronger than originally anticipated ...

A synthetic shunt for piezoelectric-based state switching

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.

State switching in regions of high modal density

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.