scholarly journals Vibration Reduction of Mistuned Bladed Disks Via Piezoelectric-Based Resonance Frequency Detuning

2018 ◽  
Vol 140 (5) ◽  
Author(s):  
Garrett K. Lopp ◽  
Jeffrey L. Kauffman
Keyword(s):  
Resonance Frequency ◽  
Electromechanical Coupling ◽  
Short Circuit ◽  
Damping Ratio ◽  
Vibration Reduction ◽  
Sweep Rate ◽  
Open Circuit ◽  
Frequency Detuning ◽  
Blade Vibration ◽  
Direct Numerical Integration

This paper extends the resonance frequency detuning (RFD) vibration reduction approach to cases of turbomachinery blade mistuning. Using a lumped parameter mistuned blade model with included piezoelectric elements, this paper presents an analytical solution of the blade vibration in response to frequency sweep excitation; direct numerical integration confirms the accuracy of this solution. A Monte Carlo statistical analysis provides insight regarding vibration reduction performance over a range of parameters of interest such as the degree of blade mistuning, linear excitation sweep rate, inherent damping ratio, and the difference between the open-circuit (OC) and short-circuit (SC) stiffness states. RFD reduces vibration across all degrees of blade mistuning as well as the entire range of sweep rates tested. Detuning also maximizes vibration reduction performance when applied to systems with low inherent damping and large electromechanical coupling.

Resonance Frequency Detuning With Application Towards Blade Mistuning

2017 ◽  
Author(s):  
Garrett K. Lopp ◽  
Jeffrey L. Kauffman
Keyword(s):  
Resonance Frequency ◽  
Electromechanical Coupling ◽  
Short Circuit ◽  
Damping Ratio ◽  
Vibration Reduction ◽  
Sweep Rate ◽  
Frequency Detuning ◽  
Lumped Parameter ◽  
The Difference ◽  
Direct Numerical Integration

This paper extends the Resonance Frequency Detuning vibration reduction approach by analyzing the performance in cases of turbomachinery blade mistuning. A lumped parameter mistuned blade model with included piezoelectric elements is utilized and an analytical solution for frequency sweep excitation is presented and validated using direct numerical integration. A Monte Carlo statistical analysis is then conducted to provide insight regarding vibration reduction performance over a range of parameters of interest such as the degree of blade mistuning, linear excitation sweep rate, damping ratio, and the difference between the open- and short-circuit stiffness states. Vibration reduction is shown to exist across all degrees of blade mistuning as well as the entire range of sweep rates tested. This vibration reduction performance is also maximized for systems with low inherent damping and large electromechanical coupling values.

Switch Triggers for Optimal Vibration Reduction via Resonance Frequency Detuning

2014 ◽  
Author(s):  
Garrett K. Lopp ◽  
Jeffrey L. Kauffman
Keyword(s):  
Resonance Frequency ◽  
Coupling Coefficient ◽  
Electromechanical Coupling ◽  
Damping Ratio ◽  
Vibration Reduction ◽  
Electromechanical Coupling Coefficient ◽  
Peak Strain ◽  
Frequency Detuning ◽  
Optimal Frequency ◽  
Response Dynamics

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.

Switch Triggers for Optimal Vibration Reduction Via Resonance Frequency Detuning

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
Garrett K. Lopp ◽  
Jeffrey L. Kauffman
Keyword(s):  
Resonance Frequency ◽  
Coupling Coefficient ◽  
Electromechanical Coupling ◽  
Vibration Reduction ◽  
Excitation Frequency ◽  
Electromechanical Coupling Coefficient ◽  
Peak Strain ◽  
Frequency Detuning ◽  
Response Dynamics ◽  
Modal Damping

Resonance frequency detuning (RFD) reduces vibration of systems subjected to frequency sweep excitation by altering the structural stiffness state as the excitation frequency passes through resonance. This vibration reduction technique applies to turbomachinery experiencing changes in rotation speed, for example, on spool-up and spool-down, and can be achieved through the inclusion of piezoelectric material and manipulation of its electrical boundary conditions. Key system parameters—the excitation sweep rate, modal damping ratio, electromechanical coupling coefficient, and, most importantly, the switch trigger that initiates the stiffness state switch (represented here in terms of excitation frequency)—determine the peak response dynamics. This paper exploits an analytical solution to a nondimensional single degree-of-freedom equation of motion to provide this blade response and recasts the equation in scaled form to include the altered system dynamics following the stiffness state switch. An extensive study over a range of sweep rates, damping ratios, and electromechanical coupling coefficients reveals the optimal frequency switch trigger that minimizes the peak of the blade 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 frequency-based switch trigger decreases, approximately linearly with the square of the coupling coefficient. Furthermore, as with other state-switching techniques, the optimal stiffness switch occurs on peak strain energy; however, the degradation in vibration reduction performance associated with a switch occurring at a nonoptimal phase is negligible for slow sweep rates and low modal damping.

scholarly journals Experimental validation of piezoelectric shunt tuning with residual mode correction: Damping of plate-like structures

2020 ◽  
Vol 31 (9) ◽  
pp. 1220-1239
Author(s):  
Johan Frederik Toftekær ◽  
Jan Høgsberg
Keyword(s):  
Electromechanical Coupling ◽  
Copper Wire ◽  
Short Circuit ◽  
Single Mode ◽  
Magnetic Core ◽  
Open Circuit ◽  
Electromechanical Coupling Coefficient ◽  
Tuning Method ◽  
Multi Mode ◽  
Free Beam

The effective vibration mitigation properties of piezoceramic patches with inductive-resistive shunts are investigated experimentally. A shunt tuning method is proposed, in which a consistent correction for the influence from residual vibration modes is included by an effective modal capacitance, evaluated from measured charge and voltage amplitudes in short- and open-circuit conditions, respectively. The robustness of the proposed method is verified experimentally for both a free beam and a free plate structure with four shunted piezoceramic patch pairs. A stable and fully passive inductor is produced by winding a copper wire around a magnetic core, which requires precise inductance tuning to determine the final number of turns. It is demonstrated that the effective modal capacitance interpolates consistently between the blocked and static capacitances, commonly used for single-mode tuning of piezoelectric inductive-resistive shunts. By imposing pseudo-random vibrations, the piezoelectric current and voltage signals are measured and evaluated by their frequency response functions. Spectrum peak values determine the apparent short-circuit charge to open-circuit voltage ratio for each shunt, which directly determines the shunt components by explicit tuning formulas. Good correlation between numerical and experimental results are obtained for the free beam, while for the free plate experiment effective multi-mode shunt tuning is obtained by a modified effective electromechanical coupling coefficient.

scholarly journals Active Piezoelectric Vibration Control of Subscale Composite Fan Blades

2012 ◽  
Author(s):  
Kirsten P. Duffy ◽  
Benjamin B. Choi ◽  
Andrew J. Provenza ◽  
James B. Min ◽  
Nicholas Kray
Keyword(s):  
Vibration Control ◽  
Electromechanical Coupling ◽  
New Technologies ◽  
Piezoelectric Materials ◽  
Fiber Composite ◽  
Damping Ratio ◽  
Active Vibration Control ◽  
Rotor Speed ◽  
Blade Vibration ◽  
Active Vibration

As part of the Fundamental Aeronautics program, researchers at NASA Glenn Research Center (GRC) are investigating new technologies supporting the development of lighter, quieter, and more efficient fans for turbomachinery applications. High performance fan blades designed to achieve such goals will be subjected to higher levels of aerodynamic excitations which could lead to more serious and complex vibration problems. Piezoelectric materials have been proposed as a means of decreasing engine blade vibration either through a passive damping scheme, or as part of an active vibration control system. For polymer matrix fiber composite blades, the piezoelectric elements could be embedded within the blade material, protecting the brittle piezoceramic material from the airflow and from debris. To investigate this idea, spin testing was performed on two General Electric Aviation (GE) subscale composite fan blades in the NASA GRC Dynamic Spin Rig Facility. The first bending mode (1B) was targeted for vibration control. Because these subscale blades are very thin, the piezoelectric material was surface-mounted on the blades. Three thin piezoelectric patches were applied to each blade — two actuator patches and one small sensor patch. These flexible macro-fiber-composite patches were placed in a location of high resonant strain for the 1B mode. The blades were tested up to 5000 rpm, with patches used as sensors, as excitation for the blade, and as part of open- and closed-loop vibration control. Results show that with a single actuator patch, active vibration control causes the damping ratio to increase from a baseline of 0.3% critical damping to about 1.0% damping at 0 RPM. As the rotor speed approaches 5000 RPM, the actively controlled blade damping ratio decreases to about 0.5% damping. This occurs primarily because of centrifugal blade stiffening, and can be observed by the decrease in the generalized electromechanical coupling with rotor speed.

Thermal Conductivities of PZT Piezoelectric Ceramics under Different Electrical Boundary Conditions

2020 ◽  
Vol 3 (1) ◽  
pp. 10
Author(s):  
Husain N.  Shekhan ◽  
Erkan A.  Gurdal ◽  
Lalitha Ganapatibhotla ◽  
Janna K.  Maranas ◽  
Ron Staut ◽  
...  
Keyword(s):  
Thermal Conductivity ◽  
Thermal Properties ◽  
Boundary Conditions ◽  
Lead Zirconate Titanate ◽  
Electromechanical Coupling ◽  
Short Circuit ◽  
Coupling Factor ◽  
Open Circuit ◽  
Electrical Boundary Conditions ◽  
Poling Direction

<p>Physical properties of polycrystalline lead-zirconate-titanate (PZT) changes according to electrical boundary conditions and poling. This paper reports the thermal properties of poled and unpoled PZT's in the poling direction for open circuit and short circuit conditions. The authors found that the short-circuit condition exhibited the largest thermal conductivity than the open-circuit condition. In the relationship between these two thermal properties, the authors propose the "electrothermal" coupling factor k<sup>κ</sup><sub>33</sub>, which is similar to the electromechanical coupling factor k<sub>33</sub> relating the elastic compliances under short- and open-circuit conditions. On the other hand, the thermal conductivity of the unpoled specimen exhibits the lowest thermal conductivity, in comparison with the poled specimens, which suggests the importance of phonon mode scattering on the thermal conductivity with respect to elastic compliance.</p>

scholarly journals A New Electrical Circuit With Negative Capacitances to Enhance Resistive Shunt Damping

2015 ◽  
Author(s):  
Marta Berardengo ◽  
Stefano Manzoni ◽  
Olivier Thomas ◽  
Christophe Giraud-Audine
Keyword(s):  
Electromechanical Coupling ◽  
Short Circuit ◽  
Electromechanical Coupling Factor ◽  
Coupling Factor ◽  
Open Circuit ◽  
Electrical Circuit ◽  
Structural Vibration ◽  
Electrical Network ◽  
Negative Capacitance ◽  
Shunt Damping

This article proposes a new layout of electrical network based on two negative capacitance circuits, aimed at increasing the performances of a traditional resistive piezoelectric shunt for structural vibration reduction. It is equivalent to artificially increase the modal electromechanical coupling factor of the electromechanical structure by both decreasing the short-circuit natural frequencies and increasing the open-circuit ones. This leads to higher values of the modal electromechanical coupling factor with respect to simple negative capacitance configurations, when the same margin from stability is considered. This technique is shown to be powerful in enhancing the control performance when associated to a simple resistive shunt, usually avoided because of its poor performances.

A Distributed Parameter Electromechanical Model for Cantilevered Piezoelectric Energy Harvesters

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
A. Erturk ◽  
D. J. Inman
Keyword(s):  
Electromechanical Coupling ◽  
Mechanical Response ◽  
Exact Analytical Solution ◽  
Short Circuit ◽  
Open Circuit ◽  
Distributed Parameter ◽  
Energy Harvesters ◽  
Piezoelectric Energy ◽  
Cantilevered Beams ◽  
Power Outputs

Cantilevered beams with piezoceramic layers have been frequently used as piezoelectric vibration energy harvesters in the past five years. The literature includes several single degree-of-freedom models, a few approximate distributed parameter models and even some incorrect approaches for predicting the electromechanical behavior of these harvesters. In this paper, we present the exact analytical solution of a cantilevered piezoelectric energy harvester with Euler–Bernoulli beam assumptions. The excitation of the harvester is assumed to be due to its base motion in the form of translation in the transverse direction with small rotation, and it is not restricted to be harmonic in time. The resulting expressions for the coupled mechanical response and the electrical outputs are then reduced for the particular case of harmonic behavior in time and closed-form exact expressions are obtained. Simple expressions for the coupled mechanical response, voltage, current, and power outputs are also presented for excitations around the modal frequencies. Finally, the model proposed is used in a parametric case study for a unimorph harvester, and important characteristics of the coupled distributed parameter system, such as short circuit and open circuit behaviors, are investigated in detail. Modal electromechanical coupling and dependence of the electrical outputs on the locations of the electrodes are also discussed with examples.

scholarly journals Active Piezoelectric Vibration Control of Subscale Composite Fan Blades

2012 ◽  
Vol 135 (1) ◽  
Author(s):  
Kirsten P. Duffy ◽  
Benjamin B. Choi ◽  
Andrew J. Provenza ◽  
James B. Min ◽  
Nicholas Kray
Keyword(s):  
Vibration Control ◽  
Electromechanical Coupling ◽  
New Technologies ◽  
Piezoelectric Materials ◽  
Fiber Composite ◽  
Damping Ratio ◽  
Active Vibration Control ◽  
Rotor Speed ◽  
Blade Vibration ◽  
Active Vibration

As part of the Fundamental Aeronautics program, researchers at NASA Glenn Research Center (GRC) are investigating new technologies supporting the development of lighter, quieter, and more efficient fans for turbomachinery applications. High performance fan blades designed to achieve such goals will be subjected to higher levels of aerodynamic excitations which could lead to more serious and complex vibration problems. Piezoelectric materials have been proposed as a means of decreasing engine blade vibration either through a passive damping scheme, or as part of an active vibration control system. For polymer matrix fiber composite blades, the piezoelectric elements could be embedded within the blade material, protecting the brittle piezoceramic material from the airflow and from debris. To investigate this idea, spin testing was performed on two General Electric Aviation (GE) subscale composite fan blades in the NASA GRC Dynamic Spin Rig Facility. The first bending mode (1B) was targeted for vibration control. Because these subscale blades are very thin, the piezoelectric material was surface-mounted on the blades. Three thin piezoelectric patches were applied to each blade—two actuator patches and one small sensor patch. These flexible macro-fiber-composite patches were placed in a location of high resonant strain for the 1B mode. The blades were tested up to 5000 rpm, with patches used as sensors, as excitation for the blade, and as part of open- and closed-loop vibration control. Results show that with a single actuator patch, active vibration control causes the damping ratio to increase from a baseline of 0.3% critical damping to about 1.0% damping at 0 rpm. As the rotor speed approaches 5000 rpm, the actively controlled blade damping ratio decreases to about 0.5% damping. This occurs primarily because of centrifugal blade stiffening, and can be observed by the decrease in the generalized electromechanical coupling with rotor speed.

Effect of Switching Impulse on Piezoelectric-Based Vibration Reduction With Multiple Patches

2019 ◽  
Author(s):  
Christopher R. Kelley ◽  
Jeffrey L. Kauffman
Keyword(s):  
Piezoelectric Material ◽  
Electromechanical Coupling ◽  
Structural Integrity ◽  
Experimental Testing ◽  
Vibration Reduction ◽  
Excitation Frequency ◽  
Open Circuit ◽  
Piezoelectric Transducers ◽  
Voltage Response ◽  
Self Powered

Abstract Piezoelectric-based vibration reduction has the potential to improve the lifetime and structural integrity of turbomachinery blades by reducing the risk of high-cycle fatigue. Semi-active techniques produce small, self-powered implementations that can meet the strict design requirements for rotating machinery. Most semi-active techniques switch piezoelectric transducers between an open circuit and a shunt circuit in a way that reduces vibration. However, these switches produce a small impulse on the structure due to the electromechanical coupling of the piezoelectric material. Since multiple-mode vibration reduction typically requires distributed sections of piezoelectric material, the switching impulse generated by one transducer may affect others. This study investigates the effect of the switching impulse on the non-switched piezoelectric transducers. Experimental testing shows the switching impulse induces a voltage response at the natural frequencies of the structure, with the strongest responses occurring at modes where both the switched and non-switched piezoelectric transducers have high electromechanical coupling. Furthermore, piezoelectric sections that lack coupling at the excitation frequency of the structure exhibit a more noticeable response to the switching impulse. This response enables remote sensing of switches, which may facilitate wireless coordinated switch timing.

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