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.

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.

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 Design and Analysis of a Novel Piezoceramic Stack-based Smart Aggregate

Sensors ◽  
2020 ◽  
Vol 20 (22) ◽  
pp. 6438
Author(s):  
Guangtao Lu ◽  
Xin Zhu ◽  
Tao Wang ◽  
Zhiqiang Hao ◽  
Bohai Tan
Keyword(s):  
Resonance Frequency ◽  
Electromechanical Coupling ◽  
Structural Parameters ◽  
Electromechanical Coupling Factor ◽  
Coupling Factor ◽  
Stress Waves ◽  
Parallel Connection ◽  
Smart Aggregate ◽  
In Series ◽  
Piezoelectric Wafers

A novel piezoceramic stack-based smart aggregate (PiSSA) with piezoceramic wafers in series or parallel connection is developed to increase the efficiency and output performance over the conventional smart aggregate with only one piezoelectric patch. Due to the improvement, PiSSA is suitable for situations where the stress waves easily attenuate. In PiSSA, the piezoelectric wafers are electrically connected in series or parallel, and three types of piezoelectric wafers with different electrode patterns are designed for easy connection. Based on the theory of piezo-elasticity, a simplified one-dimensional model is derived to study the electromechanical, transmitting and sensing performance of PiSSAs with the wafers in series and parallel connection, and the model was verified by experiments. The theoretical results reveal that the first resonance frequency of PiSSAs in series and parallel decreases as the number or thickness of the PZT wafers increases, and the first electromechanical coupling factor increases firstly and then decrease gradually as the number or thickness increases. The results also show that both the first resonance frequency and the first electromechanical coupling factor of PiSSA in series and parallel change no more than 0.87% as the Young’s modulus of the epoxy increases from 0.5 to 1.5 times 3.2 GPa, which is helpful for the fabrication of PiSSAs. In addition, the displacement output of PiSSAs in parallel is about 2.18–22.49 times that in series at 1–50 kHz, while the voltage output of PiSSAs in parallel is much less than that in parallel, which indicates that PiSSA in parallel is much more suitable for working as an actuator to excite stress waves and PiSSA in series is suitable for working as a sensor to detect the waves. All the results demonstrate that the connecting type, number and thickness of the PZT wafers should be carefully selected to increase the efficiency and output of PiSSA actuators and sensors. This study contributes to providing a method to investigate the characteristics and optimize the structural parameters of the proposed PiSSAs.

scholarly journals Simulation Analysis on Cymbal Transducer

2011 ◽  
Vol 2-3 ◽  
pp. 140-143
Author(s):  
Qing Feng Yang ◽  
Peng Wang ◽  
Yu Hong Wang ◽  
Kai Zhang
Keyword(s):  
Finite Element ◽  
Resonance Frequency ◽  
Piezoelectric Ceramic ◽  
Electromechanical Coupling ◽  
Free Field ◽  
Voltage Sensitivity ◽  
Element Analysis ◽  
Cavity Bottom ◽  
Finite Element Software ◽  
Cymbal Transducer

The resonance frequency of the cymbal transducer ranges from 2kHz to 40kHz and its effective electromechanical coupling factor is around 20%. Finite element analysis has been performed to ascertain how the transducer’s makeup affect the transducer’s performance parameters. Two-dimensional axisymmetric model of the cymbal transducer was founded by finite element software-ANSYS, the application of the element type was discussed and the FEM models were built up under the far field condition. Eight groups of cymbal transducers of resonance frequency around 3kHz with different structural dimensions were designed. It was better for choosing the cymbal transducer of the 8mm cavity coping diameter, 20.8mm cavity bottom diameter and 26.8mm piezoelectric ceramic wafer diameter than others for reducing distortion degree of the signal and improving communication turnover in the researched cymbal transducers. It was appropriate for choosing the cymbal transducer of the 8mm cavity coping diameter, 22.4mm cavity bottom diameter and 26.4mm piezoelectric ceramic wafer diameter in order to improve the free-field voltage sensitivity and transmission efficient.

Determination of optimal parameters of the tuned mass damper to reduce the torsional vibration of the shaft by using the principle of minimum kinetic energy

2018 ◽  
Vol 233 (2) ◽  
pp. 327-335 ◽  
Author(s):  
Duy-Chinh Nguyen
Keyword(s):  
Kinetic Energy ◽  
Torsional Vibration ◽  
Damping Ratio ◽  
Vibration Reduction ◽  
Tuned Mass Damper ◽  
Optimal Parameters ◽  
Lagrangian Equations ◽  
Tuning Ratio ◽  
Mass Damper

In this paper, an analytical method is presented to determine the optimal parameters of the symmetric tuned mass damper, such as the ratio between natural frequency of tuned mass damper and shaft (tuning ratio) and the ratio of the viscous coefficient of tuned mass damper (damping ratio). The optimal parameters of tuned mass damper are applied to reduce the torsional vibration of the shaft based on consideration of the vibration duration and stability criterion. The dynamic equations of the shaft are provided via Lagrangian equations, and the optimal parameters of tuned mass damper are derived by using the principle of minimum kinetic energy. Analytical and numerical examples are implemented to verify the reliability of the proposed method. The analytical and numerical results indicate that the optimal parameters of tuned mass damper have significant effects in the torsional vibration reduction of the shaft.

scholarly journals Identification of the Essential Features of the Transient Amplification of Mistuned Systems

2020 ◽  
Author(s):  
Luigi Carassale ◽  
Vincent Denoël ◽  
Carlos Martel ◽  
Lars Panning-von Scheidt
Keyword(s):  
Linear System ◽  
Numerical Simulations ◽  
Mechanical System ◽  
Asymptotic Expansions ◽  
Damping Ratio ◽  
Multiple Scale ◽  
Analytic Solutions ◽  
Sweep Rate ◽  
Scale Method ◽  
Complex Manner

Abstract The dynamic behavior of bladed disks in resonance crossing has been intensively investigated in the community of turbomachinery, addressing the attention to (1) the transienttype response that appear when the resonance is crossed with a finite sweep rate and (2) the localization of the vibration in the disk due to the blade mistuning. In real conditions, the two mentioned effects coexist and can interact in a complex manner. This paper investigates the problem by means of analytic solutions obtained through asymptotic expansions, as well as numerical simulations. The mechanical system is assumed as simple as possible: a 2-dof linear system defined through the three parameters: damping ratio ξ, frequency mistuning Δ, rotor acceleration Ω˙. The analytic solutions are calculated through the multiple-scale method.

Vibration reduction of a flexible robot link using a frictional damper

2020 ◽  
pp. 107754632093609
Author(s):  
Hamed Biglari ◽  
Masoud Golmohammadi ◽  
Sajad Hayati ◽  
Siroos Hemmati
Keyword(s):  
Damping Ratio ◽  
Vibration Reduction ◽  
Flexible Manipulator ◽  
Test Results ◽  
The Finite Element Method ◽  
Flexible Robot ◽  
Nsga Ii ◽  
Modal Test ◽  
Realistic Situation ◽  
Euler Bernoulli Beam

One of the most important factors reducing flexible manipulator efficiency is the residual vibration occurrence. In this research, vibration reduction of flexible manipulators is investigated using an internal frictional damper. At first, the vibration equation of a manipulator is obtained using the finite element method with the Euler–Bernoulli beam element to study its vibrations in a reciprocal motion. In addition, an analytical model is developed to investigate the effect of the frictional damper on robot link vibrations. Using particle swam optimization, ICA, NSGA-II, and GWO methods, the optimal structure for the damper is obtained to maximize its effect. The optimally damped link is fabricated, and its dynamic characteristics are extracted from a modal test experiment. The modal test results show a considerable improvement in the damping ratio of the damped link in comparison with a simple link. The fabricated link samples are then tested in a realistic situation. The experimental results are in coincidence with the simulation results, certifying the performance of the proposed plan in vibration reduction of a robot link.

Test Method of the εrms-N Curves of Laminated Composite Beams

2008 ◽  
Vol 44-46 ◽  
pp. 311-316
Author(s):  
Chuang Shao ◽  
Sen Ge ◽  
Hua Tao ◽  
Claude Bathias
Keyword(s):  
Resonance Frequency ◽  
Fatigue Test ◽  
Laminated Composite ◽  
Test Method ◽  
Cantilever Beams ◽  
Test Results ◽  
Vibration Fatigue ◽  
The Difference ◽  
Double Cantilever Beams ◽  
Laminated Composite Beams

Two kinds of beam specimens made of composite laminated panel were designed and used to do vibration fatigue test for ε-N curves. the shapes of various simulated joint configurations for the specimens were adopted in order to get the accurate results. They were two kinds of double-cantilever beams supplied by T-mode stiffener and L-mode stiffener. All beam specimens were tested under the same shape of narrowband spectrum and the several loadings of random vibration by shaker excitation. The bandwidth of the narrowband random spectrum was 1/3 octave bandwidth whose centre frequency was the first resonance frequency of the cantilever beam, so that it reduced influences of the difference of specimens resonance frequency. Fitting vibration fatigue test results, the ε-N curves would be obtained then. The vibration test shows that this method of getting ε-N vibration curve is feasible. It can be used in practice.

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