scholarly journals Vibration Parameters Estimation by Blade Tip-Timing in Mistuned Bladed Disks in Presence of Close Resonances

2020 ◽  
Vol 10 (17) ◽  
pp. 5930
Author(s):  
Saeed Bornassi ◽  
Christian Maria Firrone ◽  
Teresa Maria Berruti
Keyword(s):  
Frequency Response ◽  
Optimization Technique ◽  
Numerical Test ◽  
Parameters Estimation ◽  
Least Square ◽  
Response Curves ◽  
Bladed Disks ◽  
Bladed Disk ◽  
Resonance Frequencies ◽  
Blade Tip

The present paper is focused on the post processing of the data coming from the Blade Tip-Timing (BTT) sensors in the case where two very close peaks are present in the frequency response of the vibrating system. This type of dynamic response with two very close peaks can occur quite often in bladed disks. It is related to the fact that the bladed disk is not perfectly cyclic symmetric and the so called “mistuning” is present. A method based on the fitting of the BTT sensors data by means of a 2 degrees of freedom (2DOF) dynamic model is proposed. Nonlinear least square optimization technique is employed for identification of the vibration characteristics. A numerical test case based on a lump parameter model of a bladed disk assembly is used to simulate different response curves and the corresponding sensors signals. The Frequency Response Function (FRF) constructed at the resonance region is compared with the traditional Sine fitting results, the resonance frequencies and damping values estimated by the fitting procedure are also reported. Accurate predictions are achieved and the results demonstrate the considerable capacity of the 2DOF method to be used as a standalone or as a complement to the standard Sine fitting method.

scholarly journals Test-Model Correlation of Dry-Friction Damping Phenomena in Aero-Engines

2008 ◽  
Author(s):  
P. Jean ◽  
C. Gibert ◽  
C. Dupont ◽  
J.-P. Lombard
Keyword(s):  
Dry Friction ◽  
Forced Response ◽  
Test Model ◽  
Friction Damping ◽  
Bladed Disks ◽  
Friction Dampers ◽  
Bladed Disk ◽  
Resonance Frequencies ◽  
Non Linear ◽  
Aero Engines

In order to control the risk of high cycle fatigue of bladed disks, it is important to predict precisely the vibration levels and to design damping solutions to attenuate them. Therefore, Snecma has made some efforts in the last years in order to characterize better the damping in aero-engines. Among the various damping sources, friction damping is particularly difficult to model due to its non-linear behaviour [1]. For that purpose, two methods based on multi-harmonic balance strategy have been especially developed for Snecma, dedicated to the study of the non-linear forced response of bladed disks. The first one enables to model the bladed disk equipped with dry-friction dampers [2], and the second one takes into account intrinsic friction located in disk-blade interface [3]. To validate both models experimentally, a test campaign has been carried out in a vacuum chamber on a rotating bladed disk excited by piezoelectric actuators. The blade shanks have been softened in order to increase friction effects. Experimental results show a regular and reproducible behaviour of the non-linear forced response, over various rotation speed and excitation levels. The contributions of friction dampers and friction in blade attachment have been decoupled thanks to glue applied in the blade root. Both friction phenomena that were observed experimentally at resonance of the blade first bending mode have been reproduced numerically. After updating modeling parameters, an acceptable correlation was found on resonance frequencies, amplitudes and damping levels over the full experimental setup range, which validates these numerical tools for their use in design process.

Experimental Investigation of 2:1 and 3:1 Internal Resonances in Nonlinear MEMS Arch Resonators

2016 ◽  
Author(s):  
Abdallah Ramini ◽  
Amal Hajjaj ◽  
Mohammad I. Younis
Keyword(s):  
Experimental Investigation ◽  
Frequency Response ◽  
Electrical Current ◽  
Vibrational Modes ◽  
Response Curves ◽  
Internal Resonances ◽  
Mems Resonators ◽  
Resonance Frequencies ◽  
Doped Silicon

We demonstrate experimentally internal resonances in MEMS resonators. The investigation is conducted on in-plane MEMS arch resonators fabricated with a highly doped silicon. The resonators are actuated electrostatically and their stiffness are tuned by electrothermal loading by passing an electrical current though the microstructures. We show that through this tuning, the ratio of the various resonance frequencies can be varied and set at certain ratios. Particularly, we adjust the resonance frequencies of two different vibrational modes to 2:1 and 3:1. Finally, we validate the internal resonances at these ratios through frequency-response curves and FFTs.

Frequency Response Curves and Dynamic Characteristics of a Ginkgo Tree in Different Growth Periods

2020 ◽  
Vol 63 (6) ◽  
pp. 1673-1684
Author(s):  
Jie Zhou ◽  
Linyun Xu ◽  
Guanhua Liu ◽  
Yan Xuan ◽  
Hongping Zhou ◽  
...  
Keyword(s):  
Frequency Response ◽  
Frequency Domain ◽  
Dynamic Characteristics ◽  
Natural Frequencies ◽  
Excitation Frequency ◽  
Fruit Trees ◽  
Modal Parameters ◽  
Response Curves ◽  
Resonance Frequencies ◽  
Modal Parameters Identification

HighlightsThe frequency domain modal parameters identification method was applied to a ginkgo tree.Dynamic characteristics of the ginkgo tree were tested during five phenological periods.Almost all resonance frequencies were near the peaks of the frequency response curves.Leaves caused the number of natural frequencies of the ginkgo tree to be greatly reduced.Abstract. Understanding the dynamic characteristics of fruit trees is the premise of effective mechanized harvesting. This study performed a tracking test on a ginkgo tree in five phenological periods from the dormant period to the leaf-unfolding period. The frequency domain modal parameters identification method was applied to the ginkgo tree, and the relationship between the natural frequencies and resonance frequencies of the ginkgo tree was obtained. The main factors affecting the fundamental frequency and damping ratio of the ginkgo tree were not the elastic modulus and moisture content but rather the growth of the leaves. The growth of leaves caused the number of natural frequencies in the low-frequency band to be greatly reduced, and the value of the natural frequencies exhibited a slightly decreasing tendency. The damping caused by leaves had a significant weakening effect on the transmission of vibrational energy on the lateral branches. The resonance frequencies that caused strong response of the ginkgo tree were mostly near the peak frequencies of the frequency response curves (natural frequencies), but eccentric motor excitation could not effectively stimulate all the natural frequencies of the ginkgo tree to reach resonance. In the frequency response curves of the ginkgo tree, the main natural frequency with the maximum energy might not cause the maximum vibration response of the ginkgo tree, even if this excitation frequency could induce resonance. Resonance could be used to maximize the transfer of excitation energy, but each position of the tree had its own independent frequency spectrum characteristics. A single excitation frequency could not cause all positions of the ginkgo tree to resonate simultaneously. Changing the excitation frequency of harvesting equipment within a small frequency range could achieve the maximum resonance response of most positions on fruit trees. Keywords: Dynamic characteristics, Growth periods, Leaves, Natural frequencies, Resonance.

scholarly journals Design of Multilayer Frequency-Selective Surfaces by Equivalent Circuit Method and Basic Building Blocks

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Yuan Xu ◽  
Mang He
Keyword(s):  
Frequency Response ◽  
Equivalent Circuit ◽  
Building Blocks ◽  
Least Square ◽  
Design Parameters ◽  
Frequency Selective Surfaces ◽  
Response Curves ◽  
Band Pass ◽  
Equivalent Circuit Method ◽  
Frequency Selective

An equivalent circuit method (ECM) is proposed for the design of multilayer frequency-selective surfaces (FSSs). In contrast to the existing ECMs that were developed mainly for the analysis of the properties of a given FSS, the presented ECM aims at providing the initial design parameters of an FSS from the desired frequency response. In this method, four types of basic FSS structures are used as the building blocks to construct the multilayer FSSs, and their surface impedances in both the normal- and the oblique-incidence situations are studied in detail in order to achieve more accurate equivalent circuit (EC) representation of the entire FSS. For a general FSS design with expected frequency response, the EC parameters and the geometrical sizes of the required basic building blocks can be synthesized from a few typical S-parameter (S11/S12) samplings of the response curves via a simple least-square curve-fitting process. The effectiveness and accuracy of the method are shown by the designs of a band-pass FSS with steep falling edge and a miniaturized band-pass FSS with out-of-band absorption. The prototype of one design is fabricated, and the measured frequency response agrees well with the numerical results of the ECM and the full-wave simulations.

Effect of Static/Dynamic Coupling on the Forced Response of Turbine Bladed Disks With Underplatform Dampers

2009 ◽  
Author(s):  
Christian M. Firrone ◽  
Stefano Zucca ◽  
Muzio Gola
Keyword(s):  
Static Analysis ◽  
Normal Load ◽  
Tangential Force ◽  
Numerical Test ◽  
Forced Response ◽  
Dissipated Energy ◽  
Bladed Disks ◽  
Common Procedure ◽  
Bladed Disk ◽  
Static Contact

Friction contacts are often used in turbomachinery design as passive damping systems. In particular underplatform dampers are mechanical devices used to decrease the vibration amplitudes of bladed disks. Numerical codes are used to optimize during design the underplatform damper parameters in order to limit the resonant stress level of the blades. In such codes the contact model plays the most relevant role in the calculation of the dissipated energy at friction interfaces. One of the most important contact parameters is the static normal load acting at the contact, since its value strongly affects the area of the hysteresis loop of the tangential force and therefore the amount of dissipation. A common procedure to estimate the static normal loads acting on underplatform dampers consists in decoupling the static and the dynamic balance of the damper. A preliminary static analysis of the contact is performed in order to get the static contact/gap status to use in the calculation, assuming that it does not change when vibration occurs. In this paper a novel approach is proposed. The static and the dynamic displacements of the system (bladed disk + underplatform dampers) are coupled together during the forced response calculation. Static loads acting at the contacts follow from static displacements and no preliminary static analysis of the system is necessary. The proposed method is applied to a numerical test case representing a simplified bladed disk with underplatform dampers. Results are compared with those obtained with the classical approach.

Effects of nonlinear interactions of flexural modes on the performance of a beam autoparametric vibration absorber

2019 ◽  
Vol 26 (7-8) ◽  
pp. 459-474
Author(s):  
Saeed Mahmoudkhani ◽  
Hodjat Soleymani Meymand
Keyword(s):  
Frequency Response ◽  
Internal Resonance ◽  
Continuation Method ◽  
Harmonic Balance Method ◽  
Vibration Absorber ◽  
Primary System ◽  
Lumped Mass ◽  
Response Curves ◽  
Internal Resonances ◽  
The One

The performance of the cantilever beam autoparametric vibration absorber with a lumped mass attached at an arbitrary point on the beam span is investigated. The absorber would have a distinct feature that in addition to the two-to-one internal resonance, the one-to-three and one-to-five internal resonances would also occur between flexural modes of the beam by tuning the mass and position of the lumped mass. Special attention is paid on studying the effect of these resonances on increasing the effectiveness and extending the range of excitation amplitudes at which the autoparametric vibration absorber remains effective. The problem is formulated based on the third-order nonlinear Euler–Bernoulli beam theory, where the assumed-mode method is used for deriving the discretized equations of motion. The numerical continuation method is then applied to obtain the frequency response curves and detect the bifurcation points. The harmonic balance method is also employed for detecting the type of internal resonances between flexural modes by inspecting the frequency response curves corresponding to different harmonics of the response. Parametric studies on the performance of the absorber are conducted by varying the position and mass of the lumped mass, while the frequency ratio of the primary system to the first mode of the beam is kept equal to two. Results indicated that the one-to-five internal resonance is especially responsible for the considerable enhancement of the performance.

Study of plate vibrating in fluids having part-through crack at random angles and locations

2021 ◽  
pp. 095440622110127
Author(s):  
Ruqia Ikram ◽  
Asif Israr
Keyword(s):  
Frequency Response ◽  
Multiple Scales ◽  
Peak Amplitude ◽  
Nonlinear Frequency ◽  
Response Curves ◽  
Crack Location ◽  
Cracked Plate ◽  
Nonlinear Frequency Response ◽  
Angle Crack ◽  
Crack Angle

This study presents the vibration characteristics of plate with part-through crack at random angles and locations in fluid. An experimental setup was designed and a series of tests were performed for plates submerged in fluid having cracks at selected angles and locations. However, it was not possible to study these characteristics for all possible crack angles and crack locations throughout the plate dimensions at any fluid level. Therefore, an analytical study is also carried out for plate having horizontal cracks submerged in fluid by adding the influence of crack angle and crack location. The effect of crack angle is incorporated into plate equation by adding bending and twisting moments, and in-plane forces that are applied due to antisymmetric loading, while the influence of crack location is also added in terms of compliance coefficients. Galerkin’s method is applied to get time dependent modal coordinate system. The method of multiple scales is used to find the frequency response and peak amplitude of submerged cracked plate. The analytical model is validated from literature for the horizontally cracked plate submerged in fluid as according to the best of the authors’ knowledge, literature lacks in results for plate with crack at random angle and location in the presence of fluid following validation with experimental results. The combined effect of crack angle, crack location and fluid on the natural frequencies and peak amplitude are investigated in detail. Phenomenon of bending hardening or softening is also observed for different boundary conditions using nonlinear frequency response curves.

Magnification curves of electromagnetic seismographs

1964 ◽  
Vol 54 (5A) ◽  
pp. 1459-1471
Author(s):  
S. K. Chakrabarty ◽  
G. C. Choudhury ◽  
S. N. Roy Choudhury
Keyword(s):  
General Solution ◽  
Frequency Response ◽  
Experimental Method ◽  
Phase Shifts ◽  
Response Curves ◽  
Operating Condition ◽  
Coil Inductance ◽  
The World ◽  
Electromagnetic Seismograph ◽  
Proper Design

Abstract The general solution of the equations connecting the motion of the two coupled components in an electromagnetic seismograph has been obtained in another paper and it shows that the magnification of a seismograph depend on seven instrumental constants. Using these results, equations and curves have been derived in the present paper from which the Magnification as well as Phase shifts in the response of a seismograph and their variations with damping and coil inductance can be easily obtained. Based on these curves a number of magnification curves for different combinations, which are in operation at the different seismological stations of the world, have been derived. Suitable equations and curves have also been obtained which can be used for estimating the absolute Magnification of a Seismograph. An experimental method of obtaining the frequency response curves of seismographs in their operating condition has been described and the results obtained by this method has been given. It has been indicated how the results incorporated in the present paper can be used in the proper design of seismographs required for the different purposes.

Vibration Suppression of Mistuned Coupled-Blade-Disk Systems Using Piezoelectric Circuitry Network

2009 ◽  
Vol 131 (2) ◽  
Author(s):  
Hongbiao Yu ◽  
K. W. Wang
Keyword(s):  
Piezoelectric Transducer ◽  
Vibration Suppression ◽  
Structural Vibration ◽  
Bladed Disks ◽  
Disk Model ◽  
Bladed Disk ◽  
Engine Order ◽  
Optimal Network ◽  
Random Mistuning ◽  
Engine Components

For bladed-disk assemblies in turbomachinery, the elements are often exposed to aerodynamic loadings, the so-called engine order excitations. It has been reported that such excitations could cause significant structural vibration. The vibration level could become even more excessive when the bladed disk is mistuned, and may cause fatigue damage to the engine components. To effectively suppress vibration in bladed disks, a piezoelectric transducer networking concept has been explored previously by the authors. While promising, the idea was developed based on a simplified bladed-disk model without considering the disk dynamics. To advance the state of the art, this research further extends the investigation with focus on new circuitry designs for a more sophisticated and realistic system model with the consideration of coupled-blade-disk dynamics. A novel multicircuit piezoelectric transducer network is synthesized and analyzed for multiple-harmonic vibration suppression of bladed disks. An optimal network is derived analytically. The performance of the network for bladed disks with random mistuning is examined through Monte Carlo simulation. The effects of variations (mistuning and detuning) in circuit parameters are also studied. A method to improve the system performance and robustness utilizing negative capacitance is discussed. Finally, experiments are carried out to demonstrate the vibration suppression capability of the proposed piezoelectric circuitry network.

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