State Space Implementation of the Algorithm of Mode Isolation

2003 ◽  
Vol 125 (2) ◽  
pp. 205-213 ◽  
Author(s):  
Michael V. Drexel ◽  
Jerry H. Ginsberg ◽  
Bassem R. Zaki
Keyword(s):  
Frequency Response ◽  
Normal Mode ◽  
Natural Frequencies ◽  
Damping Ratio ◽  
Analytical Framework ◽  
Complex Frequency ◽  
Response Data ◽  
Modal Damping Ratio ◽  
Mode Isolation ◽  
The Time Domain

The Algorithm of Mode Isolation (AMI) extracts modal properties from complex frequency response data. Previous work used classic undamped modes as the analytical framework for the algorithm. The present work extends the algorithm to implement damped modal analysis, in which the eigenvalues and eigenvectors are complex. In order to assess how well this reformulation performs when natural frequencies are close and drive point mobilities are low, a prototypical system consisting of a cantilever beam with attached subsystems is introduced. One of these subsystems is selected to be a tuned vibration absorber for the isolated beam, so the system features a combination of modes whose natural frequencies are close and modes whose drive point mobility is low. The time domain response of this system is evaluated, contaminated with substantial white noise, and then FFT processed in order to obtain synthetic complex frequency response data. The performance of AMI is evaluated by comparing extracted values for natural frequency, modal damping ratio, and complex normal mode vectors to the analytical values. The results reveal that the pair of modes having proximite natural frequencies are accurately identified. Natural frequencies and damping ratios for those modes whose drive mobility is low are identified by processing the ensemble of frequency response functions, but identification of normal mode coefficients for such modes remains problematic.

Recent Improvements of the Algorithm of Mode Isolation

2003 ◽  
Author(s):  
Jerry H. Ginsberg ◽  
Matthew S. Allen
Keyword(s):  
Frequency Response ◽  
Least Squares ◽  
Natural Frequencies ◽  
Least Squares Method ◽  
A Priori ◽  
Single Mode ◽  
Computational Effort ◽  
Complex Frequency ◽  
Linear Least Squares ◽  
Mode Isolation

The Algorithm of Mode Isolation (AMI) identifies the natural frequencies, modal damping ratios, and mode vectors of a system by proceesing complex frequency response data. It uses an iterative procedure based on the fact that a general frequency response function is a superposition of modal contributions. The iterations focus successively on a singel mode. The mode that is in focus is isolated by subtracting the other modal contributions using prior estimates of their modal properties. This process leads to a self-contained identification of the number of modes that participate in any frequency band, whereas other techniques require a priori guesses. This paper describes modifications intended to improve AMI’s accuracy and reduce its computational effort. These involve the use of a new linear least squares method for identifying the natural frequency and dmaping ratio of a single mode, a linear least squares global fit of the data in order to identify mode vectors. Results are presented for a model of a cantilever beam with suspended spring-mass-dashpot system. This system was used by Drexel, Ginsberg, and Zaki [Journal of Vibration and Acoustics, 2003 (forthcoming)] to assess the prior version’s ability to identify weakly excited modes and modes having close natural frequencies in the presence of high noise levels. Application of the modeified version of AMI to the same system is shown to lead to significantly more accurate damping ratios are mode vectors, with equally good natural frequencies.

Experimental Study for Extraction of Normal Modes

1995 ◽  
Author(s):  
S. Y. Chen ◽  
M. S. Ju ◽  
Y. G. Tsuei
Keyword(s):  
Frequency Response ◽  
Normal Mode ◽  
Normal Modes ◽  
Measurement Data ◽  
Mode Shapes ◽  
Complex Frequency ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Incomplete System ◽  
Coupled Structures

Abstract A frequency-domain technique to extract the normal mode from the measurement data for highly coupled structures is developed. The relation between the complex frequency response functions and the normal frequency response functions is derived. An algorithm is developed to calculate the normal modes from the complex frequency response functions. In this algorithm, only the magnitude and phase data at the undamped natural frequencies are utilized to extract the normal mode shapes. In addition, the developed technique is independent of the damping types. It is only dependent on the model of analysis. Two experimental examples are employed to illustrate the applicability of the technique. The effects due to different measurement locations are addressed. The results indicate that this technique can successfully extract the normal modes from the noisy frequency response functions of a highly coupled incomplete system.

scholarly journals Vibrational Analysis of Composite Beam Embedded with Nitinol Shape Memory Alloy Wires

2018 ◽  
Vol 7 (3.4) ◽  
pp. 143
Author(s):  
Omer Muwafaq Mohmmed Ali ◽  
Rawaa Hamid Mohammed Al-Kalali ◽  
Ethar Mohamed Mahdi Mubarak
Keyword(s):  
Shape Memory Alloy ◽  
Shape Memory ◽  
Frequency Response ◽  
Response Curve ◽  
Natural Frequencies ◽  
Damping Ratio ◽  
Vibrational Analysis ◽  
Laminated Composite ◽  
Vibration Modes ◽  
Frequency Response Curve

In this paper, laminated composite materials were hybridized with fibers (E-glass) and shape memory alloy wires which considered a smart material. The effect of changing frequency on the (acceleration- frequency) response curve, the damping ratio of the vibration modes, the natural frequencies of the vibration mode, the effect of shape memory alloy wires number on the damping characteristics were studied. Hand lay-up technique was used to prepare the specimens, epoxy resin type was used as a matrix reinforced by fiber, E-glass. The specimens were manufactured by stacking 2 layers of fibers. Shape memory alloy, type Nitinol (nickel-titanium) having a diameter (1 and 2mm), was used to manufacture the specimens by embedding (1,2 and 3) wires into epoxy. Experimentally, the acceleration- frequency response curve was plotted for the vibration modes, this curve was used to measure the natural frequencies of the vibration modes and calculate the damping ratio of the vibration modes. ANSYS 15- APDL was used to determine the mode shape and find the natural frequencies of the vibration modes then compared with the experimental results. The results illustrated that, for all specimens increasing the natural frequency leads to decreasing the damping ratio. Increasing the number of shape memory alloy wires leads to increase the values of the damping ratio of the vibration modes and the natural frequencies of the vibration modes at room temperature. 

An Approximate Normal Mode Method for Damped Lumped Parameter Systems

1967 ◽  
Vol 89 (4) ◽  
pp. 597-604 ◽  
Author(s):  
A. Seireg ◽  
L. Howard
Keyword(s):  
White Noise ◽  
Normal Mode ◽  
Damping Ratio ◽  
Conservative System ◽  
Random Excitation ◽  
Mass System ◽  
Response Data ◽  
Lumped Parameter ◽  
Mode Method ◽  
Normal Mode Method

An approximate normal mode method is introduced which permits any linear non-conservative system to be solved by super position of uncoupled coordinates. Accuracy of the method was found to be good when checked by digital computer for dynamic damper systems subjected to sinusoidal and white noise random excitation. A technique is presented which permits a mathematical model for a damped multimass system to be constructed entirely from experimentally obtained sinusoidal frequency response data. An expression is derived for optimum damping ratio and natural frequency ratio that will minimize the response of a two-mass system to white noise random excitation.

scholarly journals Vibration Analysis of Cylindrical Sandwich Aluminum Shell with Viscoelastic Damping Treatment

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Tai-Hong Cheng ◽  
Zhen-Zhe Li ◽  
Yun-De Shen
Keyword(s):  
Frequency Response ◽  
Frequency Response Function ◽  
Natural Frequencies ◽  
Damping Ratio ◽  
Viscoelastic Damping ◽  
Viscoelastic Layer ◽  
Response Functions ◽  
Out Of Plane ◽  
Displacement Theory ◽  
Damping Treatments

This paper has applied the constrained viscoelastic layer damping treatments to a cylindrical aluminum shell using layerwise displacement theory. The transverse shear, the normal strains, and the curved geometry are exactly taken into account in the present layerwise shell model, which can depict the zig-zag in-plane and out-of-plane displacements. The damped natural frequencies, modal loss factors, and frequency response functions of cylindrical viscoelastic aluminum shells are compared with those of the base thick aluminum panel without a viscoelastic layer. The thickness and damping ratio of the viscoelastic damping layer, the curvature of proposed cylindrical aluminum structure, and placement of damping layer of the aluminum panel were investigated using frequency response function. The presented results show that the sandwiched viscoelastic damping layer can effectively suppress vibration of cylindrical aluminum structure.

On the Use of Modal Parameters as Metrics for Condition-Based Monitoring of Rotating Machinery

2005 ◽  
Author(s):  
Jerry H. Ginsberg ◽  
Benjamin B. Wagner
Keyword(s):  
Frequency Response ◽  
Modal Analysis ◽  
Great Accuracy ◽  
Response Data ◽  
Modal Properties ◽  
Modern Technique ◽  
Mode Isolation ◽  
Modal Description ◽  
Frequency Domain Response ◽  
Condition Based Monitoring

Deterioration of a rotordynamic system changes its modal properties. This paper initiates a study of the degree to which such changes can be detected by monitoring modal metrics obtained by a modern technique for experimental modal analysis (EMA). The eigenvalues and residues associated with a complex modal description of the frequency response are identified by processing response data derived from an analytical model. This model, which features an elastic shaft with attached rigid rotor and supported by hydrodynamic bearings, was previously used by Wagner and Ginsberg [Proc. of the 23rd International Modal Analysis Conf. (IMAC), forthcoming, 2005] to explore the merits of using standard or directional frequency response functions to perform EMA. The techniques used there, specfically the original version of the Algorithm of Mode Isolation (AMI) for FRFs and Two-Sided AMI for dFRFs, are used to extract the modal properties from the model’s frequency domain response. The modal eigenvalues and residues are identified for a range of bearing clearances within the limit of acceptable wear. One set of metrics that are considered describes the behavior of the system’s eigenvalues as clearance increases. Another set of metrics describes the modal residue factors, which depend on the drive and response locations. A defect is considered to be detectable if the change in the value of a metric due to deterioration exceeds the uncertainty in that metric’s value associated with the inexact nature of EMA. Although the eigenvalues are identified with great accuracy, they are found to be relatively insensitive to bearing clearance, so that metrics derived from them do not meet the detectability criterion. In contrast, the residue values are identified less accurately, but they are highly sensitivity to the clearance. It is concluded that metrics describing the behavior of the modal residue factors can unambiguously indicate bearing wear that is large, but still acceptable for continued operation. It also is found that it is preferable to monitor the residues obtained by processing standard FRFs using the original AMI version, rather than using Two-Sided AMI to process dFRFs.

scholarly journals Detection and localization of multiple small damages in beam

2021 ◽  
Vol 13 (1) ◽  
pp. 168781402098732
Author(s):  
Ayisha Nayyar ◽  
Ummul Baneen ◽  
Syed Abbas Zilqurnain Naqvi ◽  
Muhammad Ahsan
Keyword(s):  
Frequency Response ◽  
Natural Frequencies ◽  
Signal To Noise Ratio ◽  
Moving Average ◽  
A Priori ◽  
Damage Index ◽  
High Signal ◽  
Frequency Range ◽  
Spatial Locality ◽  
System Frequency

Localizing small damages often requires sensors be mounted in the proximity of damage to obtain high Signal-to-Noise Ratio in system frequency response to input excitation. The proximity requirement limits the applicability of existing schemes for low-severity damage detection as an estimate of damage location may not be known  a priori. In this work it is shown that spatial locality is not a fundamental impediment; multiple small damages can still be detected with high accuracy provided that the frequency range beyond the first five natural frequencies is utilized in the Frequency response functions (FRF) curvature method. The proposed method presented in this paper applies sensitivity analysis to systematically unearth frequency ranges capable of elevating damage index peak at correct damage locations. It is a baseline-free method that employs a smoothing polynomial to emulate reference curvatures for the undamaged structure. Numerical simulation of steel-beam shows that small multiple damages of severity as low as 5% can be reliably detected by including frequency range covering 5–10th natural frequencies. The efficacy of the scheme is also experimentally validated for the same beam. It is also found that a simple noise filtration scheme such as a Gaussian moving average filter can adequately remove false peaks from the damage index profile.

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