A Unified Matrix Polynomial Approach to Modal Identification

Allemang, Randall J.; Brown, David L.

doi:10.1006/jsvi.1997.1321

Cited by 183 publications

(141 citation statements)

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“…Allemang and Brown [10] showed how most of these can be viewed in a common framework, and texts by Maia et al [11] and Ewins [12] also review a number of methods. There are a few questions that one should consider for the present application.…”

Section: Suitable Linear Response Identification Methodsmentioning

confidence: 99%

Estimating the degree of nonlinearity in transient responses with zeroed early-time fast Fourier transforms

Allen

Mayes

2010

Mechanical Systems and Signal Processing

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Abstract:This work presents a class of time-frequency methods for detecting and characterizing nonlinearity in transient response measurements. The methods are intended for systems whose response becomes increasingly linear as the response amplitude decays. The discrete Fourier Transform of the response data is found with various sections of the initial response set to zero. These frequency responses, dubbed Zeroed Early-time Fast Fourier Transforms (ZEFFTs), acquire the usual shape of linear Frequency Response Functions (FRFs) as more of the initial nonlinear response is nullified. Hence, nonlinearity is evidenced by a qualitative change in the shape of the ZEFFT as the length of the initial nullified section is varied. These spectra are shown to be sensitive to nonlinearity, revealing its presence even if it is active in only the first few cycles of a response, as may be the case with macro-slip in mechanical joints. They also give insight into the character of the nonlinearity, potentially revealing nonlinear energy transfer between modes or the modal amplitudes below which a system behaves linearly. In some cases one can identify a linear model from the late time, linear response, and use it to reconstruct the response that the system would have executed at previous times if it had been linear. This gives an indication of the severity of the nonlinearity and its effect on the measured response. The methods are demonstrated on both analytical and experimental data from systems with slip or impact nonlinearities.

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Section: Suitable Linear Response Identification Methodsmentioning

confidence: 99%

Estimating the degree of nonlinearity in transient responses with zeroed early-time fast Fourier transforms

Allen

Mayes

2010

Mechanical Systems and Signal Processing

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“…Force and exponential windows used on the input and output signals, respectively, reduce noise and improve coherence. Also used in this analysis was the Complex Mode Indication Function (CMIF) [15], an algorithm based on singular value decomposition methods, which, when applied to multiple reference FRF measurements yields the corresponding mode shapes and modal participation vector. For modal parameter (frequency and damping) estimation, X-Modal TM software [16], developed by the Structural Dynamics Research…”

Section: Methodsmentioning

confidence: 99%

“…The data was first observed using a CMIF plot so that the well excited modal frequencies could be identified. An estimate of the modes was found using the poly-reference time domain algorithm (chosen because of its short computation time) with a modal order of 2 to 5 [15]. The films used for the experiments were not straight cantilevers for large lengths, but curved beams.…”

Section: Methodsmentioning

confidence: 99%

Experimental Determination of Bending Resonances of Millimeter Size PVF2 Cantilevers

Mukherjee

Shukla

Roseman

et al. 2003

Sensors

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Abstract:The polymer piezoelectric polvinylidene fluoride has found widespread use in sensors and actuators. The bending mode of piezoelectricity offers very high sensitivities and low mechanical input impedance, but has not been studied in as much detail for sensor applications. We report the dynamic electromechanical properties of millimeter size cantilevers made from electroded films of PVF 2 . All devices tested had a single polymer layer. Several resonances are found below 1 kHz and the experimentally observed resonance frequency dependence on cantilever thickness and length are seen to agree well with published models which take the properties of the electrodes into account. It is found that bending resonances are also modulated by the width of the cantilever. Therefore, though the length and thickness control the resonance frequency most strongly, the actual realized value can be fine-tuned by changing cantilever width and the electrode material and its thickness. Further, all resonances display high piezoelectric coupling coefficients (k eff ), ranging between 0.2 -0.35. The data presented here will be extremely useful in the design of sensors and actuators for a number of applications, since the combination of millimeter size scales and high piezoelectric sensitivities in the low audio range can be realized with this marriage of polymeric materials and cantilever geometries. Such an array of sensors can be used in cochlear implant applications, and when integrated with a resonance interrogation Sensors 2003, 3 264 circuit can be used for the detection of low frequency vibrations of large structures. If appropriate mass/elasticity sensitive layers are coated on the electrodes, such a sensor can be used for the detection of a wide range of chemicals and biochemicals.

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“…The traditional methods to improve the accuracy of parameters identification in noisy situations are based on over-determined system, and the distinguishing procedure (such as stability diagrams) could be used to get the true system modes [4][5][6]. However, it is still difficult to sort out noise modes, as the distinguishing procedure relies on the user's experience and judgment.…”

Section: Introductionmentioning

confidence: 99%

Application of Structured Low Rank Approximation in Modal Analysis

Yang¹,

Yang²,

Zhao³

et al. 2017

dtetr

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Abstract. The quality of measured vibration response signals is adversely affected by noise in modal testing. This situation often leads to serious difficulties in estimating the modal parameters with proper accuracy. This paper presents a signal de-noising method for measured impulsive response functions (IRFs) based on structured low rank approximation (SLRA) so as to improve the accuracy of the modal parameters identification. The proposed method is verified by simulation study of a cantilever beam. The results show that this method can eliminate noise from measured IRFs efficiently, and significant improvement in modal parameters estimation could be obtained based on the filtered IRFs.

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A Unified Matrix Polynomial Approach to Modal Identification

Cited by 183 publications

References 0 publications

Estimating the degree of nonlinearity in transient responses with zeroed early-time fast Fourier transforms

Estimating the degree of nonlinearity in transient responses with zeroed early-time fast Fourier transforms

Experimental Determination of Bending Resonances of Millimeter Size PVF2 Cantilevers

Application of Structured Low Rank Approximation in Modal Analysis

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