Comments on “On the Physical Interpretation of Proper Orthogonal Modes in Vibrations”

Ravindra, B.

doi:10.1006/jsvi.1998.1895

Cited by 26 publications

(13 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…However, the reduced system loses most of the dynamical characteristics of the original one based on the traditional POD method [16,17]. We apply the modified POD method to reduce the original system, and then we calculate the eigenvalues of the covariance matrix and confirm the first few POMs associated with the first few largest POVs to occupy the energy percentage of all nonnegative POVs, i.e., the physical interpretation of POM energy in the vibration is applied [21][22][23][24][25][26]. The mathematical construction process of the modified POD method is introduced particularly in ref.…”

Section: Mode Energy Analysis Based On Modified Pod Methodsmentioning

confidence: 99%

Stability analysis of reduced rotor pedestal looseness fault model

Jin

Chen

et al. 2015

Nonlinear Dyn

View full text Add to dashboard Cite

In this paper, the nonlinear dynamic characteristics of a rotor system supported by ball bearings with pedestal looseness are analyzed. The model of seven-degrees of freedom (DOFs) rotor system is established by the Newton's second law, which comprises a pair of ball bearings with pedestal looseness at one end. Energy analysis of the original model states that the first two-order proper orthogonal modes occupy almost all the energy of the system, and it demonstrates that the reduced model reserves main dynamical topological characteristics of the original one. A modified proper orthogonal decomposition method is applied in order to reduce the DOFs from seven to two, and the reduced system preserves the bifurcation and amplitude-frequency characteristics of the original one. The harmonic balance method with the alternating frequency-time domain technique is used to calculate the periodic response of the reduced system. Moreover, stability of the two-DOFs model is analyzed based on the known harmonic solution by the Floquet theory.

show abstract

Section: Mode Energy Analysis Based On Modified Pod Methodsmentioning

confidence: 99%

Stability analysis of reduced rotor pedestal looseness fault model

Jin

Chen

et al. 2015

Nonlinear Dyn

View full text Add to dashboard Cite

show abstract

“…It is also worth pointing out that POD is closely related to principal component analysis (PCA) introduced by Hotelling [12]. For a detailed historical review of POD or PCA, the reader is referred to references [10,13].…”

Section: Proper Orthogonal Decompositionmentioning

confidence: 99%

Physical Interpretation of the Proper Orthogonal Modes Using the Singular Value Decomposition

Kerschen

Golinval

2002

Journal of Sound and Vibration

250

116

View full text Add to dashboard Cite

“…The problem is that autocorrelation is a linear operation, and we are generally dealing with nonlinear data. And while this method is often successful, there are some examples in which it generates unsatisfactory results [6,7].…”

Section: Choosing the Delay Timementioning

confidence: 99%

Fractional Derivatives Applied to Phase-Space Reconstructions

Feeny

Lin

2004

Nonlinear Dyn

View full text Add to dashboard Cite

The concept and application of phase-space reconstructions are reviewed. Fractional derivatives are then proposed for the purpose of reconstructing dynamics from a single observed time history. A procedure is presented in which the fractional derivatives of time series data are obtained in the frequency domain. The method is applied to the Lorenz system. The ability of the method to unfold the data is assessed by the method of global false nearest neighbors. The reconstructed data is used to compute recurrences and correlation dimensions. The reconstruction is compared to the commonly used method of delays in order to assess the choice of reconstruction parameters, and also the quality of results.

show abstract

Comments on “On the Physical Interpretation of Proper Orthogonal Modes in Vibrations”

Cited by 26 publications

References 0 publications

Stability analysis of reduced rotor pedestal looseness fault model

Stability analysis of reduced rotor pedestal looseness fault model

Physical Interpretation of the Proper Orthogonal Modes Using the Singular Value Decomposition

Fractional Derivatives Applied to Phase-Space Reconstructions

Contact Info

Product

Resources

About