BEHAVIOR OF DERIVATIVES OF EIGENVALUES AND EIGENVECTORS IN CURVE VEERING AND MODE LOCALIZATION AND THEIR RELATION TO CLOSE EIGENVALUES

2002 ◽  
Vol 256 (3) ◽  
pp. 551-564 ◽  
Author(s):  
X.L. LIU
Keyword(s):  
Eigenvalues And Eigenvectors ◽  
Mode Localization ◽  
Curve Veering ◽  
Derivatives Of

Derivatives of Eigenvalues and Eigenvectors of Matrix Functions

1993 ◽  
Vol 14 (4) ◽  
pp. 903-926 ◽  
Author(s):  
Alan L. Andrew ◽  
K.-W. Eric Chu ◽  
Peter Lancaster
Keyword(s):  
Matrix Functions ◽  
Eigenvalues And Eigenvectors ◽  
Derivatives Of

scholarly journals Dynamic and Sensitivity Analysis General Non-Conservative Asymmetric Mechanical Systems

2018 ◽  
Vol 68 (2) ◽  
pp. 105-124 ◽  
Author(s):  
Milan Žmindák
Keyword(s):  
Sensitivity Analysis ◽  
Modal Analysis ◽  
Dynamic Systems ◽  
Mechanical Systems ◽  
Conservative System ◽  
Eigenvalues And Eigenvectors ◽  
Linear Dynamic Systems ◽  
Discretization Methods ◽  
Linear Dynamic ◽  
Derivatives Of

AbstractIn this paper the concept of generalized form of proportional damping is proposed. Classical modal analysis of non-conservative continua is extended to multi DOF linear dynamic systems with asymmetric matrices. Mode orthogonality relationships have been generalized to non-conservative systems. Several discretization methods of continua are presented. Finally, an expression for derivatives of eigenvalues and eigenvectors of non-conservative system is presented. Examples are provided to illustrate the proposed methods.

Mode Localization and Delocalization in Constrained Strings and Beams

1997 ◽  
Author(s):  
Chris H. Riedel ◽  
Chin An Tan
Keyword(s):  
Bernoulli Beam ◽  
Constrained System ◽  
Reflection And Transmission ◽  
Mode Localization ◽  
High Frequencies ◽  
Transmission Coefficients ◽  
Curve Veering ◽  
Elastic Constraints ◽  
Euler Bernoulli Beam ◽  
Free Vibration Response

Abstract The free vibration response of a string and a Euler-Bernoulli beam supported by intermediate elastic constraints is studied and analyzed by the transfer function method. The constrained system consists of three subsystems coupled by constraints imposed at the subsystem interfaces. For both the string and beam systems, curve veering and mode localization are observed in the lower modes when the distance between the elastic constraints is varied. As the mode number increases, the modes of the system become extended indicating that the coupling springs have little effect on the system at higher modes. A wave analysis is employed to further investigate the behavior of the systems at high frequencies. Reflection and transmission coefficients are formulated to show the effects of the constraints on the coupling of the subsystems. The weakly bi-coupled beam produces an interesting phenomena where a particular mode experiences no localization while neighboring modes are localized. The frequency at which this occurs is termed the delocalization frequency. Only one delocalization frequency exists and it occurs where the reflection coefficient of the propagating wave becomes zero.

Wave Analysis of Mode Localization and Delocalization in Elastically Constrained Strings and Beams

1999 ◽  
Vol 121 (2) ◽  
pp. 169-173 ◽  
Author(s):  
C. A. Tan ◽  
C. H. Riedel
Keyword(s):  
Wave Analysis ◽  
Bernoulli Beam ◽  
Transmission Resonance ◽  
Mode Localization ◽  
Curve Veering ◽  
Frequency Behavior ◽  
Elastic Constraints ◽  
And Behavior ◽  
Euler Bernoulli Beam ◽  
Free Vibration Response

The free vibration response of both a string and a Euler-Bernoulli beam supported by intermediate elastic constraints is studied and analyzed. For both the string and beam systems, curve veering and mode localization are observed in the lower modes when the distance between the elastic constraints is varied. As the mode number increases, the modes of the system become extended indicating that the coupling springs have little effect on the systems at higher modes. A wave analysis is employed to show the effects of the constraints on the coupling of the subsystems and high frequency behavior. The beam may exhibit a delocalization phenomenon where a particular mode experiences no localization while other neighboring modes may be localized. The frequency (termed the delocalization frequency) at which this occurs corresponds to a transmission resonance. The delocalization frequency is predicted well by the vibration ratio (Langley, 1995). The existence and behavior of the delocalization are explained analytically by the wave approach.

Direct computation of derivatives of eigenvalues and eigenvectors

1990 ◽  
Vol 36 (3-4) ◽  
pp. 251-255 ◽  
Author(s):  
Alan L Andrew ◽  
Frank R De Hoog ◽  
Roger C.E Tan
Keyword(s):  
Eigenvalues And Eigenvectors ◽  
Direct Computation ◽  
Derivatives Of
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