Sensitivity Analysis of the Eigenvector in the Non-Conservative System with Repeated Eigenvalues

2012 ◽  
Author(s):  
Lan Yu ◽  
Xiaozhong Geng
Keyword(s):  
Sensitivity Analysis ◽  
Conservative System ◽  
Repeated Eigenvalues

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.

Sensitivity Analysis of Dissipative Reversible and Hamiltonian Systems: A Survey

2009 ◽  
Author(s):  
Oleg N. Kirillov ◽  
Ferdinand Verhulst
Keyword(s):  
Sensitivity Analysis ◽  
Hopf Bifurcation ◽  
Structural Stability ◽  
Hamiltonian Systems ◽  
Perturbation Analysis ◽  
Stability Boundary ◽  
Conservative System ◽  
Small Dissipation ◽  
Whitney Umbrella ◽  
The Stability

The paradox of destabilization of a conservative or non-conservative system by small dissipation, or Ziegler’s paradox (1952), has stimulated an ever growing interest in the sensitivity of reversible and Hamiltonian systems with respect to dissipative perturbations. Since the last decade it has been widely accepted that dissipation-induced instabilities are closely related to singularities arising on the stability boundary. What is less known is that the first complete explanation of Ziegler’s paradox by means of the Whitney umbrella singularity dates back to 1956. We revisit this undeservedly forgotten pioneering result by Oene Bottema that outstripped later findings for about half a century. We discuss subsequent developments of the perturbation analysis of dissipation-induced instabilities and applications over this period, involving structural stability of matrices, Krein collision, Hamilton-Hopf bifurcation and related bifurcations.

System Reliability-Based Design Optimization Under Tradeoff Between Reduction of Sampling Uncertainty and Design Shift

2019 ◽  
Vol 141 (4) ◽  
Author(s):  
Sangjune Bae ◽  
Nam H. Kim ◽  
Seung-gyo Jang
Keyword(s):  
Sensitivity Analysis ◽  
Bayesian Network ◽  
Design Optimization ◽  
Failure Probability ◽  
System Reliability ◽  
Global Sensitivity Analysis ◽  
Conservative System ◽  
Reliability Based Design Optimization ◽  
Sampling Uncertainty ◽  
Reliability Based Design

This paper presents a tradeoff between shifting design and controlling sampling uncertainty in system reliability-based design optimization (RBDO) using the Bayesian network. The sampling uncertainty is caused by a finite number of samples used in calculating the reliability of a component, and it propagates to the system reliability. A conservative failure probability is utilized to consider sampling uncertainty. In this paper, the sensitivity of a conservative system failure probability is derived with respect to the design change and the number of samples in a component using Bayesian network along with global sensitivity analysis (GSA). In the sensitivity analysis, GSA is used for local sensitivity calculation. The numerical results show that sampling uncertainty can significantly affect the conservative system reliability and needs to be controlled to achieve the desired level of system reliability. Numerical examples show that both shifting design and reducing sampling uncertainty are crucial in the system RBDO.

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