The Convergence of Harmonic Ritz Vectors and Harmonic Ritz Values, Revisited

2017 ◽  
Vol 38 (1) ◽  
pp. 118-133 ◽  
Author(s):  
Gang Wu
Keyword(s):  
Ritz Values ◽  
Ritz Vectors ◽  
Harmonic Ritz Values

Effects of Noise on Measured Ritz Vectors

1997 ◽  
Author(s):  
David C. Zimmerman ◽  
Timothy T. Cao
Keyword(s):  
Structural Damage ◽  
Element Model ◽  
Mode Shapes ◽  
Structural Damage Detection ◽  
Structural Dynamic ◽  
Response Data ◽  
Statistical Variation ◽  
Ritz Vectors ◽  
Traditional Mode ◽  
Model Correlation

Abstract Ritz vectors offer many advantages over the traditional mode shapes in the areas of model reduction and structural dynamic simulation. Building upon the recent development of an experimental method to extract Ritz vectors from measured dynamic response data, these vectors were also demonstrated to offer great potential in the areas of finite element model correlation and structural damage detection. In this paper, a Monte Carlo simulation is performed to study the accuracy and stability of Ritz vectors extracted from this new procedure using noise corrupted response data. The statistical variation of Ritz parameters and modal parameters extracted from the same data is made to assess the sensitivity of Ritz vector extraction to measured noise.

Modeling of Flexible Bodies for Dynamic Analysis of Multi-Body Dynamic Systems Using Ritz Vectors

1991 ◽  
Author(s):  
Henry T. Wu ◽  
Neel K. Mani
Keyword(s):  
Dynamic Analysis ◽  
Mechanical Systems ◽  
Normal Modes ◽  
Flexible Bodies ◽  
Static Correction ◽  
Ritz Vectors ◽  
Regeneration Procedure ◽  
Efficient Vector ◽  
Multi Body ◽  
Body Dynamic

Abstract Vibration normal modes and static correction modes have been previously used to model flexible bodies for dynamic analysis of mechanical systems. The efficiency and accuracy of using these modes to model a system depends on both the flexibility of each body and the applied loads. This paper develops a generalized method for the generation of a set of Ritz vectors to model flexible bodies for dynamic analysis of multi-body mechanical systems. The Ritz vectors are generated using the distribution of dynamic loading on a flexible body. Therefore they form the most efficient vector basis for the spatial distribution of the loadings. The Ritz vectors can be re-generated when the system undergoes significant changes of its configuration and the regeneration procedure is inexpensive. The combinations of vibration normal modes and the proposed Ritz vectors thus form more efficient and accurate vector bases for the modeling of flexible bodies for dynamic analysis.

scholarly journals Majorization Bounds for Ritz Values of Self-Adjoint Matrices

2020 ◽  
Vol 41 (2) ◽  
pp. 554-572
Author(s):  
Pedro G. Massey ◽  
Demetrio Stojanoff ◽  
Sebastian Zarate
Keyword(s):  
Ritz Values

Frequency dependent ritz vectors

1992 ◽  
Vol 21 (3) ◽  
pp. 215-231 ◽  
Author(s):  
Hong Xia ◽  
J. L. Humar
Keyword(s):  
Frequency Dependent ◽  
Ritz Vectors
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