Advances in Ritz Vector Identification

2003 ◽  
Vol 129 (8) ◽  
pp. 1131-1140 ◽  
Author(s):  
Thomas Boxoen ◽  
David C. Zimmerman
Keyword(s):  
Ritz Vector

Comparison of eigenanalysis and Ritz vector approaches for response spectrum analysis of soil-pile-bridge systems

2021 ◽  
Vol 17 (3-4) ◽  
pp. 89-100
Author(s):  
M. Davidson ◽  
A. Patil ◽  
S.A. Rosenfeld ◽  
Z. Zhu
Keyword(s):  
Spectrum Analysis ◽  
Soil Structure ◽  
Response Spectrum ◽  
Active Regions ◽  
Ritz Vector ◽  
Response Spectrum Analysis ◽  
Fixed Base ◽  
Potential Benefits ◽  
Eigenvectors And Eigenvalues ◽  
Vector Approach

Frequency-based analysis techniques such as response spectrum analysis (RSA) are widely used for designing bridges in seismically active regions. Two well-known analysis procedures that underlie RSA are the solution of the eigenproblem and the approximation of the solution to the eigenproblem (i.e., approximation of eigenvectors and eigenvalues) through use of force-dependent Ritz vectors. While frequency-based methods have achieved widespread adoption in practice, certain simplifications remain common, such as neglecting soil-structure interaction (SSI) due to a fixed-base assumption. In the present study, frequency-based techniques packaged within a research version of a design-oriented computational tool are employed to analyze, assess, and compare results obtained from RSA with use of the eigenanalysis, and separately, Ritz vector approaches. Importantly, for the bridge configurations analyzed, SSI is taken into account. As outcomes, the potential benefits of the Ritz vector approach (as well as modeling strategies) are demonstrated. The study outcomes are intended to aid practicing engineers when the need to account for SSI is recognized as pertinent to a given bridge seismic design application.

scholarly journals Nonlinear Structural Dynamic Finite Element Analysis Using Ritz Vector Reduced Basis Method

1996 ◽  
Vol 3 (4) ◽  
pp. 259-268 ◽  
Author(s):  
M.S. Yao
Keyword(s):  
Finite Element ◽  
Equations Of Motion ◽  
Computational Cost ◽  
Finite Amplitude ◽  
Basis Vector ◽  
Reduced Basis ◽  
Ritz Vector ◽  
Element Analysis ◽  
Structural Dynamic ◽  
Nonlinear Equations Of Motion

The large number of unknown variables in a finite element idealization for dynamic structural analysis is represented by a very small number of generalized variables, each associating with a generalized Ritz vector known as a basis vector. The large system of equations of motion is thereby reduced to a very small set by this transformation and computational cost of the analysis can be greatly reduced. In this article nonlinear equations of motion and their transformation are formulated in detail. A convenient way of selection of the generalized basis vector and its limitations are described. Some illustrative examples are given to demonstrate the speed and validity of the method. The method, within its limitations, may be applied to dynamic problems where the response is global in nature with finite amplitude.

scholarly journals The static substructure method for dynamic analysis of structures

1987 ◽  
Vol 20 (4) ◽  
pp. 264-268
Author(s):  
Menglin Lou
Keyword(s):  
Dynamic Response ◽  
Dynamic Analysis ◽  
Static Analysis ◽  
Superposition Method ◽  
Ritz Vector ◽  
Substructure Method ◽  
Large Structures

In this paper, the static substructure method based on the Ritz vector direct superposition method is suggested for analysing the dynamic response of structures. The advantage of this algorithm is that the computer cost can be reduced and the static analysis and the dynamic analysis of large structures can be simplified by using the identical static substructure method.

Improved Experimental Ritz Vector Extraction With Application to Damage Detection

2010 ◽  
Vol 132 (1) ◽  
Author(s):  
Stuart G. Taylor ◽  
David C. Zimmerman
Keyword(s):  
Damage Detection ◽  
State Space ◽  
Noisy Data ◽  
Space System ◽  
Ritz Vector ◽  
Damage Location ◽  
System Realization ◽  
Extraction Algorithm ◽  
Ritz Vectors ◽  
State Space System

Load-dependent Ritz vectors, or Lanczos vectors, are alternatives to mode shapes as a set of orthogonal vectors used to describe the dynamic behavior of a structure. Experimental Ritz vectors are extracted recursively from a state-space system realization, and they are orthogonalized using the Gram–Schmidt process. In addition to the Ritz vectors themselves, the associated nonorthogonalized vectors are required for application to damage detection. First, this paper presents an improved experimental Ritz vector extraction algorithm to correctly extract the nonorthogonalized Ritz vectors. Second, this paper introduces a Ritz vector accuracy indicator for use with noisy data. This accuracy indicator is applied as a tool to guide the deflation of a state-space system realization identified from simulated noisy data. The improved experimental Ritz vector extraction algorithm produces experimental nonorthogonalized Ritz vectors that match the analytically computed vectors. The use of the accuracy indicator with simulated noisy data enables the identification of a state-space realization for Ritz vector extraction from which damage location and extent are correctly estimated. The improved Ritz vector extraction algorithm improves the application of Ritz vectors to damage detection, more accurately estimating damage location and extent. The accuracy indicator extends the application of Ritz vectors to damage detection in noisy systems as well.

Nonlinear analysis using ritz vector reduced basis

1992 ◽  
Vol 44 (1-2) ◽  
pp. 117-124 ◽  
Author(s):  
W. Kanok-Nukulchai ◽  
S.F. Lin
Keyword(s):  
Nonlinear Analysis ◽  
Reduced Basis ◽  
Ritz Vector
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