Estimation of Mass, Stiffness and Damping Matrices from Frequency Response Functions

1996 ◽  
Vol 118 (1) ◽  
pp. 78-82 ◽  
Author(s):  
S. Y. Chen ◽  
M. S. Ju ◽  
Y. G. Tsuei
Keyword(s):  
Frequency Response ◽  
Least Squares Method ◽  
Transformation Matrix ◽  
Frequency Domain Method ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Damping Matrix ◽  
Stiffness Matrices ◽  
Normal Frequency ◽  
Stiffness And Damping

A frequency-domain method for estimating the mass, stiffness and damping matrices of the model of a structure is presented. The developed method is based on our previous work on the extraction of normal modes from the complex modes of a structure. A transformation matrix is obtained from the relationship between the complex and the normal frequency response functions of a structure. The transformation matrix is employed to calculate the damping matrix of the system. The mass and the stiffness matrices are identified from the normal frequency response functions by using the least squares method. Two simulated systems are employed to illustrate the applicability of the proposed method. The results indicate that the damping matrix can be identified accurately by the proposed method. The reason for the good results is that the damping matrix is identified independently from the mass and the stiffness matrices. In addition, the robustness of the new approach to uniformly distributed measurement noise is also addressed.

Model Updating of Dynamic Systems Using Structural Reanalysis Method

2013 ◽  
Vol 365-366 ◽  
pp. 268-272
Author(s):  
Kyoung Bong Han ◽  
Doo Yong Cho
Keyword(s):  
Frequency Response ◽  
Dynamic Systems ◽  
Model Updating ◽  
Least Squares Method ◽  
Simulated Data ◽  
Transformation Matrix ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Stiffness Matrices ◽  
Normal Frequency

Model updating methodologies are invariably successful when used on noise-free simulated data, but tend to be unpredictable when presented with real experimental data that are unavoidably corrupted with uncorrelated noise content. In this paper, reanalysis using frequency response functions for correlating and updating dynamic systems is presented. A transformation matrix is obtained from the relationship between the complex and the normal frequency response functions of a structure. The transformation matrix is employed to calculate the modified damping matrix of the system. The modified mass and stiffness matrices are identified from the normal frequency response functions by using the least squares method. A numerical example is employed to illustrate the applicability of the proposed method. The result indicates that the present method is effective.

Analysis of Structural System Dynamic Model Updating Method

2013 ◽  
Vol 5 (3) ◽  
pp. 66-74
Author(s):  
Mao Shaoqing
Keyword(s):  
Frequency Response ◽  
Response Function ◽  
Frequency Response Function ◽  
Model Updating ◽  
Least Squares Method ◽  
Simulated Data ◽  
Transformation Matrix ◽  
Damping Matrix ◽  
Stiffness Matrices ◽  
Function Relationship

Model updating methods are successful in use of simulated data without noise, but inevitably lead to damaged uncorrelated noise levels and real experimental data, and it is often unpredictable. In this paper, the use of the frequency response function associated with re-analysis and updating of dynamic systems are proposed. Transformation matrix complexity and the normal frequency response function relationship between the structures are obtained. The transformation matrix is used to calculate the modified damping matrix of the system. The modified mass and stiffness matrices by using the least squares method is used to determine the frequency response function from the normal. A numerical example is tested to illustrate the applicability of the proposed method. The results show that this method is effective.

Dynamic characterization of a mechanical coupling for a rotating shaft

2010 ◽  
Vol 225 (3) ◽  
pp. 604-616 ◽  
Author(s):  
A T Tadeo ◽  
K L Cavalca ◽  
M J Brennan
Keyword(s):  
Frequency Response ◽  
Response Functions ◽  
Dynamic Characterization ◽  
Rotating Shaft ◽  
Frequency Response Functions ◽  
Mechanical Coupling ◽  
Lumped Parameter ◽  
Parameter Coupling ◽  
Stiffness And Damping

This article concerns the dynamic characterization of a flexible coupling that connects two co-axial shafts. Four different lumped parameter coupling models from the literature are investigated to see which model could best predict the dynamic behaviour of the coupling. The finite-element method was used to model the rotor dynamic system incorporating the coupling. Frequency response functions from this model were compared with measured frequency response functions from the rotor test rig with the shaft and coupling rotating at a specific speed. Parameters from the model were adjusted to minimize an objective function involving the measured and predicted frequency response functions. It was found that the simplest model of the coupling that could reasonably represent the coupling involves rotational (bending) stiffness and damping.

A method for vibration absorber tuning based on baseline frequency response functions

2007 ◽  
Vol 221 (9) ◽  
pp. 1071-1078 ◽  
Author(s):  
C Q Liu ◽  
C C Chang
Keyword(s):  
Frequency Response ◽  
Experimental Methods ◽  
Vibration Absorber ◽  
Physical Parameters ◽  
Primary System ◽  
Vibration Absorbers ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Baseline Frequency ◽  
Stiffness And Damping

This paper presents explicit expressions for new frequency response functions (FRFs) of a primary system when a vibration absorber is attached to it. The new FRF is expressed in terms of the baseline (‘old’) FRFs of the primary system and the physical parameters (the mass, stiffness, and damping) of the vibration absorber. The baseline FRF of the primary system can be obtained by either analytical or experimental methods. This approach allows engineers and designers to evaluate a number of alternative vibration absorbers before these absorbers are physically implemented on the structure. Therefore a considerable amount of time and effort for engineers and designers can be saved. Several examples are provided to illustrate the use of the method.

scholarly journals Identification of relevant acoustic transfer paths for WT drivetrains with an operational transfer path analysis

2021 ◽  
Author(s):  
W. Schünemann ◽  
R. Schelenz ◽  
G. Jacobs ◽  
W. Vocaet
Keyword(s):  
Path Analysis ◽  
Wind Turbine ◽  
Frequency Response ◽  
Mechanical System ◽  
Reference Point ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Transfer Path ◽  
Transfer Path Analysis ◽  
Turbine Model

AbstractThe aim of a transfer path analysis (TPA) is to view the transmission of vibrations in a mechanical system from the point of excitation over interface points to a reference point. For that matter, the Frequency Response Functions (FRF) of a system or the Transmissibility Matrix is determined and examined in conjunction with the interface forces at the transfer path. This paper will cover the application of an operational TPA for a wind turbine model. In doing so the path contribution of relevant transfer paths are made visible and can be optimized individually.

Calculation of Component Mode Synthesis Matrices From Measured Frequency Response Functions, Part 2: Application

1998 ◽  
Vol 120 (2) ◽  
pp. 509-516 ◽  
Author(s):  
J. A. Morgan ◽  
C. Pierre ◽  
G. M. Hulbert
Keyword(s):  
Frequency Response ◽  
Coupled System ◽  
Companion Paper ◽  
Component Mode Synthesis ◽  
Response Functions ◽  
Frequency Response Functions ◽  
Measured Frequency ◽  
Measured Frequency Response ◽  
Coupled Beams ◽  
The Individual

This paper demonstrates how to calculate Craig-Bampton component mode synthesis matrices from measured frequency response functions. The procedure is based on a modified residual flexibility method, from which the Craig-Bampton CMS matrices are recovered, as presented in the companion paper, Part I (Morgan et al., 1998). A system of two coupled beams is analyzed using the experimentally-based method. The individual beams’ CMS matrices are calculated from measured frequency response functions. Then, the two beams are analytically coupled together using the test-derived matrices. Good agreement is obtained between the coupled system and the measured results.

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