Updating the Damping Matrix Using Frequency Response Data

1995 ◽  
Author(s):  
Cécile Reix ◽  
Alain Gerard ◽  
Christian Tombini
Keyword(s):  
Frequency Response ◽  
Weighted Least Squares ◽  
Element Model ◽  
Mode Shapes ◽  
Minor Effect ◽  
Sensitivity Matrix ◽  
Damping Matrix ◽  
Stiffness Matrices ◽  
Weighted Least Squares Estimation ◽  
A Minor

Abstract This paper presents a method for the updating of the damping matrix of a linear dynamic system. For this dynamic study, it is presumed that the characteristic mass and stiffness matrices are perfectly known thanks to the updating of the experimental and calculed frequencies and mode shapes as from a finit element model. Furthermore, it is accepted that damping has only a minor effect on the frequencies and mode shapes of a structure (a hypothesis that has been verified for structures with low damping). It is proposed to adjuste the coefficients of the [D] hysteretic damping matrix as from the superposition of the experimental and analytical Frequency Response Functions (FRF). The frequencies and mode shapes are extracted from the solutions of the caracteristic equation (3) resulting from the classic dynamic equation. An analytical FRF is calculed and then used to establish the sensitivity matrix, translating the influence of the updating parameters on the FRF. To update the [D] matrix, we use a non-linear weighted least squares estimation.

Tuned Sloshing Dampers With Large Rectangular Core Penetrations

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
J. S. Love ◽  
K. P. McNamara ◽  
M. J. Tait ◽  
T. C. Haskett
Keyword(s):  
Energy Dissipation ◽  
Frequency Response ◽  
Tall Buildings ◽  
Element Model ◽  
Mode Shapes ◽  
Rectangular Tank ◽  
Core Energy ◽  
Sloshing Frequency ◽  
Mechanical Mass ◽  
Broad Dimension

Abstract Space restrictions at the top of tall buildings may necessitate using tuned sloshing dampers (TSD) tanks with large rectangular penetrations to accommodate the structural core of the tower. A finite element model is employed to predict the natural sloshing frequencies and mode shapes of liquid sloshing in a rectangular tank with a rectangular core. Equivalent mechanical properties are determined to predict the sloshing response. Frequency response predictions of wave heights, sloshing forces, and energy-dissipation per cycle agree with results from shake table testing conducted on a rectangular tank with a rectangular core. Energy dissipation due to flow around the core adds considerable damping to the liquid and is proportional to the response velocity-squared. Nonlinear coupling among sloshing modes results in multiple peaks in the frequency response plots near the fundamental resonant frequency. An interior core with a broad dimension in one direction substantially reduces the fundamental sloshing frequency and equivalent mechanical mass in the perpendicular direction; however, the fundamental sloshing frequency and equivalent mechanical mass in the parallel direction are only influenced marginally. Large rectangular cores reduce the proportion of the total water mass that is effective in controlling tower motion. A TSD with a rectangular penetrating core may enable a TSD option to be considered for the control of a tall building in cases where a traditional rectangular TSD is infeasible.

Damping Matrix Identification by Finite Element Model Updating Using Frequency Response Data

2017 ◽  
Vol 17 (01) ◽  
pp. 1750004 ◽  
Author(s):  
S. Pradhan ◽  
S. V. Modak
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Frequency Response ◽  
Model Updating ◽  
Experimental Studies ◽  
Element Model ◽  
Fe Model ◽  
Damping Matrix ◽  
Steel Cast ◽  
Identification Techniques

Accurate modeling of damping is essential for prediction of vibration response of a structure. This paper presents a study of damping matrix identification method using experimental data. The identification is done by performing finite element (FE) model updating using normal frequency response functions (FRFs). The paper addresses some key issues like data incompleteness and computation of the normal FRFs for carrying out the model updating using experimental data. The effect of various levels of damping in structures on the performance of the identification techniques is also investigated. Experimental studies on three beam structures made up of mild steel, cast iron and acrylic are presented to demonstrate the effectiveness of the identification techniques for different levels of damping.

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.

Identification of a Nonproportional Damping Matrix from Incomplete Modal Information

1991 ◽  
Vol 113 (2) ◽  
pp. 219-224 ◽  
Author(s):  
C. Minas ◽  
D. J. Inman
Keyword(s):  
Experimental Data ◽  
Weighted Least Squares ◽  
Positive Semidefinite ◽  
Eigenvalues And Eigenvectors ◽  
Damping Matrix ◽  
Reduction Techniques ◽  
Stiffness Matrices ◽  
Hysteretic Damping ◽  
Nonproportional Damping ◽  
Pseudo Inverse

In modeling structures the damping matrix is the most difficult to represent. This is even more difficult in complicated structures that are not lightly damped. The work presented here provides a method of modeling the damping matrix of a structure from incomplete experimental data combined with a reasonable representation of the mass and stiffness matrices developed by finite element methods and reduced by standard model reduction techniques. The proposed technique uses the reduced mass and stiffness matrices and the experimentally obtained eigenvalues and eigenvectors in a weighted least squares or a pseudo-inverse scheme (depending on the number of the equations that are available) to solve for the damping matrix. The results are illustrated through several examples. As an indication of the accuracy of the method, fictitious examples where the damping matrix is originally known are considered. The proposed method identifies the exact viscous or hysteretic damping matrix by only using a partial set, half of the system’s eigenvalues and eigenvectors. The damping matrix is assumed to be real, symmetric, and positive semidefinite.

Identification of non-proportional viscous damping matrix of beams by finite element model updating

2016 ◽  
Vol 24 (11) ◽  
pp. 2134-2148 ◽  
Author(s):  
Subhajit Mondal ◽  
Sushanta Chakraborty
Keyword(s):  
Finite Element ◽  
Finite Element Model ◽  
Model Updating ◽  
Random Noise ◽  
Current Method ◽  
Element Model ◽  
Finite Element Model Updating ◽  
Viscous Damping ◽  
Damping Matrix ◽  
Stiffness Matrices

A methodology has been proposed to estimate non-proportional viscous damping matrix of beams from measured complex eigendata using finite element model updating technique. Representation of damping through a proportional damping matrix ignoring the complexity of eigenvectors may not be appropriate when external damping devices are employed. The current literature of determination of non-proportional damping matrix demands measurement of a large number of complex modes which is extremely difficult in practice. A gradient based finite element model updating algorithm implementing inverse eigensensitivity method has been presented through a series of numerically simulated cantilever beams. The method can accurately predict the non-proportional damping matrix even if the measured eigenvectors are polluted with random noise. The novelty of the current method is that it can sustain a high level of modal and coordinate sparsity in measurement. The method assumes prior determination or updating of the mass and stiffness matrices.

Substructure-Joint Based Approach to Damped FE Model Updating of Complex Assembly Structure

2012 ◽  
Vol 463-464 ◽  
pp. 1169-1174
Author(s):  
Parivash Soleimanian ◽  
Morteza H.Sadeghi ◽  
Akbar Tizfahm
Keyword(s):  
Finite Element ◽  
Model Updating ◽  
Element Model ◽  
Modal Testing ◽  
Fe Model ◽  
Complex Assembly ◽  
Modal Data ◽  
Damping Matrix ◽  
Stiffness Matrices ◽  
Assembly Structure

Model updating techniques are used to update the finite element model of a structure, so that updated model can be predicted the dynamic behavior of an actual assembly structure more accurately. Most of the model updating techniques neglects damping and so amplitudes of vibration at resonance and antiresonance frequencies cannot be predicted by using of these updated models. In dynamic design of structures predicting of these properties is necessary. This paper presents a new technique to create an accurate finite element (FE) updated model of complex assembly structures consisting of substructures and real joint by considering damping of them. Given the fact that modal testing of real joints (such as bolt with some washers) are almost impossible. The updated model of assembly structure is obtained in four steps. In the first step, mass and stiffness matrix of substructures, joint and assembly structure are updated using modal data and Eigen-sensitivity approach. In the second step, damping of assembly structure is identified using complex modal data and updated mass and stiffness matrices which are obtained in first step. In the third step, the effect of damping of joint on frequency response functions (FRFs) extracted from updated model was shown. In the forth step, damping matrix of joint is updated by using FRF-based model updating method and finally damped updated model of assembly structure compared with measured data.

Matching Finite Element Models to Modal Data

1990 ◽  
Vol 112 (1) ◽  
pp. 84-92 ◽  
Author(s):  
C. Minas ◽  
D. J. Inman
Keyword(s):  
Finite Element ◽  
Control Algorithm ◽  
Natural Frequencies ◽  
Mass Matrix ◽  
Element Model ◽  
Mode Shapes ◽  
Finite Element Models ◽  
Test Results ◽  
Stiffness Matrices ◽  
Stiffness And Damping

A technique is proposed which systematically adjusts a finite element model of a structure to produce an updated model in agreement with measured modal results. The approach suggested here is to consider the desired perturbations in stiffness and damping matrices as gain matrices in a feedback control algorithm designed to perform eigenstructure assignment. The improved stiffness and damping matrices combined with the analytical mass matrix, more closely predict the modal test results. The technique is applicable to undamped, proportionally damped, as well as non-proportionally damped models. The proposed method assumes that the analytical mass, damping and stiffness matrices are known and that vibration test data is available in the form of natural frequencies, damping ratios, and mode shapes.

Identification of Multi-Degree of Freedom Systems With Nonproportional Damping Using the Resonant Decay Method

2004 ◽  
Vol 126 (2) ◽  
pp. 298-306 ◽  
Author(s):  
Steven Naylor ◽  
Michael F. Platten ◽  
Jan R. Wright ◽  
Jonathan E. Cooper
Keyword(s):  
Measurement Noise ◽  
Mode Shapes ◽  
Damping Matrix ◽  
Modal Damping ◽  
Stiffness Matrices ◽  
Rigid Body Modes ◽  
Nonproportional Damping ◽  
Modal Mass ◽  
Damped Systems ◽  
Modal Space

This paper describes an extension of the force appropriation approach which permits the identification of the modal mass, damping and stiffness matrices of nonproportionally damped systems using multiple exciters. Appropriated excitation bursts are applied to the system at each natural frequency, followed by a regression analysis in modal space. The approach is illustrated on a simulated model of a plate with discrete dampers positioned to introduce significant damping nonproportionality. The influence of out-of-band flexible and rigid body modes, imperfect appropriation, measurement noise and impure mode shapes is considered. The method is shown to provide adequate estimates of the modal damping matrix.

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.

Helically Perforated Thin Films -- Dependence of Mechanical Properties on Microstructure

2006 ◽  
Vol 977 ◽  
Author(s):  
Sumudu P. Fernando ◽  
Anastasia L. Elias ◽  
Michael J. Brett
Keyword(s):  
Thin Film ◽  
Pitch Angle ◽  
Finite Size ◽  
Element Model ◽  
Film Structure ◽  
Minor Effect ◽  
Helical Pitch ◽  
Microstructural Parameters ◽  
A Minor ◽  
Infinite Model

AbstractThe effects of several microstructural parameters on the mechanical behaviour of a helically perforated thin film structure, or inverse microspring, were investigated using a finite element model[1]. The parameters investigated were the helical pitch angle, the cross-section radius, and the coil spacing. The elastic modulus was found to depend most strongly on the helical pitch angle (changing by a factor of 1.3 as the pitch angle went from 35° to 70°). Variations in the coil radius and the film thickness had a minor effect on the modulus. It was also found that using a finite size model (as opposed to an infinite model using periodic boundary conditions) produced better conditioned results. A preliminary confirmation of the model's validity was performed by comparison to nanoindentation results of a nickel helically perforated thin film.

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