Identification of damping: Part 3, symmetry-preserving methods (original) (raw)

Identification of damping: part 1, viscous damping

2001

Characterization of damping forces in a vibrating structure has long been an active area of research in structural dynamics. The most common approach is to use “viscous damping” where the instantaneous generalized velocities are the only relevant state variables that affect damping forces. However, viscous damping is by no means the only damping model within the scope of linear analysis. Any model which makes the energy dissipation functional non-negative is a possible candidate for a valid damping model.

Damping modelling and identification using generalized proportional damping

2005

ABSTRACT In spite of a large amount of research, the understanding of damping forces in vibrating structures is not well developed. A major reason for this is that, by contrast with inertia and stiffness forces, the physics behind the damping forces is in general not clear. As a consequence, modelling of damping from the first principle is difficult, if not impossible, for real-life engineering structures.

Identification of Highly Damped Systems and Its Application to Vibro-Acoustic Modeling

A highly damped system such as a trimmed car body is more difficult to model accurately by means of experimental modal analysis than for instance a body-in-white. This can be explained by the fact that resonant peaks are not always apparent in the frequency response measurements of highly damped systems. Consequently, simple SDOF estimators are unusable while more advanced MDOF estimators often fail to produce clear stabilization diagrams resulting in poor modal parameter estimates. This can be an important bottleneck with implications on the vibro-acoustic optimization of cars as well as many other systems. The aim of this contribution is to provide better system identification tools to improve the modeling of highly damped systems.

An assessment of damping identification methods

Journal of Sound and Vibration, 2009

A study is carried out into the philosophy and performance of different approaches for the determination of linear viscous damping in elasto-mechanical systems. The methods studied include a closed-form solution, identification methods based on inverting the matrix of receptances, energy expressions developed from single-frequency excitation and responses as well as first-order perturbation methods. The work is concentrated particularly upon modal truncation and how this affects the distribution of matrix terms and the ability of the identified damping (together with known mass and stiffness terms) to reproduce the complex eigenvalues and eigenvectors of the full-order system. A simulated example is used to illustrate various points covered in the theoretical discussion of the methods considered. r

Towards identification of a general model of damping

SPIE proceedings series, 2000

R��sum��/Abstract Characterization of damping forces in a vibrating structure has long been an active area of research in structural dynamics. In spite of a large amount of research, understanding of damping mechanisms is not well developed. A major reason for this is that unlike inertia and stiffness forces it is not in general clear what are the state variables that govern the damping forces. The most common approach is to use viscous damping where the instantaneous generalized velocities are the only relevant state variables. However, ...

Identification of Damping Using Proper Orthogonal Decomposition

A new efficient method for identification of the damping matrix of general linear dynamic systems is proposed. For a given frequency band, the proposed method estimates the equivalent reduced-order damping matrix of a general linear dynamical system, with the mass and stiffness matrices known a priori. Proper orthogonal decomposition (POD) method is used to represent an optimal reduced order model in the frequency range of interest. To mitigate the ill-conditioned nature of this inverse problem, Tikhonov regularisation is applied. The proposed methodology circumvents, or at least alleviates, the difficulties encountered in applying conventional modal analysis techniques in the high and mid frequency range.

Identification of damping: part 2, non-viscous damping

2001

In a companion paper (see pp. 43���61 of this issue), it was shown that when a system is non-viscously damped, an identified equivalent viscous damping model does not accurately represent the damping behaviour. This demands new methodologies to identify non-viscous damping models. This paper takes a first step, by outlining a procedure for identifying a damping model involving an exponentially decaying relaxation function.

Modal identification of non-classically damped structures

2015

This thesis focuses on modal identification of structural systems. System Identification can be used to create mathematical models of structures which can then be used in simulation and design. Modal identification provides a valuable means of calibrating, validating, and updating finite element models of structures. This thesis reviews the standard techniques of system identification. Basic theoretical background of the different methods of practical use is presented. Demonstrations of the described methods are provided by using response simulated from known systems which are then used in system identification. Starting with single degrees of freedom systems, basic theory in relation to dynamics and modal analysis of multi degree of freedom systems are presented with examples used in the identification procedure, along with methods for non-classically damped systems. As a case study, system identification of a base-isolated bridge is undertaken. Modal properties of the bridge are computed from a finite element model. A simulated response is used in system identification to check whether the identified modal properties match that of the finite element model. One of the issues investigated is the effect of damping provided by the rubber bearings of the base isolation system. This damping makes the system nonclassically damped. The results indicate that system identification for a structure like this is feasible and reliable estimates of vibration periods and damping ratios are obtained. It was also observed that increase in damping ratio in the rubber bearings results in modal damping ratios that are different than the commonly used Rayleigh damping model.

Frequency Based Spatial Damping Identification—Theoretical and Experimental Comparison

Conference proceedings of the Society for Experimental Mechanics, 2017

This research compares spatial damping identification methods, both theoretically and experimentally. In contrast to the commonly used damping methods (modal, proportional) the spatial damping information improves structural models with a known location of the damping sources. The real case robustness of full FRF matrix and local equation of motion methods were tested against: modal and spatial incompleteness, differences in viscous and hysteretic damping models and the effect of damping treatments. To obtain accurate results, a careful analysis of measurements in terms of reciprocity in the raw measurements, and in terms of how to preserve symmetry has to be done. It was found that full FRF matrix needs to be symmetrisized due to small deviations in reciprocity before the damping identification. Full frequency response function (FRF) matrix methods (e.g.: Lee-Kim) can identify the spatial damping if spatial and modal incompleteness are carefully evaluated, but the measurement effort increases with second order and, consequently, the size of the FRF matrix. Keywords Spatial damping • Inverse identification • Frequency response • Modal incompleteness • Spatial incompleteness 3.1 Introduction Numerical and analytical prediction of the structural responses depends on the identified spatial damping throughout the structure. Good damping prediction is important for validation of analytical/numerical models in civil, mechanical and aerospace engineering. Damping in linear mechanical systems is usually identified using one of the methods such as logarithmic decay [1] in time domain, continuous wavelet transform [2], the Morlet wave method [3] or the synchrosqueezed wavelet [4] in time-frequency domain or half-power point [1] and first order perturbation [5] in frequency domain. Damping identification methods form the basis of several model updating methods [6, 7], where accurate damping identification can further improve numerical models [8, 9]. Two other examples where exact damping spatial location is needed are: identification of damping sources on existing structures and precise application of damping treatment. However, typically used damping identification methods [1, 8] do not provide spatial information (damping distribution throughout the structure). An alternative approach is to use direct damping identification methods that were developed for identification of damping distribution directly from the frequency response functions (FRF) without the transformation to the modal coordinates. One of the typically used direct methods is the Lee and Kim's dynamic stiffness method [10]. The core of the method is a inverse identification of linear damping model from the complex part of the measured data which have been found to be very sensitive to real world problems in most follow-on studies, e.g. phase error [11], noise when the modal overlap is low [5] and leakage [12]. Ozgen and Kim [12] proposed a new experimental procedure with simultaneous excitation of all nodes to overcome described measurement errors, but the procedure is not practical with lots of measurement degrees of freedom because demands as many shakers as there are measurement degrees of freedom. Some direct methods, not considered in this research, are reviewed in [5, 11, 13]. This research focuses on the modal and spatial incompleteness effect on the identification of spatial damping. Modal incompleteness deals with limited frequency span over number of modes whereas spatial incompleteness covers effects of non-measured points on the structure [14]. Modal and spatial incompleteness for spatial damping have been studied numerically [5, 15] and experimentally [11] on low DOF models.

Damping identification using perturbation techniques and higher-order spectra

2000

Perturbation techniques and spectral moments are combined to characterize and quantify the damping and nonlinear· parameters of the first mode of a three-beam two-mass frame. The frame is excited harmonically near twice its lowest natural frequency. The response is modeled with a second-order nardinear equation with quadratic and cubic terms and linear and quadratic damping terms. The method of multiple scales is used to obtain a second-order approximate solution for this model. Bispectral analysis is used to quantify the level of coupling between modes and measure their phase difference. The amplitudes and phase difference of modes with different frequencies are substituted into the approximate solution to determine the damping and nonlinear parameters.