Modal Damping Identification Research Articles

On the modal damping ratios of mixed reinforced concrete – steel buildings

Two methods to derive the modal damping ratios of mixed reinforced concrete (R/C) – steel buildings are presented and discussed. In the first method bounds to the proportionality factors for the formation of the damping matrix of the mixed building are set, whereas in the second method the combined damping matrix of the mixed building is formed from the damping matrices of its distinct R/C and steel parts. After the formation of the damping matrix in each method, the linear seismic response of the mixed building is computed and a modal damping identification scheme is employed for the calculation of the modal damping ratios. Numerical examples involving a five-storey mixed building are performed in order to demonstrate the two methods and compare the damping ratio results provided by them. It is concluded that both methods can be used in the context of linear seismic analysis of a mixed R/C – steel building and the selection of the one method over the other is only a matter of the features of the software used.

Experimental Investigations of Brake Pad Shim Properties

AbstractThe understanding of NVH problems in brake systems becomes a strongly dominant remit in modern days. Finding solutions is the central task to achieve a calm and smooth system behavior.Brake squeal on automotive disk brakes represents a high frequency noise phenomenon resulting in potential customer complaints. The avoidance of squeal causes high costs in the automotive industry worldwide. One countermeasure for this disruptive noise issue is the application of thin composites named shims bonded to back plates of brake pads. The selection of appropriate shims is according to the state of the art still mainly based on trial and error. Current approaches seem to map the effects of shims on brake squeal insufficiently. To describe the shim behavior in an improved manner, prior experimental investigations have to be carried out, focusing on the identification of modal damping and stiffness values.The contribution shows experimental results of shims firmly bonded to brake pads and rectangular steel plates. Temperature variations and the analysis of nonlinearities like various excitation levels are examined in greater detail. As a result, the general influence of shims is presented and compared to measurements without damping materials. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)

모드 연성을 수반하는 분할 모형의 비틀림 감쇠비 추정

The identification of modal damping of a segmented hull model with torsional response is difficult task due to the coupling of modal response. This is because the 1st and 2nd torsional vibration modes are closely spaced in frequency domain leading to the situation that the modal decomposition is difficult to achieve by simple band-pass filter. Present study applied several different modal decomposition methods to derive the damping ratio of different modes. The modal decomposition methods considered in this study are simple band-pass filter, Hilbert vibration decomposition, Wavelet transform and proper orthogonal decomposition. Coupled free decay signal obtained from the torsional hammering test on a segmented hull model was processed with four different methods and the derived damping ratios were compared with each other. Discussions also have been made on the pros and cons of the different methodologies.

On the application of blind source separation for damping estimation of bridges under traffic loading

The accurate and reliable estimation of modal damping from output-only vibration measurements of structural systems is a continuing challenge in the fields of operational modal analysis (OMA) and system identification. In this paper a modified version of the blind source separation (BSS)-based Second-Order Blind Identification (SOBI) method was used to perform modal damping identification on a model bridge structure under varying loading conditions. The bridge model was created with finite elements and consisted of a series of stringer beams supported by a larger girder. The excitation was separated into two categories: ambient noise and traffic loads with noise modeled with random forcing vectors and traffic simulated with moving loads for cars and partially distributed moving masses for trains. The acceleration responses were treated as the mixed output signals for the BSS algorithm. The modified SOBI method used a windowing technique to maximize the amount of information used for blind identification from the responses. The modified SOBI method successfully found the mode shapes for both types of excitation with strong accuracy, but power spectral densities (PSDs) of the recovered modal responses showed signs of distortion for the traffic simulations. The distortion had an adverse affect on the damping ratio estimates for some of the modes but no correlation could be found between the accuracy of the damping estimates and the accuracy of the recovered mode shapes. The responses and their PSDs were compared to real-world collected data and patterns similar to distortion were observed implying that this issue likely affects real-world estimates.

Measurement point selection and modal damping identification for bladed disks

A novel measurement point selection (MPS) technique for bladed disks and integrally bladed disks (blisks) is presented and applied to a new modal damping identification method. When gathering data to be used for applications such as damping identification in blisks, it is important to measure points which provide sufficient and accurate information for the analysis. However, to reduce the experimental time and cost, the measurement points should be chosen optimally so that the minimum number of measurements have to be collected. This paper discusses a modified form of the effective independence distribution vector (EIDV) method presented by Penny et al. and adapted by Holland et al. The key aspect of the proposed method is that it uses only single sector-level calculations instead of the full system. A residual weighting optimizes the MPS technique by ranking individual measurement locations according to their noise sensitivity. The method presented provides results equivalent to the full-system EIDV method, but it decreases the computational cost, increases the robustness of the identification, and minimizes the measurement time. Also, a novel method to identify a damping parameter for each mode in a frequency range of interest is presented. This method utilizes the proposed MPS technique to increase the accuracy of the identification. Measurement locations and modal damping results for a 30 degree of freedom system and a blisk with a more complex geometry are presented. Using the proposed methodologies it is possible to obtain an accurate modal damping identification with a decreased computational and measurement cost.

Frequency slice algorithm for modal signal separation and damping identification

This paper focuses on modal signal separation and damping parameter identification by a new time-frequency analysis method. With the aid of the random decrement technique (RDT), an accurate estimation method is firstly introduced both in time and frequency domains for single modal damping identification. Next, the background of a new concept of frequency slice wavelet transform (FSWT) is revealed clearly. Then, some new properties of the FSWT are briefly discussed in contrast with the wavelet transform (WT). Based on the analysis of RDT and FSWT, a frequency slice algorithm (FSA) is designed for modal separation and parameter identification. The merits of FSWT and FSA with numerical simulations and experiments are demonstrated in this paper. We finally apply the proposed methods to analyze the free-decay responses (FDR) collected from a small laboratory bridge monitoring system (LBMS). Some conclusions are drawn that the RDT being used directly in FSWT domain can bring a good damping estimator. The FSA is not limited to FDR, and also can be used to random impacting response directly. FSWT itself is a new kind of good filter, and has high performance against noise. It is significant to get damping parameter with higher accuracy through modal separation by FSWT, and FSWT can be controlled adaptively in modal separation by dynamic scale method.

On a modal damping identification model for non-classically damped linear building structures subjected to earthquakes

A simple modal damping identification model developed by the present authors for classically damped linear building frames is extended here to the non-classically damped case. The modal damping values are obtained with the aid of the frequency domain modulus of the roof-to-basement transfer function and the resonant frequencies of the structure (peaks of the transfer function) as well as the modal participation factors and mode shapes of the undamped structure. The assumption is made that the modulus of the transfer function of the non-classically damped structure matches the one of the classically damped structure in a discrete manner, i.e., at the resonant frequencies of that function modulus. This proposed approximate identification method is applied to a number of plane building frames with and without pronounced non-classical damping under different with respect to their frequency content earthquakes and its limitations and range of applicability are assessed with respect to the accuracy of both the identified damping ratios and that of the seismic structural response obtained by classical mode superposition and use of those identified modal damping ratios.

Numerical and experimental studies of the Braga Sports Stadium suspended roof

This paper describes a set of dynamic numerical and experimental studies conducted on the suspended roof of the Braga Municipal Sports Stadium. Modal parameters, calculated from a numerical model of the constructed structure that takes into account the geometrically nonlinear structural behaviour and the progressive application of loads, are compared with the corresponding parameters identified on the basis of an ambient vibration test. Particular attention is given to modal damping identification due to the necessity of analysing the susceptibility of the suspended roof to buffeting effects.

Measurement of SEA damping loss factor for complex structures

Statistical Energy Analysis has become extremely popular in the transportation industry. As a prediction tool, it offers appealing advantages such as its wide frequency range and short computational time, which conventional methods do not offer. Critical parameter in every SEA model, the damping characteristics of the subsystems must be determined by way of experimentations. A variety of different techniques of measuring the damping loss factor were developed. These techniques can be divided into three main groups: (i) method based on the identification of modal damping by curve-fitting frequency response function, (ii) decay techniques based on-determination of the reverberation time and, (iii) steady-state techniques involving measurements of power input method much closely related to the definition of SEA since its starting point is the power balance. This work presents an experimental study of these techniques for various structures such as flat metallic panels, aircraft side walls (ribbed curved panels) and sandwich-composite panels in both low and high damping configurations (additions of damping materials, sound packages in both single wall and double wall configurations, mounting effects, ...). In particular, a critical discussion is made on the implementation, advantages and drawbacks of each method regarding its use in SEA modeling of complex structures.

On a modal damping identification model of building structures

The simple modal damping identification model of Hart and Vasudevan is generalized. The model works in the frequency domain and provides time-invariant modal damping ratios of building structures under seismic excitations in terms of modal participation factors and the roof-to-basement transfer function. Translational as well as torsional modes of vibration are considered. The performance of the model is assessed through a small, yet indicative, number of numerical examples involving steel plane and space frames under seismic excitations and on the basis of a number of criteria an ideal identification model should satisfy. It is concluded that the presented model, in spite of its simplicity, gives very good results for low-amplitude seismic excitations resulting in linear elastic structural behavior (with damping) even for cases of closely spaced modes, local modes, and very small or large amounts of damping. Some numerical pitfalls regarding the application of the model are mentioned and carefully treated. The limitations of the model when used in conjunction with inelastic structural behavior are determined and discussed. Experimental verification of the model is also provided.

Automatic Identification of Modal Damping from Floquet Analysis

A practical method is proposed to identify the mode associated with the frequency part of the eigenvalue of the Floquet transition matrix (FTM). From the FTM eigenvector, which contains the states and their derivatives, the ratio of the derivative and the state corresponding to the largest component is computed. The method exploits the fact that the imaginary part of this (complex) ratio closely approximates the frequency of the mode. It also lends itself well to automation and has been tested over a large number of FTMs of order as high as 250.