Study on Equivalent Damping Ratio of Shenzhen Baoan International Airport T3 Terminal

2012 ◽  
Vol 446-449 ◽  
pp. 871-877
Author(s):  
Yu Chen Yang ◽  
Lei Gu ◽  
Zhong Yi Zhu ◽  
Kai Qin ◽  
Lin Zhang
Keyword(s):  
Modal Analysis ◽  
Damping Ratio ◽  
Earthquake Response ◽  
Structural System ◽  
Equivalent Damping ◽  
Damping Matrix ◽  
Modal Damping ◽  
Modal Coupling ◽  
Response Equation ◽  
Energy Theory

Today, the structures constituted by different materials, increase more and more, especially the lower part is concrete, the upper is steel. For this type of structural system, modal damping matrix is non-diagonal matrix, the earthquake response equation is coupled on the modal damping matrix, the modal coupling of the non-proportional damping system leads to the traditional real modal analysis methods not be directly applied. For such structure, the changes of the damping ratio are analyzed in this article. Finally, the equivalent damping ratio of Shenzhen Airport is obtained using the energy theory.

Diagonal Dominance and the Decoupling Approximation in Damped Discrete Linear Systems

2007 ◽  
Author(s):  
Matthias Morzfeld ◽  
Nopdanai Ajavakom ◽  
Fai Ma
Keyword(s):  
Diagonal Element ◽  
Diagonal Dominance ◽  
Damping Matrix ◽  
Damped System ◽  
Modal Damping ◽  
Principal Coordinates ◽  
Discrete Linear Systems ◽  
Modal Coupling ◽  
Decoupling Approximation ◽  
Damped Systems

The principal coordinates of a non-classically damped linear system are coupled by nonzero off-diagonal element of the modal damping matrix. In the analysis of non-classically damped systems, a common approximation is to ignore the off-diagonal elements of the modal damping matrix. This procedure is termed the decoupling approximation. It is widely accepted that if the modal damping matrix is diagonally dominant, then errors due to the decoupling approximation must be small. In addition, it is intuitively believed that the more diagonal the modal damping matrix, the less will be the errors in the decoupling approximation. Two quantitative measures are proposed in this paper to measure the degree of being diagonal dominant in modal damping matrices. It is demonstrated that, over a finite range, errors in the decoupling approximation can continuously increase while the modal damping matrix becomes more and more diagonal with its off-diagonal elements decreasing in magnitude continuously. An explanation for this unexpected behavior is presented. Within a practical range of engineering applications, diagonal dominance of the modal damping matrix may not be sufficient for neglecting modal coupling in a damped system.

Free Vibration Analysis of Frame-Core Tube Structures Attached with Damped Outriggers

2012 ◽  
Vol 238 ◽  
pp. 648-651
Author(s):  
Zhi Hao Wang
Keyword(s):  
Damping Ratio ◽  
Free Vibration Analysis ◽  
Structural System ◽  
Viscous Dampers ◽  
Core Tube ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
New Energy ◽  
Energy Dissipation System ◽  
Simplified Calculation

The classical outrigger in frame-core tube structure cantilevering from the core tube or shear wall connected to the perimeter columns directly, which can effectively improve the lateral stiffness of the structure. A new energy-dissipation system for such structural system is studied, where the outrigger and perimeter columns are separate and vertical viscous dampers are equipped between the outrigger and perimeter columns to make full use of the relative big displacement of two components. The effectiveness of proposed system is evaluated by means of the modal damping ratio based on the proposed simplified model. The mathematic models of the structural system are obtained with both the assumed mode shape method and finite element method according to the simplified calculation diagram. Based on the modal damping ratio, the optimal damping coefficients of linear viscous dampers are determined, and effectiveness of proposed system is confirmed.

scholarly journals Equivalent Modal Damping Ratios of a Composite Tube-Type Tall Building to Dynamic Wind Loading

1996 ◽  
Vol 3 (2) ◽  
pp. 99-105 ◽  
Author(s):  
B.C. Huang ◽  
K.M. Lam ◽  
A.Y.T. Leung ◽  
Y.K. Cheung
Keyword(s):  
Damping Ratio ◽  
Computing Methods ◽  
Tall Building ◽  
Wind Loading ◽  
Composite Tube ◽  
Equivalent Damping ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Detailed Method ◽  
Tube Type

This article discusses computing methods of the equivalent modal damping ratio for a composite tube-type tall building. The equivalent damping ratio of a composite structure under wind-induced vibrations encompasses the combined effects from the different values of damping, mass, and stiffness of the external and internal tubes. A detailed method incorporating Rayleigh damping and the transfer matrix method is proposed for the determination of the equivalent modal damping ratio. A simplified method for engineering applications is also proposed. Results for a 40-story building are presented exemplifying the computation and relationships between the properties of the external and internal tubes.

Characterization of Modal Coupling in Nonclassically Damped Systems

1992 ◽  
Author(s):  
F. Ma ◽  
I. W. Park ◽  
J. S. Kim
Keyword(s):  
Large Scale ◽  
Substantial Reduction ◽  
Computational Effort ◽  
Frequency Separation ◽  
Common Procedure ◽  
Damping Matrix ◽  
Natural Modes ◽  
Modal Damping ◽  
Modal Coupling ◽  
Damped Systems

Abstract A common procedure in the solution of a nonclassically damped linear system is to neglect the off-diagonal elements of the associated damping matrix. For a large-scale system, substantial reduction in computational effort is achieved by this method of decoupling the system. Clearly, the decoupling approximation is valid only if modal coupling can somehow be neglected. The purpose of this paper is to study the characteristics of modal coupling, which is amenable to a complex representation. An analytical formulation that facilitates the evaluation of modal coupling is developed. Contrary to widely accepted beliefs, it is shown that neither frequency separation of the natural modes nor strong diagonal dominance of the modal damping matrix would be sufficient to suppress the sometimes significant effect of modal coupling.

scholarly journals Model Updating for Systems with General Proportional Damping Using Complex FRFs

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Xinhai Wu ◽  
Huan He ◽  
Yang Liu ◽  
Guoping Chen
Keyword(s):  
Model Updating ◽  
Damping Ratio ◽  
Viscous Damping ◽  
Rayleigh Damping ◽  
Damping Matrix ◽  
Modal Damping Ratio ◽  
Modal Damping ◽  
Resonance Frequencies ◽  
Updating Procedure ◽  
Damping Model

In this paper, we propose a model updating method for systems with nonviscous proportional damping. In comparison to the traditional viscous damping model, the introduction of nonviscous damping will not only reduce the vibration of the system but also change the resonance frequencies. Therefore, most of the existing updating methods cannot be directly applied to systems with nonviscous damping. In many works, for simplicity, the Rayleigh damping model has been applied in the model updating procedure. However, the assumption of Rayleigh damping may result in large errors of damping for higher modes. To capture the variation of modal damping ratio with frequency in a more general way, the diagonal elements of the modal damping matrix and relaxation parameter are updated to characterize the damping energy dissipation of the structure by the proposed method. Spatial and modal incompleteness are both discussed for the updating procedure. Numerical simulations and experimental examples are adopted to validate the effectiveness of the proposed method. The results show that the systems with general proportional damping can be predicted more accurately by the proposed updating method.

Optimal Method for Determination of Rayleigh Damping Co-efficients for Different Materials using Modal Analysis

2021 ◽  
Vol 13 (1) ◽  
Author(s):  
B. Rahul ◽  
J. Dharani ◽  
R. Balaji
Keyword(s):  
Boundary Conditions ◽  
Dynamic Analysis ◽  
Modal Analysis ◽  
Degrees Of Freedom ◽  
Damping Ratio ◽  
Optimal Method ◽  
Multiple Degrees Of Freedom ◽  
Rayleigh Damping ◽  
Damping Matrix

Rayleigh damping co-efficients are the essential parameters to determine the damping matrix of a system in dynamic analysis. For the systems with multiple degrees of freedom, it is difficult to arrive for suitable Rayleigh damping co-efficients. This paper represents a simple and effective method for the determination of Rayleigh co-efficients α and β for the system with multiple degrees of freedom. An unrealistic constant damping ratio for all modes is assumed to get rational value of α and β, which leads the determination of progressively varying damping ratio for all modes. By comparing the damping ratio arrived from assumed α and β with assumed unrealistic damping ratio, the suitable and most precise values are determined. This method is implemented for different materials with different boundary conditions by considering different significant modes and the effect of above parameters on α and β values are also discussed.

Characteristics of Modal Coupling in Nonclassically Damped Systems Under Harmonic Excitation

1994 ◽  
Vol 61 (1) ◽  
pp. 77-83 ◽  
Author(s):  
I. W. Park ◽  
J. S. Kim ◽  
F. Ma
Keyword(s):  
Harmonic Excitation ◽  
Frequency Separation ◽  
Diagonal Dominance ◽  
Normal Coordinates ◽  
Damping Matrix ◽  
Damped System ◽  
Natural Modes ◽  
Modal Damping ◽  
Modal Coupling ◽  
Damped Systems

The normal coordinates of a nonclassically damped system are coupled by nonzero off-diagonal elements of the modal damping matrix. The purpose of this paper is to study the characteristics of modal coupling, which is amenable to a complex representation. An analytical formulation is developed to facilitate the evaluation of modal coupling. Contrary to widely accepted beliefs, it is shown that enhancing the diagonal dominance of the modal damping matrix or increasing the frequency separation of the natural modes need not diminish the effect of modal coupling. The effect of modal coupling may even increase. It is demonstrated that, within the practical range of engineering applications, neither diagonal dominance of the modal damping matrix nor frequency separation of the natural modes would be sufficient for neglecting modal coupling.

scholarly journals Estimation of Modal Dampings for Unmeasured Modes

2012 ◽  
Vol 20 (4) ◽  
pp. 17-27 ◽  
Author(s):  
Ferenc Pápai ◽  
Sondipon Adhikari ◽  
Bor-Tsuen Wang
Keyword(s):  
Structural Analysis ◽  
Damping Ratio ◽  
Element Model ◽  
Analytical Form ◽  
Damping Matrix ◽  
Damping Characteristics ◽  
Modal Damping ◽  
Rate Versus ◽  
Regression Functions ◽  
Points Of View

ABSTRACTDamping effects are of great interest for structural analysis and evaluations. Structuralmodal damping characteristics can be obtained from experiments. This paper introducesnew possibilities for the modelling of the damping of a dynamic system with classical normalmodes and provides an overview of the known methods for formulating a damping matrixbase with experimental modal damping values. The proposed method offers an opportunityto extrapolate modal damping values for unmeasured modes by a regression method basedon the measured modal properties. The points of view on the choice of an analytical formfor damping regression functions are examined. An analytical form of regression functionscan be chosen as the modal decay rate versus the square of the frequency or the modaldamping ratio versus the frequency. Damping regressions can be performed based ona group of typical vibration modes, such as bending, torsion and lateral, symmetrical oranti-symmetrical modes. The regression data obtained for the damping constants can thenbe applied in a finite element model for further structural analysis.

scholarly journals Modal analysis and insights into damping phenomena of a special vibration chain

2021 ◽  
Author(s):  
Peter C. Müller ◽  
Wolfgang E. Weber
Keyword(s):  
Fluid Flow ◽  
Modal Analysis ◽  
Mode Shape ◽  
Mode Shapes ◽  
Hydraulic Systems ◽  
Practical Applications ◽  
Damping Matrix ◽  
Modal Damping ◽  
Future Work

AbstractVibration chains are of interest in many fields of practical applications. In this contribution, a modal analysis of the rather special Mikota’s vibration chain  is performed. Herein, focus is set on the mode shapes of this multibody oscillator, which was firstly introduced by Mikota as a solid body compensator in hydraulic systems for filtering out fluid flow pulsations. The mode shapes show interesting properties, e.g. an increase in the polynomial representing the coordinates of each mode shape with an increasing eigenfrequency associated with the respective mode shape. This and other properties are discussed exemplary. Some of these properties still have to be proven, which is the task of future work. Additionally, modal damping of Mikota’s vibration chain is discussed. Moreover, an approach for determining the damping matrix for given Lehr’s damping measures without knowing the mode shapes in advance is introduced. This approach involves the determination of a matrix root.

Effect of Bass Bar Tension on Modal Parameters of a Violin's Top Plate

2015 ◽  
Vol 39 (1) ◽  
pp. 145-149 ◽  
Author(s):  
Ewa B. Skrodzka ◽  
Bogumił B.J. Linde ◽  
Antoni Krupa
Keyword(s):  
Modal Analysis ◽  
Experimental Modal Analysis ◽  
Mode Shapes ◽  
Modal Parameters ◽  
Normal Value ◽  
Modal Damping

Abstract Experimental modal analysis of a violin with three different tensions of a bass bar has been performed. The bass bar tension is the only intentionally introduced modification of the instrument. The aim of the study was to find differences and similarities between top plate modal parameters determined by a bass bar perfectly fitting the shape of the top plate, the bass bar with a tension usually applied by luthiers (normal), and the tension higher than the normal value. In the modal analysis four signature modes are taken into account. Bass bar tension does not change the sequence of mode shapes. Changes in modal damping are insignificant. An increase in bass bar tension causes an increase in modal frequencies A0 and B(1+) and does not change the frequencies of modes CBR and B(1-).

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