scholarly journals Computation of Rayleigh Damping Coefficients for the Seismic Analysis of a Hydro-Powerhouse

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Zhiqiang Song ◽  
Chenhui Su
Keyword(s):  
Seismic Response ◽  
Seismic Analysis ◽  
Damping Ratio ◽  
Least Square Method ◽  
Least Square ◽  
Dynamic Responses ◽  
Damping Coefficients ◽  
Rayleigh Damping ◽  
Damping Matrix ◽  
Fundamental Frequencies

The mass and stiffness of the upper and lower structures of a powerhouse are different. As such, the first two vibration modes mostly indicate the dynamic characteristics of the upper structure, and the precise seismic response of a powerhouse is difficult to obtain on the basis of Rayleigh damping coefficients acquired using the fundamental frequencies of this structure. The damping ratio of each mode is relatively accurate when the least square method is used, but the accuracy of the damping ratios that contribute substantially to seismic responses is hardly ensured. The error of dynamic responses may even be amplified. In this study, modes that greatly influence these responses are found on the basis of mode participation mass, and Rayleigh damping coefficients are obtained. Seismic response distortion attributed to large differences in Rayleigh damping coefficients because of improper modal selection is avoided by using the proposed method, which is also simpler and more accurate than the least square method. Numerical experiments show that the damping matrix determined by using the Rayleigh damping coefficients identified by our method is closer to the actual value and the seismic response of the powerhouse is more reasonable than that revealed through the least square method.

The Influence of Support Hardware and Piping System Seismic Response on Snubber Support Damping

1997 ◽  
Vol 119 (4) ◽  
pp. 451-456 ◽  
Author(s):  
C. Lay ◽  
O. A. Abu-Yasein ◽  
M. A. Pickett ◽  
J. Madia ◽  
S. K. Sinha
Keyword(s):  
Seismic Response ◽  
Fundamental Frequency ◽  
Damping Ratio ◽  
Damping Coefficient ◽  
Piping System ◽  
Nodal Displacement ◽  
Damping Coefficients ◽  
Fundamental Frequencies ◽  
Piping Systems

The damping coefficients and ratios of piping system snubber supports were found to vary logarithmically with pipe support nodal displacement. For piping systems with fundamental frequencies in the range of 0.6 to 6.6 Hz, the support damping ratio for snubber supports was found to increase with increasing fundamental frequency. For 3-kip snubbers, damping coefficient and damping ratio decreased logarithmically with nodal displacement, indicating that the 3-kip snubbers studied behaved essentially as coulomb dampers; while for the 10-kip snubbers studied, damping coefficient and damping ratio increased logarithmically with nodal displacement.

A constrained optimal Rayleigh damping coefficients for structures with closely spaced natural frequencies in seismic analysis

2016 ◽  
Vol 20 (1) ◽  
pp. 81-95 ◽  
Author(s):  
DG Pan ◽  
GD Chen ◽  
LL Gao
Keyword(s):  
Seismic Analysis ◽  
Lattice Structure ◽  
Damping Ratio ◽  
Optimization Method ◽  
Accurate Analysis ◽  
Damping Coefficients ◽  
Rayleigh Damping ◽  
Optimal Load ◽  
Parametric Studies ◽  
Response Spectral Analysis

A constrained optimization method is proposed to determine Rayleigh damping coefficients for the accurate analysis of complex structures. To this end, an objective function was defined to be a complete quadratic combination of the modal errors of a peak base reaction evaluated by response spectral analysis. An optimization constraint was enforced to make the damping ratio of a prominent contribution mode exact. Parametric studies were conducted to investigate the effects of the constraint, the cross term of modes, and weighting factors on the optimization objective. A two-story building and a real-world lattice structure were analyzed under six earthquake ground motions to understand the characteristics and demonstrate the accuracy and effectiveness of the proposed optimization method. Unlike the conventional Rayleigh damping, the optimization method provided an optimal load-dependent reference frequencies that account for varying frequency characteristics of earthquakes around the prominent contribution mode.

Study on Seismic Response Characteristics of Double Cables Suspension Bridge

2011 ◽  
Vol 105-107 ◽  
pp. 408-411
Author(s):  
Nan Hong Ding ◽  
Li Xia Lin ◽  
Yong Jiu Qian ◽  
Lei Huang
Keyword(s):  
Seismic Response ◽  
Damping Ratio ◽  
Dynamic Performance ◽  
Equations Of Motion ◽  
Suspension Bridge ◽  
Dynamic Responses ◽  
Independent Effect ◽  
Shape Coefficient ◽  
Response Characteristics ◽  
Coupled Equations

Damping in double Cables suspension bridge composed of steel reinforcement beams and reinforced concrete tower is non-classical, which leads to coupled equations of motion in main coordinate system. Based on the complex damping theory, the viscous damping ratio is solved, which can be used to describe energy dissipation characteristics of non-classical damping system approximately. Seismic response of double chains suspension bridge is analyzed through an example of double chains suspension bridge, considering the geometric nonlinearity and non-classical damping. And numerical calculation is presented for seismic response subjected to independent effect or combination effect of three orthogonal components of seismic wave. Single cable suspension bridge can be taken as a special case of double cable suspension bridge, after the main cable shape coefficient is introduced. The dynamic responses of double cable suspension bridge and single cable suspension bridge are compared to reveal the characteristics of Seismic Response of double cable suspension bridge. The study of the dynamic responses characteristics of double cable suspension bridge has a positive significance on structural form selection of such type bridge during designing, dynamic performance evaluation and reinforcement design has positive significance.

A New Method for the Identification of Coulomb and Viscous Friction

Tribology ◽  
2005 ◽  
Author(s):  
Lilan Liu ◽  
Hongzhao Liu ◽  
Ziying Wu ◽  
Daning Yuan
Keyword(s):  
Damping Ratio ◽  
Viscous Friction ◽  
Least Square Method ◽  
Least Square ◽  
New Method ◽  
Exponential Fitting ◽  
Viscous Damping ◽  
Equivalent Viscous Damping ◽  
Fitting Method ◽  
Friction Parameters

In this paper, a new method for simultaneously estimating Coulomb and viscous friction parameters from the free vibration of a damped oscillator is put forward. In the method, the nonlinear vibration equation with Coulomb and viscous friction is transformed into a linear procedure with equivalent viscous damping which is a function of velocity. The proposed method works well with both the displacement and velocity response data, while the case of zero velocity is not considered. From the displacement decaying curve, the equivalent viscous damping ratios are obtained by means of the local exponential fitting method, and different velocities corresponding to the equivalent viscous damping ratios are also obtained from the velocity decaying curve. Then, according to the relationship between the equivalent viscous damping ratio and the velocity, the Coulomb friction and the viscous damping are achieved using the least square method. The validity and accuracy of the proposed method are demonstrated through good simulation results.

Modal Parameter Identification of Time-Varying Systems Using the Time-Varying Multivariate Autoregressive Model

2005 ◽  
Author(s):  
Lilan Liu ◽  
Hongzhao Liu ◽  
Ziying Wu ◽  
Daning Yuan ◽  
Pengfei Li
Keyword(s):  
Parameter Identification ◽  
Linear Time ◽  
Damping Ratio ◽  
Least Square Method ◽  
Least Square ◽  
Time Varying ◽  
Recursive Least Square ◽  
Modal Parameter ◽  
Modal Parameter Identification ◽  
Multivariate Autoregressive

A new time-varying multivariate autoregressive (TVMAR) model method for modal parameter identification of linear time-varying (TV) systems with multi-output is introduced. Besides, a modified recursive least square method based on the traditional one is presented to determine the coefficient matrices of the TVMAR model. In the proposed method, multi-dimensional nonstationary response signals of the vibrating system can be processed simultaneously. Not only the TV modal frequency and damping ratio of the system, but also the changing behavior of the mode shape in the course of vibration are identified by the proposed procedure. Numerical simulations, in which a three-degree-of-freedom system with TV stiffness is respectively subjected to impulse excitation and white noise excitation, are presented. The validity and accuracy of the method are demonstrated by the good simulation results.

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.

Seismic Response Analysis of Double Chains Suspension Bridge Considering Non-Classical Damping

2011 ◽  
Vol 255-260 ◽  
pp. 826-830 ◽  
Author(s):  
Nan Hong Ding ◽  
Li Xia Lin ◽  
Jia De Chen
Keyword(s):  
Seismic Response ◽  
Seismic Analysis ◽  
Damping Ratio ◽  
Suspension Bridge ◽  
Response Analysis ◽  
Equivalent Viscous Damping ◽  
Damping Theory ◽  
Damping Model ◽  
Equivalent Viscous Damping Ratio ◽  
Complex Damping

Damping in double chains suspension bridge is non-uniform, which leads to coupled motion equations in main coordinate system. Based on the complex damping theory to solve equivalent viscous damping ratio used to describe energy dissipation characteristics of non-classical damping system approximately, a method is proposed to analyze seismic response of double chains suspension bridge considering non-classical damping modified by measured value. Influence of different damping forms on seismic response of double chains suspension bridge is analyzed, considering classical damping and non-classical damping respectively, through an example of double chains suspension bridge. The analysis shows that non-classical damping has significant effect on seismic response, and response based on the classical damping model is not reliable to double chains suspension bridge. Non-classical damping model should be used in seismic analysis of double chains suspension bridge, however, the seismic response of non-classical damping system under the longitudinal or vertical seismic wave can be substituted approximately by the seismic response calculated according to damping ratio of concrete tower and steel stiffening girder respectively, which can simplify the calculation during preliminary analysis.

Seismic Response Analysis of Tower Crane in Consideration of the Building-Crane Interaction

2013 ◽  
Vol 353-356 ◽  
pp. 1981-1985 ◽  
Author(s):  
Bing Ai ◽  
Jia Lin Yang ◽  
Zeng Zhuang Pei
Keyword(s):  
Seismic Response ◽  
Seismic Analysis ◽  
Dynamic Responses ◽  
Response Analysis ◽  
Analysis Method ◽  
Ansys Software ◽  
Seismic Response Analysis ◽  
3D Fem ◽  
Fem Model ◽  
Tower Crane

Interaction between buildings and tower has not been considered in former research..In this paper an integrated seismic analysis method is proposed considering the interaction between the building and the tower crane. A 3D-FEM model of the building and the crane is established with ANSYS software and seismic responses such as the displacement, the acceleration and the stress of the crane are analyzed. The sensitivity of the stiffness of the building on the dynamic responses is also analyzed. The results with consideration of the building-crane interaction, is higher than the results without interaction, and it becomes more significant with the increase of stiffness of the building.

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