Comparative Study of SDOF Response between Viscous Damping and Complex Damping Model

2011 ◽  
Vol 368-373 ◽  
pp. 938-941
Author(s):  
Rui Xue Chen ◽  
Ling Yun Peng ◽  
Wei Ming Yan
Keyword(s):  
Damping Ratio ◽  
Harmonic Excitation ◽  
Viscous Damping ◽  
Natural Period ◽  
Displacement Spectra ◽  
Earthquake Records ◽  
The Difference ◽  
Velocity Spectra ◽  
Damping Model ◽  
Complex Damping

This article summarizes the work regarding the complex and viscous damping models of SDOF system. Through calculating dynamic equations based on harmonic excitation, the result is that: when the excitation's period is less than the structure natural period, the displacement, velocity, acceleration responses of the complex damping system are stronger than the latter. Further, the displacement and the velocity spectra of some representative earthquake records are provided of two models, which show the similar trend as harmonic excitation. But the absolute acceleration spectra values of the complex damping model are higher than the other one at most time. And generally with the growing damping ratio and structure natural period, the difference is more significant. Under certain earthquake records, the structure displacement spectra values may differ by 17%, the velocity values differ by 20%, the acceleration values differ by 15%.

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.

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.

Anti-Seismic Energy Dissipation of Structures with Stress-Dependent Complex Damping with Consideration of Zero Amplitude Damping

2010 ◽  
Vol 163-167 ◽  
pp. 358-365
Author(s):  
Hui Dong Zhang ◽  
Yuan Feng Wang
Keyword(s):  
Energy Dissipation ◽  
Evaluation Method ◽  
Damping Ratio ◽  
Fuzzy Evaluation ◽  
Equivalent Viscous Damping ◽  
Amplitude Damping ◽  
Stress Dependent ◽  
Damping Theory ◽  
Damping Model ◽  
Complex Damping

Under most cases, the non-liner energy dissipation is approximately replaced with Rayleigh damping model which belongs to Maxwell-Kelvin type, the method is a fuzzy evaluation method of damping. Based on complex damping theory, equivalent dynamics equation of complex damping model is derived and loss factor is discussed, the accuracy of the equation is theoretically confirmed in this paper. Based on the existing damping theories, a new damping model is proposed, which is a zero amplitude damping model combing with stress dependent complex damping model. The model is used in seismic resistance analysis. Taking a steel beam for an example, the relationship between response amplitude and damping ratio is analyzed with the new damping model. It shows that the method of stress-dependent damping with consideration of zero amplitude damping can precisely describe the energy input and energy dissipation principles and the dynamic response under seismic loads can be precisely obtained. A solid foundation is laid for the further study of complex damping theory, its equivalent viscous damping model and engineering application.

A Resonance Chart for Damped Vibration

1955 ◽  
Vol 59 (540) ◽  
pp. 850-852 ◽  
Author(s):  
R. E. D. Bishop
Keyword(s):  
Linear System ◽  
Convenient Method ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Viscous Damping ◽  
Similar Form ◽  
Hysteretic Damping ◽  
Resonance Curves ◽  
Phase Angles

A convenient method is pointed out for calculating the response of a damped linear system with one degree of freedom to harmonic excitation. Results of such calculations are usually represented by the familiar “ resonance curves ”—one curve being plotted for each intensity of damping. These curves are not particularly convenient to use and Yates has overcome several of their defects by throwing them into a nomographic form. Yates' nomogram is based upon the concept of viscous damping and it does not give the information of a conventional set of resonance curves in that it relates to the velocity of vibration. By changing over to hysteretic damping, a nomogram of somewhat similar form may be constructed such that it gives amplitudes and phase angles of displacements while retaining the advantages, over resonance curves, of this form of representation.

Energy Balancing Method to Identify Nonlinear Damping of Bolted-Joint Interface

2016 ◽  
Vol 693 ◽  
pp. 318-323 ◽  
Author(s):  
Xin Liao ◽  
Jian Run Zhang
Keyword(s):  
Dry Friction ◽  
Harmonic Excitation ◽  
Joint Interface ◽  
Damping Factor ◽  
Viscous Damping ◽  
Bolted Joint ◽  
Energy Balancing ◽  
Stick Slip ◽  
Non Linear ◽  
Linear Damping

The interface of bolted joint commonly focuses on the research of non-linear damping and stiffness, which affect structural response. In the article, the non-linear damping model of bolted-joint interface is built, consisting of viscous damping and Coulomb friction. Energy balancing method is developed to identify the dry-friction parameter and viscous damping factor. The corresponding estimation equations are acquired when the input is harmonic excitation. Then, the vibration experiments with different bolted preloads are conducted, from which amplitudes in various input levels are used to work out the interface parameters. Also, the fitting curves of dry-friction parameters are also obtained. Finally, the results illustrate that the most interface of bolted joint in lower excitation levels occurs stick-slip motion, and the feasibility of the identification approach is demonstrated.

The Dynamic Response of a Simple Elastic System to Antisymmetric Forcing Functions Characteristic of Airplanes in Unsymmetric Landing Impact

1949 ◽  
Vol 16 (3) ◽  
pp. 310-316
Author(s):  
Joseph B. Woodson
Keyword(s):  
Dynamic Response ◽  
Sine Wave ◽  
Response Curves ◽  
Response Factors ◽  
Natural Period ◽  
Wave Pulse ◽  
Pulse Disturbance ◽  
Landing Impact ◽  
Forcing Functions ◽  
The Difference

Abstract This paper presents an analysis of the dynamic response of an undamped mechanical system with one degree of freedom subjected to disturbances which are described by antisymmetric forcing functions. The analysis was undertaken to throw light on the effect on the vibration of the wings caused by unsymmetric landing impact of an airplane. Two types of disturbances are considered; a full-sine-wave pulse, and a pulse which is the difference between two overlapping half sine waves. The results are presented in the form of dynamic-response curves and dynamic-response-factor curves. The numerically greatest dynamic-response factors, approximately 3.24 and −3.26, resulted for a full-sine-wave pulse disturbance with a ratio of duration of impact to natural period, Ti/T ≅ 1.11. When Ti/T is in the neighborhood of 1, the first positive peak of dynamic response is numerically less than the negative and positive peaks which follow it. For much of the range, the positive and negative dynamic-response factors are numerically approximately equal. The analysis was confined to values of Ti/T between 0.33 and 12. As Ti/T increases without limit, the positive and negative dynamic-response factors tend to 1 and −1, respectively.

A statistical study on artificially generated earthquake records

1976 ◽  
Vol 3 (1) ◽  
pp. 11-19
Author(s):  
W. K. Tso ◽  
B. P. Guru
Keyword(s):  
Statistical Study ◽  
Spectral Response ◽  
Flexible Structures ◽  
Time History ◽  
Maximum Response ◽  
Response Analysis ◽  
Seismic Region ◽  
Natural Period ◽  
Earthquake Records ◽  
Time History Response

A statistical study has been done to investigate (i) the variation of spectral responses of structures due to artificially generated earthquake records with identical statistical properties, (ii) the effect of duration of strong shaking phase of artificial earthquakes on the response of structures, and (iii) the number of earthquake records needed for time-history response analysis of a structure in a seismic region. The results indicate that the flexible structures are more sensitive to the inherent statistical variations among statistically identical earthquake records. Consequently several records must be used for time-history response analysis. A sample of eight or more records appear to provide a good estimate of mean maximum response. The duration of strong shaking can significantly affect the maximum response. Based on the results, it is suggested that for the purpose of estimating peak response, the strong shaking duration of the input earthquake motion should be at least four times the natural period of the structure. The maximum responses due to statistically identical ground motion records are observed to fit approximately the type 1 extreme value distribution. Thus, it is rationally possible to choose a design value based on the mean, standard deviation of the spectral response values and tolerable probability of exceedance.

scholarly journals INFLUENCE OF MATERIAL DAMPING ON THE RESPONSE OF UNDERGROUND STRUCTURES SUBJECTED TO EARTHQUAKE

2020 ◽  
Vol 26 ◽  
pp. 64-70
Author(s):  
Veronika Pavelcová ◽  
Tereza Poklopová ◽  
Michal Šejnoha ◽  
Tomáš Janda
Keyword(s):  
Damping Ratio ◽  
Underground Structure ◽  
Eurocode 8 ◽  
Viscous Damping ◽  
Material Damping ◽  
Underground Structures ◽  
Fixed Boundary ◽  
Design Spectrum ◽  
Rayleigh Damping ◽  
Element Simulation

The paper describes a finite element simulation of the response of a real underground structure subjected to earthquake using GEO5 FEM program. It concentrates on the influence of material damping with respect to a specific type of boundary condition prescribed at the bottom of the analyzed domain. It is seen that considering material damping is inevitable particularly in case of so called fixed boundary conditions to arrive at meaningful results. This is demonstrated on an artificial earthquake generated according to a design spectrum defined in Eurocode 8. A viscous damping ratio combined with the results of eigenvalue analysis is used to derive parameters of Rayleigh damping for three specific scenarios promoting the approach based on the lowest natural frequency as sufficiently accurate for the present task.

scholarly journals A New Semisubmersible Design for Improved Heave Motion, Vortex-Induced Motion and Quayside Stability

2011 ◽  
Author(s):  
Qi Xu
Keyword(s):  
Floating Platform ◽  
Natural Period ◽  
Suppression Effect ◽  
Structural Rigidity ◽  
Hull Design ◽  
Induced Motion ◽  
Steel Catenary Risers ◽  
The Difference ◽  
Touchdown Point ◽  
Heave Motion

Recently the semisubmersible has become a favorable choice as a wet-tree floating platform supporting steel catenary risers (SCRs), mainly due to its capability of quayside topside integration and cost-effectiveness. However, it is still a challenge for a conventional semisubmersible to support SCRs, particularly large ones, in harsh environment and relatively shallow water due to its large heave motion. To answer this challenge, a new semisubmersible design has been developed at Technip as a wet-tree floater which achieves significantly improved heave motion and vortex-induced-motion (VIM) performance through hull form optimization while maintaining the simplicity of a conventional semisubmersible design. The difference between the NexGen semi-submersible design and a conventional semi-submersible design is in the blisters attached to the columns, distribution of pontoon volume, and pontoon cross section shape. In the NexGen semi-submersible design, the pontoon volume is re-distributed to minimize heave loading while maintaining sufficient structural rigidity, a long heave natural period and adequate quayside buoyancy. The blisters attached to the columns effectively break the vortex shedding coherence along the column length and therefore suppresses VIM. The blisters also provide much needed stability at quayside and during the hull deployment process, making the hull design less sensitive to topside weight increase. In the present paper the hydrodynamic aspects of this new design are discussed in detail. A benchmark case is presented in which the new design is compared against a more conventional design with the same principal dimensions. It is shown that the heave response in extreme sea states (100-yr hurricane) at the platform center of gravity is reduced by about 30–40%, and at the SCR hang-off locations by about 25–30%. Due to the reduced heave motion, SCRs experience about one third less stress at the touchdown point. A qualitative VIM analytical model is used to predict the VIM suppression effect of the new design. A highlight of a VIM model test for the proposed design is also presented. The reduced heave and VIM significantly improve the riser stress and fatigue near the touchdown point. This new design makes the semisubmersible a more robust wet-tree floater concept, and even a potentially good candidate as a dry-tree host concept in relatively benign environment.

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