A Study of the Roll Motion by Means of a Free Decay Test

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Hamid Zeraatgar ◽  
Mohsen Asghari ◽  
Firooz Bakhtiari-Nejad
Keyword(s):  
Damping Ratio ◽  
Nonlinear Damping ◽  
Damping Coefficient ◽  
Roll Motion ◽  
Damping Force ◽  
Restoring Force ◽  
Cubic Form ◽  
Damping Coefficients ◽  
Decay Test ◽  
Nonlinear Form

In this study, a method for the extraction of damping by tracing free roll decay is presented. For this purpose, in calm waters, a bulk carrier model is given a large initial roll angle and then released. Consequently, the roll motion is recorded. Restoring coefficients and virtual moments of inertia for the model are determined by means of an inclining test and recording the damped period, respectively. The linear damping coefficient is evaluated by using the damping ratio. Four different forms of combinations of restoring moment and damping coefficient are assumed in order to determine the nonlinear form of the roll motion. These equations are numerically solved for various damping coefficients and results are compared with the experimental data. By virtue of this comparison, the damping coefficients are determined for each case. It may be concluded that the use of the nonlinear restoring moment, which is an odd polynomial of the fifth order, and the cubic form for the nonlinear damping moment best fits the roll behavior for the ship model. The amount of energy dissipated by the damping moments is also calculated in the time domain. The energy method also confirms that the nonlinear form of restoring force in conjunction with the cubic form of the damping force is the best solution of the roll motion for small to large angles.

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.

Dynamic Property Analysis of Damping Rubber in Rail Fastenings under Different Deformation Condition

2014 ◽  
Vol 494-495 ◽  
pp. 706-710
Author(s):  
Bin Zhang ◽  
Yan Yun Luo ◽  
Zhi Nan Shi
Keyword(s):  
Mechanical Model ◽  
Dynamic Stiffness ◽  
Excitation Frequency ◽  
Nonlinear Damping ◽  
Deformation Condition ◽  
Damping Force ◽  
Restoring Force ◽  
Dynamic Mechanical ◽  
Large Distortion ◽  
Hydraulic Servo

This paper studies the experimental research on dynamic characteristics of the damping rubber in high elastic fastening by the electro-hydraulic servo movement tester. Based on a hypothesis superposition theory of nonlinear elastic restoring force and nonlinear damping force, a non-linear dynamic mechanical model is proposed. The dynamic stiffness and damping parameters of the rubber are obtained in different deformation conditions based on the dynamic mechanical model. The dynamic stiffness is analyzed, and the results show that dynamic stiffness is closely related to excitation frequency and amplitude. Furthermore the dynamic stiffness is analyzed under different free surface of rubber components by using FEM. That also reveals the changeable characteristics and affected factors of the damping rubber of the high elastic fastenings in large distortion condition.

Stochastic Resonance in Strongly Coupled Duffing and Van der pol Oscillators Under Trichotomous Noise and Bearing Fault Diagnosis

2019 ◽  
Vol 19 (03) ◽  
pp. 2050023
Author(s):  
Gang Zhang ◽  
Xia Wu ◽  
Tianqi Zhang
Keyword(s):  
Stochastic Resonance ◽  
Coupling Coefficient ◽  
Damping Coefficient ◽  
System Response ◽  
Damping Force ◽  
Van Der Pol ◽  
Restoring Force ◽  
Strongly Coupled ◽  
Force Coupling ◽  
Trichotomous Noise

Weak signal detection is an important topic, which has been widely studied in various fields. Different from other signal processing methods, stochastic resonance (SR) can utilize noise to enhance the characteristic frequency. Inspired by the unique advantage of SR, the strongly coupled Duffing and Van der pol SR system (SCD-VSR) is investigated. The simulation results show that the relationship between the output average signal–noise ratio increase (MSNRI) and different jump values of trichotomous noise presents different odd symmetrical distribution. It is also found that a double SR phenomenon could be observed when the damping coefficient of Van der pol system is small. Moreover, as the damping coefficient of the Duffing system increases, the output response would become gradually smooth. In addition,a smaller damping force coupling coefficient combined with a large restoring force coupling coefficient would achieve better system response. In the case of detecting an analog signal, MSNRI of SCD-VSR is larger than that of both classical bistable SR system (CBSR) and coupled Duffing SR system (CDSR). In addition, the experiments suggest that SCD-VSR could obtain a higher MSNRI and better detection effect, which implies the performance is superior to CBSR and CDSR.

PWR Fuel Assembly Damping Characteristics

2006 ◽  
Author(s):  
Roger Y. Lu ◽  
David D. Steel
Keyword(s):  
Fuel Assembly ◽  
Temperature Effect ◽  
Damping Ratio ◽  
Damping Coefficient ◽  
Low Flow ◽  
Published Data ◽  
Viscous Damping ◽  
Flowing Water ◽  
Damping Coefficients ◽  
Flow Velocities

PWR fuel assembly damping is a key parameter in seismic/LOCA safety analysis. The damping coefficients of a fuel assembly in air, still water and flowing water are significantly different. Several researchers and engineers have published their results and methods in the past. With this paper, PWR fuel assembly damping was studied and tested in air, still water, and flowing water (including flowrate and temperature variation). The damping coefficients were obtained by the initial displacement and first response method. The coefficients are also compared with published data. Several conclusions are obtained. • The damping obtained from the tests in air gives the damping component of assembly structure damping. From the comparison of the damping in air with still water the amount of viscous damping can be determined. The viscous damping component is the effect of still water on damping. The amount of viscous damping is represented by the increase in the damping ratio from air to still water at room temperature. The results show that damping in still water is approximately two times the damping in air. • The temperature effect on damping in still water is minimal. In flowing water, the results show a very slight effect of temperature, as the damping slightly decreases with an increase in temperature. This temperature effect is much smaller than the data scatter observed in most damping measurement tests under the same test conditions. • The damping is significantly affected by flowing water. For relatively low flow velocities, compared to in-core conditions, the damping coefficient is around two times the damping in still water. For intermediate to high flow velocities, all damping coefficients are 2.5 times higher than that in still water. For high velocities and large displacement, the damping coefficient can be over 3 times higher than that in still water. The flow velocity appears to be acting on the system by suppressing the motion of the assembly. Additional damping due to flowing water is called hydraulic damping, which is generated by hydraulic force. When a fuel assembly vibrates in flowing water, the assembly is trying to change the flow direction and momentum, but the flow mass wants to retain its pure axial direction which suppresses the motion of the assembly.

Optimal Distribution of Damping Coefficients for Viscous Dampers in Buildings

2017 ◽  
Vol 17 (04) ◽  
pp. 1750054 ◽  
Author(s):  
Tzu Kang Lin ◽  
Jenn Shin Hwang ◽  
Kuan Hui Chen
Keyword(s):  
Damping Ratio ◽  
Optimization Method ◽  
Design Guidelines ◽  
Damping Coefficient ◽  
Optimal Distribution ◽  
Viscous Dampers ◽  
Moment Frame ◽  
Practical Applications ◽  
Soft Story ◽  
Damping Coefficients

Design guidelines for implementing viscous dampers to buildings have been broadly included in seismic design codes worldwide. Although the relationship between the damping coefficient of viscous dampers and the added damping ratio to the structure has been theoretically studied, the process of distributing the damping coefficient onto each story of a building has not been regulated by the codes. For practical applications, some distribution methods have been previously proposed. However, no comparison has been made between these proposed methods considering the controllability and design economy. In this paper, two search methods based on the genetic algorithms (GAs) are adopted to examine the optimal distribution of damping coefficients. The results are then compared with a variety of existing distribution methods. A comparison is made for the distribution methods assuming the same added damping ratio for the structure. Three two-dimensional frames are adopted in the comparison: a regular moment frame, a moment frame with a soft-story, and a setback building. The results indicated that similar seismic response reduction can be achieved by using different distribution methods if the supplemental damping ratio is the same, while the optimal story damping coefficient can be obtained by using the proposed optimization method. Moreover, the “story shear strain energy to efficient stories” (SSSEES) method, among others, offers advantages in terms of seismic reduction efficiency, economical design, and practical application simplicity.

Experimental Determination of Roll Damping Coefficient for FPSO

2014 ◽  
Author(s):  
Oliver A. Seelis ◽  
Longbin Tao
Keyword(s):  
Experimental Determination ◽  
Cross Section ◽  
Test Data ◽  
Transfer Functions ◽  
Damping Coefficient ◽  
Roll Damping ◽  
Damping Coefficients ◽  
Decay Test ◽  
Bilge Keel

The roll damping coefficient is a crucial parameter for several design and operational aspects of FPSOs. The accurate prediction of the coefficient is not a trivial task and generally performed experimentally. A polynomial linearization of the decay test data has been widely applied in the offshore industry. However, research has indicated that for FPSOs with rectangular cross section and attached bilge keels, this methodology may lead to inaccurate damping coefficients. This paper presents a study on the experimental determination of roll damping coefficients for FPSOs, obtained by free decay tests. For this purpose model tests are executed in the towing tank of the Marine Hydrodynamic Laboratory at Newcastle University. The model is based on the design of a purposely build FPSO, as typically applied in the central North Sea sector. The cross section of the FPSO is boxed shaped with a characteristic knuckle shaped bilge. The tests are conducted using three different bilge keel arrangements. The parametric change in bilge keel size results in the variation of the flow characteristics around the bilge knuckle. The damping coefficients are then established from the decay test data using a polynomial approach, a bi-linear approach and a hyperbolic approach. A comparison between the damping evolutions obtained with the different methodologies is performed for each bilge keel configuration. Further, a numerical model of the FPSO is created using DNVs Sesam software. With the established damping coefficients, damping matrices are manually defined as an input to Sesam and roll transfer functions are numerically established. The computational determined transfer functions are then compared against the RAOs obtained from the model tests in regular waves to determine the most appropriate methodology. The damping coefficient for the bare hull is well established by all three proposed methodologies. However, with the attached bilge keels the bi-linear and the hyperbolic methodologies produce damping coefficients reflecting the experimental results more accurately than the polynomial approach, indicating that the recently developed hyperbolic method is a valid alternative, and in certain cases, is more suitable to determine the roll damping coefficient. The experimental measurements could serve as a benchmark for further research and contribute to the practical application of FPSO roll damping determination.

The System Identification Analysis of the Rolling Motion Model for the Unmanned Boat

2014 ◽  
Vol 1037 ◽  
pp. 288-293
Author(s):  
Wang Lin Yang ◽  
Song Lin Yang ◽  
Sheng Zhang ◽  
Tian Yu Ma
Keyword(s):  
System Identification ◽  
Tilt Angle ◽  
Nonlinear Damping ◽  
Roll Motion ◽  
Motion Model ◽  
Cross Combination ◽  
Decay Test ◽  
Object Of Study ◽  
Identification Analysis ◽  
Visual Basic 6.0

In this paper, the author took an unmanned planting boat as the object of study and conducted a series of roll decay test on condition that the ship model was in different drafts and tilt angle. The author established eight kinds of mathematical model of roll decay motion model system identification by making a cross combination of linear or nonlinear righting moment and linear or nonlinear damping. Based on the principle of system identification, the author established the optimization calculation of the objective function. Then the author adapted the genetic algorithm of system identification program based on Visual Basic 6.0 and got eight kinds of identification programs. By identifying respectively the test data of the roll motion of the unmanned planting boat, the author confirmed the feasibility of the adapted program. Comparing large drafts and tilt angle identification results, the author found a reasonable hydrostatic roll motion equation of the unmanned planing boat in the case of large drafts and tilt angle, and made a preliminary analysis.

A New Damping Model for Nonlinear Stiffness Systems With Variable Preload Displacements and Constant Amplitude Decay Ratios

1994 ◽  
Vol 116 (1) ◽  
pp. 257-263 ◽  
Author(s):  
T. Xu ◽  
G. G. Lowen
Keyword(s):  
Energy Loss ◽  
Mathematical Description ◽  
Nonlinear Damping ◽  
Damping Coefficient ◽  
Nonlinear Stiffness ◽  
Constant Amplitude ◽  
Damping Force ◽  
Damping Model ◽  
Good Agreement

This study of the behavior of nonlinear stiffness systems with variable preload displacements and constant amplitude decay ratios showed that the energy loss per cycle is dependent on these preload displacements. By introducing a nonlinear damping force, which is a function of both displacement and velocity, the associated work per cycle can be made approximately the same function of the preload displacement as is the case for the energy loss. In this manner, it becomes possible to make the resulting damping coefficient essentially independent of the preload displacement. This new damping model was incorporated into the mathematical description of an over-running sprag clutch. Confirming experimentation showed very good agreement with computed results.

scholarly journals Displacement Transmissibility Characteristics of Harmonically Base Excited Damper Isolators with Mixed Viscous Damping

2013 ◽  
Vol 20 (5) ◽  
pp. 921-931 ◽  
Author(s):  
Xiaojuan Sun ◽  
Jianrun Zhang
Keyword(s):  
Damping Ratio ◽  
Harmonic Balance Method ◽  
Nonlinear Damping ◽  
Viscous Damping ◽  
Damping Force ◽  
Response Characteristics ◽  
Damping Characteristics ◽  
Linear Damping ◽  
Frequency Ratios ◽  
Good Agreement

The viscous damping force in the mixed form asfd(x˙)=c1x˙+c2|x˙|x˙can well describe damping characteristics of isolators and dampers in many cases. In this paper, performance characteristics of single-degree-of-freedom (SDOF) linear-stiffness isolators with mixed and piecewise mixed viscous damping are analytically examined under harmonic base excitation. Based on the first-order harmonic balance method (HBM), both relative and absolute displacement transmissibility expressions with the equivalent linear damping coefficient (ELDC) are given. And the analytical calculations show good agreement with the numerical results. Also, the influence of nonlinear damping on the response characteristics is investigated by comparing the transmissibility of linear and nonlinear systems. The resonant frequency always shifts to a lower value as the nonlinear damping component of the forcefd(x˙)=c1x˙+c2|x˙|x˙becomes stronger, and when the damping ratio in the corresponding linear model is relatively high, the relative transmissibility decreases at frequencies higher than the resonance frequency of the corresponding linear damping system and the absolute one increases for the frequency ratios above2. Finally, the displacement transmissibility of a nonlinear isolator with piecewise mixed viscous damping is discussed and the process shows research similarity with the non-piecewise case.

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