Type 4 bell-shaped proportional damping model and energy dissipation for structures with inelastic and softening response

In this paper two methods for modelling the damping in a narrow gap are investigated. The first method is called the Pressure Damping Model. This method has been used in studies of wave energy devices. An attractive feature of this model is that the modified input is directly related to the energy dissipation in the gap, which means that if this dissipation is estimated the input to the model can be obtained directly. The idea of the method is to add a pressure input in the gap to suppress the resonant motion. A challenge with the method is that it contains a non-linear term. The second method is the Newtonian Cooling damping model. The method is based on introducing a dissipation term in the free surface boundary condition. This dissipation term contains a coefficient which is not directly related to the energy dissipation. Hence this method is not so easy to relate directly to the estimated energy dissipation. An advantage with this method is that it is linear and hence can be expected to be more robust. In the first part of the paper a 2-dimensional problem is investigated using both methods. In addition to the numerical performance and robustness, much focus is put on investigation of the energy balance in the solution, and we attempt to relate both models to the energy dissipation in the gap. In the second part the Newtonian cooling method is implemented in a 3-dimensional potential flow solver and it is shown that the method provides a robust way to handle the resonance problem. The method will give rise to a modified set of equations which are described. Two different problems are investigated with the 3D solver. First we look at a side-by-side problem, where the 3D results are also compared with 2D results. Finally, the moonpool problem is investigated by two different 3D solvers, a classical Green’s function based method and a Rankine solver. It is also shown how this damping model can be combined with a similar model on the internal waterplane to remove irregular frequencies.

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Influence of Nonviscous Damping on Seismic Inelastic Displacements

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455414500746 ◽

2015 ◽

Vol 15 (05) ◽

pp. 1450074 ◽

Cited By ~ 2

Author(s):

Y. H. Chai ◽

Mervyn J. Kowalsky

Keyword(s):

Energy Dissipation ◽

Weighting Function ◽

Ground Motions ◽

Fading Memory ◽

Viscous Damping ◽

Damping Force ◽

Near Fault ◽

Hereditary Model ◽

Damping Model ◽

System Characteristics

Viscous damping, which assumes a resisting force proportional to the instantaneous velocity, results in energy dissipation that increases linearly with frequency. Such energy dissipation, however, is not strongly supported by experiments. The energy dissipative characteristics of damping can be improved by nonviscous hereditary model, where the damping force is treated as dependent on the response history. A weighting function with built-in exponential decay can be used to represent the fading memory of damping where the recent history is given a greater influence over its distant past. This paper investigates the seismic response of structures using exponentially decaying nonviscous damping and compares the response with that of classical viscous damping. Preliminary results show an increase in inelastic displacements in the exponential damping model for both normal and near-fault ground motions. As part of the study, system characteristics of the exponential damping model are investigated.

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

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.163-167.358 ◽

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.

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