Viscous damper

Fig. 10.1. A vibrating system vvith one degree of freedom and its transfer fnnction. (a) The vibrating system. A mass M is connected to the frame through a spring and a viscous damper. Regarding STM, there are two realizations of this model. First, the frame represents the floor, and the mass represents the STM. Second, the frame represents the base plate (with the sample) in STM, and the mass represents the tip assembly, (b) The transfer function, which is the ratio of the vibration amplitude of the mass to that of the frame at different frequencies. (After Park and Quate, 1987.)...

The Maxwell model can be represented by a purely viscous damper and a purely elastic spring connected in series, as shown in the diagram. The model can be represented by the following equation ... 

Note that the simple Hooke s law behavior of the stress in a solid is analogous to Newton s law for the stress of a fluid. For a simple Newtonian fluid, the shear stress is proportional to the rate of strain, y (shear rate), whereas in a Hookian solid, it is proportional to the strain, y, itself. For a fluid that shares both viscous and elastic behavior, the equation for the shear stress must incorporate both of these laws— Newton s and Hooke s. A possible constitutive relationship between the stress in a fluid and the strain is described by the Maxwell model (Eq. 6.3), which assumes that a purely viscous damper described by Eq. 6.1 and a pure spring described by Eq. 6.2 are connected in series (i.e., the two y from Eqs. 6.1 and 6.2 are additive). 

Viscous damping on the other hand assumes a velocity-dependent damping, whose effect is proportional to the excitation frequency co. The damping force of a viscous damper with damping constant c is defined by... 

D is the dissipative potential that can introduce viscous dampers in the equations of motions, Q contains the general forces, and Lt contains the Lagrange multipliers. 

Cancellara D., De Angelis F. (2012)—Dynamic nonlinear analysis of an hybrid base isolation system with viscous dampers and friction sliders in parallel. Applied Mechanics and Materials, Vol. 234, pp. 96-101. 

FIGURE 10.6 Smgle.degieeK>f-fi elumped-parameter biodynamic model. The mass m is supported by a spring with stiffness k and viscous damper with resistance c. The transmis-sibility of motion to the mass is shown as a function of die fiequency ratio r (=aj/oib) when the base is subjected to a displacement (After Griffin, 1990.)... 

Now, imagine deforming the Maxwell model by applying a constant strain to it at a time t = 0. The deformation is held constant and the stress is monitored. Figure 2 shows the mechanical response of the Maxwell model to an applied deformation. The first (early time) response is that the material responds only elastically because the viscous damper initially behaves rigidly (at infinite rate of strain). The total deformation of the element remains constant, but it redistributes itself between the spring and the dashpot. This results in stress relaxation that occurs exponentially with time ... 

Reigles, D.G. 6c Symans, M.D. 2006. Supervisory fuzzy control of a base isolated benchmark building utilizing a neuro-fuzzy model of controllable fluid viscous dampers. Journal of Structural Control and Health Monitoring, 13, 724—747. 

Fu, Y. Kasai, K. 1998. Comparative study of frames using viscoelastic and viscous dampers. Journal of Structural Engineering 124(5) 513-522. 

Goel, R.K. 2005. Seismic response of linear and non-linear asymmetric systems with non-linear fluid viscous dampers. Earthquake Engineering Structural Dynamics 34(7) 825-846. 

In conventional building systems, the structural damping is a result of friction among the particles of the structural members. In the present case it is increased by adding viscous dampers in each story having a damping coefficient ca to the diagonal elements. 

The range of force control that is possible with a valve-mode MR fluid damper is illustrated in Fig. 6.78. Here the force/velocity character that is typical of a passive hydraulic damper is compared to the range of forces possible with a MR damper. With appropriate control based on displacement, velocity or acceleration, any force profile between the upper and lower bounds can be realized. Unlike passive viscous dampers, with the MR damper it is easy to achieve large force at very low speed. 

The dynamic response of civil engineering structures subjected to earthquake excitation can be reduced by using passive control systems such as energy dissipation devices (e.g. viscous dampers, etc.). The advantage of these systems with respect to active and semi-active control systems consist in the fact that they don t require any power supply, therefore are quite reliable and they require least maintenance. 

The preliminary design of viscous dampers of the framed stmcture can be done starting from the dynamic characteristics of the unbraced building and in particular from the fundamental period T. The approximate method is based on the following steps ... 

The index that maximizes the energy dissipated by the viscous dampers Jl) tends to locate dampers where the velocity is higher and this usually happens in the upper floors. Therefore this performance index moves the dampers in the uppers floors. Instead the index that maximizes the damping ratio (J2) is not very sensitive and it does not bring to realistic distributions. 

In the first step, a viscous damper was designed and used such that the fundamental mode has 25% damping ratio, when one damper is placed at every story unit (uniform distribution). The structural responses of the imiformly braced structure for different seismic events are shown in Figure 12. 

In order to show the applicability of the methodology for tall buildings, a 2D model of 30-story shear building has been considered for determining the optimal locations of viscous dampers, by optimizing the objective functions described in previous paragraph. The properties of the lateral story stiffness are summarized below... 

Passive energy dissipation systems (e g. viscous dampers, metallic dampers, friction dampers etc) have been used extensively for the protection of civil engineering structures against strong earthquakes, therefore in this chapter are shown and compared three practical search methods for the optimal placement and design of dampers. They are called ... 

Xsuji, M., Nakamura, X. (1996). Optimal viscous dampers for stififiiess design of shear buildings. Structural Design of Tall Buildings, 5, 217-234. doi 10.1002/(SICI)1099-1794( 199609)5 3<217 AID-XAL70>3.0. CO 2-R... 

Lavan, 0., Levy, R. (2006). Optimal design of supplemental viscous dampers for linear framed stmctures. Earthquake Engineering Structural Dynamics, 55(3), 337-356. doi 10.1002/eqe.524... 

Occhiuzzi, A. (2009). Additional viscous dampers for civil stmctures Analysis of design methods based on effective evaluation of modal damping ratios. EngineeringStructures,31(5), 1093-1101. doi 10.1016/j.engstmct.2009.01.006... 

Roh, H. S., Cimellaro, G. P. (2010). (in review). Fragility evaluation of stmctures with controlled rocking columns and viscous dampers. Journal of Earthquake Engineering. 

Trombetti, T., Silvestri, S. (2004). Added viscous dampers in shear-type structures The effectiveness ofmassproportional damping. Journal of Earthquake Engineering, 8 2), 275-313. doi 10.1080/13632460409350490... 

Optimal Placement of Viscous Dampers for Seismic Building Design... 

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