# Current Trends in Fluid Viscous Dampers with Semi-Active and Adaptive Behavior
## 3 Semi-Active Fluid Viscous Dampers
### Variable Orifices Fluid Viscous Dampers
#### 3.2.1 FVDs with Solenoid Valves  
Semi-active FVDs equipped with solenoid valves are made of a cylinder filled with hydraulic oil, a piston attached to a piston rod, and a valve in a bypass pipe that connects the two sides of the cylinder (see Figure 20a).  
These systems are also called variable stiffness FVDs since they are capable of varying the natural frequency of the controlled structure by changing the additional stiffness introduced by the damper, thus avoiding the resonant condition during earthquakes. The solenoid valve has two stages, namely an \"on phase\" and an \"off phase\". When the valve is closed, the flow of the fluid between the two chambers within the cylinder is prevented, and the device behaves as a rigid link that provides additional stiffness to the structure. If the damper is encased in a brace, an equivalent effective stiffness (\(\Delta K_{eff}\)) is transmitted to  
Figure 19: Application of MR dampers: (**a**) Tokyo National Museum of Emerging Science and Innovation [147]; (**b**) Dongting Lake cable-stayed bridge [155].  
Figure 20: Variable stiffness damper: (**a**) section of the device [123]; (**b**) rheological model of the system composed of the damper and the brace (adapted from [46]).  
the building, which is a combination of the stiffness of the damper \((K_{D})\) and the stiffness of the brace \((K_{B})\), computed according to Equation (9):  
\[\Delta K_{eff}=\frac{K_{D}K_{B}}{K_{D}+K_{B}} \tag{9}\]  
On the contrary, when the valve is open, the fluid is free to flow between the two chambers through the bypass pipe, and there is no stiffening effect. In this configuration, the damper provides certain damping (\(C_{D}\)) [46], and the constitutive behavior corresponds to the mathematical model of a single dashpot, as shown in Figure 4.  
[PERSON] et al. [156] proposed a variable stiffness device (VSD) composed of a cylinder with two chambers that are connected by a pipe in which the solenoid valve is inserted. This system needs a low-power source to work (20 W); if the power is interrupted, the valve automatically closes the pipe that connects the two chambers, guaranteeing the protection of the structure in every situation.  
[PERSON] et al. [157] focused on variable stiffness FVDs too, in order to reduce the vibrations induced by earthquakes or by winds on cable-stayed bridges, demonstrating that these systems were able to reduce the displacement of the deck and the shear and bending moment of the bridge's towers. [PERSON] and [PERSON] [123] studied a semi-active variable stiffness damper to find the optimal stiffness ratio to be introduced into the structure. In particular, they performed a parametric study on possible structural configurations by considering different damper deployments. Their results showed that the floor displacements diminished by increasing the stiffness of the dampers and, thanks to the dissipated energy, the inter-story drifts and the top floor's acceleration were consistently reduced. [PERSON] and [PERSON] [158] studied the efficiency of an FVD with a solenoid valve applied in a single degree of freedom (SDOF) structure by demonstrating that this system allows a reduction in the displacement response greater than that obtained by a passive device.