# Current Trends in Fluid Viscous Dampers with Semi-Active and Adaptive Behavior
## 2 Passive Fluid Viscous Damper  
Conventional FVDs with passive behavior are typically composed of a hollow cylinder filled with silicon oil (or a similar type of fluid) and a piston rod with a head provided with orifices [47], which divides the cylinder's inner volume into two chambers, as shown in Figure 2[31; 48]. When an external action excites the device, the piston moves, and the fluid is forced to pass from one chamber to the other through the orifices of the piston head. Once the fluid expands into full volume in the second chamber, it slows down and loses its kinetic energy into turbulence [48]. The different pressure between the two chambers produces the damping force [48; 49], while the friction forces triggered in the orifices of the piston head dissipate energy in the form of heat. If the damper is subjected to long-duration or large-amplitude motions, the internal temperature rise can be relevant [50; 51] and may cause damage to the damper. Moreover, the temperature rise reduces the viscosity of the fluid, affecting the effectiveness of the device [52]. Figure 2: Scheme of a classical passive FVD [47]. The piston rod is made of polished stainless steel and is sufficiently rigid to avoid buckling and bending under cyclic loading. The cylinder is normally a seamless steel tube designed to withstand the pressure generated by the internal fluid. Fluid conforming with the European standard EN15129 [15] must be fire-resistant, nontoxic, thermally stable, and not degrading with age. Moreover, it must be non-flammable and non-combustible. The silicone fluids normally employed in FVDs are thermally stable, completely nontoxic, and characterized by a flash point over 340 \({}^{\circ}\)C. Other fluids are allowed only if the requirements of EN15129 [15] are respected. Seals are used in order to avoid leakage of fluid from the damper. Since dampers may remain idle for long times, these seals must be free of long-term sticking and fluid seepage; for this reason, they are made of a high-strength structural polymer, such as Teflon, stabilized nylon, or acetyl resin family members. The accumulator, shown in Figure 2, accommodates changes in volume caused by the thermal expansion of the fluid and the volumetric displacements induced by the piston rod. The accumulator has the additional function of preventing undesirable restoring forces coming from the reduction in the volume of the fluid due to the piston rod movement [53]. The orifices control the flow of fluid across the piston head and, consequently, the level of energy dissipated by the damper. FVDs generally provide an equivalent viscous damping almost equal to 25% [48]. Indeed, as an example, a reinforced concrete structure equipped with FVDs is able to reach a total damping of 30%, where approximately 25% is the damping directly introduced by the dampers, while the remaining 5% corresponds to the structural damping. It must be recalled that FVDs do not affect the fundamental period of the structure thanks to their out-of-phase behavior with respect to the structural forces and displacements [48]. The behavior of passive FVDs is generally described by using Equation (1) [54], which shows that the force of the damper \(F_{D}(t)\) is proportional to the relative axial velocity \(\dot{x}(t)\) between the piston and the cylinder:  
\[F_{D}(t)=C_{D}\cdot\big{|}\dot{x}(t)\big{|}^{\alpha}\cdot sgn\big{[}\dot{x}(t )\big{]} \tag{1}\]  
where \(C_{D}\) is the damping coefficient, \(\alpha\) is the damping exponent, \(\dot{x}(t)\) is the axial velocity of the damper, and \(sgn[\cdot\,]\) is the signum function. The values of \(C_{D}\) and \(\alpha\) depend upon the hydraulic circuit used in the device [55; 56]. FVDs are classified based on the value of the damping exponent \(\alpha\): (i) linear FVDs are characterized by \(\alpha=1\); therefore, the corresponding damping force is directly proportional to the axial velocity; (ii) non-linear FVDs are described by Equation (1) with \(\alpha<1\); (iii) ultra-linear FVDs are defined by \(\alpha>1\)[30].