### Viscous Dampers

Viscous damping has been widely used as the energy dissipation mechanism of choice in abating resonant vibration in structures. Such damping is commonly provided either by the flow of high viscosity fluid thru large openings (gaps) in ‘laminar flow viscous damping units’ (dashpots) or the flow of low-viscosity fluid thru small openings (orifices) in ‘turbulent flow viscous dampers’. The latter type is commonly used in the making of shock absorbers in automobile suspensions. ‘Turbulent flow viscous dampers’ are uni-directional with a rather complex mechanical design and require periodic maintenance, but ‘laminar flow viscous damping units’ are multi-directional with a simple mechanical design and are maintenance free.

Alternatively, viscous damping can be provided by the motion of a conductive solid material through a magnetic field in ‘magnetic dampers’ also known as
‘eddy current dampers’.
The kinetic energy of a mechanical systems being damped by a magnetic damper is transferred to the conductor and dissipated as heat.

#### Laminar Flow Viscous Dampers (Dashpots)

‘Laminar flow viscous dampers’ (dashpots) are multi-directional damping units made up of a plunger (piston) and a container (cylinder) partially filled with a highly viscous liquid. The vibratory motion of the plunger thru the viscous liquid shears the fluid, dissipating the vibration energy into heat. There is ample clearance between the plunger and the container and no seals are used in their making; as such, they have no metal to metal and/or metal to rubber (seal) contact resulting in no stiction (static friction) or other undesirable nonlinearities associated with solid to solid contacts.

DEICON uses computational fluid dynamics (CFD) tools to design viscous dampers. The cut-out image shown in Figure 1 (a) depicts the velocity field distribution predicted by the CFD analysis of a ‘laminar flow viscous damper’. Figure 1(b) shows a snapshot of the same information at the cross-section encircled in Figure 1 (a). Clear from Figure 1, the large velocity gradient induced by the motion of the plunger in conjunction with the high viscosity of fluid create the desired damping force.

Figure 1 The velocity field (a) and velocity distribution in a cross-section of a ‘laminar flow viscous damper’

The CFD software tool allows the designer to select the proper geometry for the plunger and housing as well as the right fluid so the desired damping coefficient is realized.

DEICON custom designs and fabricates ‘laminar flow viscous dampers’, dashpots, for a variety of structural damping applications.

Figure 2 The measured (blue trace) and identified (red trace) force vs. displacement of a dashpot

Highly viscous liquids such as silicone used in dashpots are somewhat elastic in addition to being viscous. This makes the dashpot force not only a function of the relative velocity but also a function of the relative displacement between the plunger (piston) and the container (cylinder). In other words, at higher frequencies dashpots are more of a viscoelastic damper than a viscous damper.

#### Modeling

Viscoelastic attributes of a realistic damper can be described by a combination of springs and ideal viscous dampers. Kelvin-Voight model (A spring and a viscous damper in parallel) is commonly used to characterize dashpots at a single frequency. The damping coefficient and stiffness used in the Kelvin-Voight model are identified, experimentally, at various frequencies. The viscoelastic dashpot model is extended to all frequencies by fitting a generalized three-parameter (also known as generalized Maxwell) viscoelastic model to the experimentally evaluated damping coefficient and stiffness at various frequencies. Figure 3 shows the experimentally evaluated damping and stiffness coefficients of a dashpot at various frequencies (the blue marks) as well as a five-term generalized three-parameter viscoelastic model fitted to that (the experimentally evaluated) data.

Figure 3 Typical frequency-dependent stiffness and damping coefficients of a dashpot

#### The Impact of Temperature Variation

With the low VTC of around 0.6 the viscosity of silicone-based damping fluid used in DEICON’s dashpots is by far less temperature dependent than that of mineral, synthetic, and petroleum-based oil. Nevertheless, there is some temperature dependency on the rheological properties of silicone fluid. Figure 4 shows the dependency of silicone fluid viscosity on temperature over the temperature range of 0-50 deg C. Although not excessive, but the fluid experiences about +/- 50% variation in viscosity around its nominal value.

Figure 4 The ratio of viscosity of silicone fluid over its viscosity at 25 deg C

Viscosity-Temperature Coefficient (VTC) is used to characterize the variation of viscosity of a fluid with temperature. VTC is a measure of the change of fluid viscosity over the temperature range 38ºC to 99ºC; VTC = 1 – (viscosity @ 99ºC / viscosity @ 38ºC). Thus, the lower the VTC., the less the viscosity variation over the temperature range.

#### Applications

Viscous dampers may be used as a stand-alone damping unit to dampen a single or multiple resonances of underdamped structures such as piping systems, buildings (to reduce interstory drift), and floor systems or in conjunction with spring elements in vibration isolation applications and realization of tuned mass dampers.

The blue traces in Figure 5 depict the magnitude and phase of frequency response function of an underdamped structure. They clearly show two resonant modes at 6 and 12 Hz. The red traces on the same figure present the same frequency response function after two dashpots were installed to the structure. Comparison of the blue and red traces in Figure 5 shows the effectiveness of the viscous dampers in dampening both resonant modes.

Figure 5 The experimentally measured frequency response functions of a structure without (blue traces) and with (red traces) viscous damping