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 forcing a low-viscosity fluid thru small openings (orifices) in ‘turbulent flow viscous dampers’ or shearing a high viscosity fluid between moving surfaces in ‘laminar flow viscous damping units’ (dashpots). The former type is commonly used in the making of shock absorbers in automobile suspensions. ‘Turbulent flow viscous dampers’ (shock absorber type dampers) are uni-directional with a rather complex mechanical design and require periodic maintenance, but ‘laminar flow viscous damping units’ (dashpots) are multi-directional with a simple mechanical design and are maintenance free. Alternatively, viscous damping can be realized by shearing viscoelastic polymers in solid viscoelastic dampers as well as moving a conductive solid material through a magnetic field in ‘magnetic dampers’ also known as ‘eddy current dampers’. The kinetic energy of the structure being dampened by viscous dampers of any type is transformed into heat and dissipated .
Fluid Viscous Dampers
Fluid viscous damping is an energy dissipation mechanism in which the damping force is a function of velocity of an object moving through a viscous fluid. Equation (1) presents the relationship between the damping force and velocity of the damper
f=cv^a (1)
where c is the damping coefficient determined mainly by the size and orifice area of the damper and v is the velocity of the damper. The exponent a can vary from 0.15 to 1.85 depending on the geometry of the piston head and the orifices. For seismic mitigation applications, the exponent is set closer to the lower end of this range. For a linear damper in which damping force is proportional to velocity, i.e., a=1.
Turbulent flow viscous dampers are similar in make-up to shock absorbers in an automobile suspension system, albeit they could be larger in size and stroke, operate with much higher forces, and be made with higher precision. Low viscosity silicone is commonly used as the fluid in these viscous damping devices. This fluid is inert, non-flammable, non-toxic, and stable.
Schematic of a shock absorber type viscous damper
The damping action is provided by moving the piston back and forth forcing the damping fluid thru the clearance between the inside of the cylinder and the outside of the piston and/or thru small orifices built into the piston, creating large pressure drops and thus energy dissipation. Note that shock absorber type viscous dampers are one-dimensional devices and can only provide damping along their axis of motion (cylinder axis). These viscous dampers require some maintenance , mainly in terms of their seals leaking after so many cycles of oscillation .
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.
Following the design of viscous dampers, they are prototyped and their damping effectiveness verified, experimentally. This is done by subjecting the dampers to harmonic motion and measuring their force and displacement. The area enclosed by harmonic loading and unloading paths of a dashpot, called the hysteresis loop, is a measure of the damping effect, and corresponds to the dissipated energy per cycle. The two traces in Figure 2 depict the measured (blue trace) and the identified (red trace) force vs. displacement of the viscous damper. The area of the hysteresis loop is used to determine the equivalent viscous damping coefficient of a dashpot. The tilt of the hysteresis loop is used to evaluate the stiffness coefficient (the elastic attribute of the dashpot).
Figure 2 The measured (blue trace) and identified (red trace) force vs. displacement of a dashpot
Modeling
Viscous dampers are not just viscous but viscoelastic devices modeled best by a series combination of pure viscous dampers and springs, known as Maxwell model.
The derivation of the mathematical model of linear fluid dampers, including its viscoelastic behavior, shows that the viscoelastic attributes of a such dampers can be described by a frequency-dependent parallel combination of springs and ideal viscous dampers known as Kelvin-Voight model,commonly used to characterize fluid dampers at various frequencies.
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
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.
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 the viscosity of silicone fluid over its viscosity at 25 deg C
Magnetic Dampers (Eddy Current Dampers)
Magnetic damping (eddy current damping) is generated when there is a relative movement between magnets and a conducting material (normally Aluminum or Copper). When either a magnet move relative to a conductor or a conductor passes thru a magnetic field, the electromotive force (emf) will be generated inside the conductive material. This in turn induces a a localized electric current (known as eddy current) within the conductor. This eddy current creates a second magnetic field that opposes the field of the original moving magnet, thus creating an opposing (damping) force proportional to the relative velocity of the magnet and conductor.
The opposing (damping) force, being proportional to the relative velocity between the conductor and the magnets, acts as a viscous damping force; this qualifies magnetic dampers (eddy current dampers) as viscous dampers. Demonstration of magnetic damping is commonly conducted by dropping a magnet down a copper tube. In addition to structural vibration abatement, magnetic dampers are used in braking applications (e.g., in roller coasters, elevators, race cars) as well as automobile suspension. The advantages of magnetic dampers include, but not limited to, being liquid-free, temperature independent, non-contact and thus nearly maintenance-free.
Applications
Viscous dampers may be used a) as a stand-alone damping units to dampen a single or multiple resonances of underdamped structures such as piping systems, buildings (to reduce interstory drift), and bridges, b) in conjunction with spring elements in shock isolation applications and c) in realization of tuned mass dampers. The images below show a stand-alone viscous damper built into a structure and two viscous dampers as the dissipative element of a tuned mass damper.
The blue traces in Figure 5 depict the magnitude and phase of the 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 Frequency response functions of a structure without (blue traces) and with (red traces) viscous damping
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Viscous dampers are not just viscous but viscoelastic devices modeled best by a series combination of pure viscous dampers and springs, known as Maxwell model.
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.
