VISCOUS DAMPERS

In fluid viscous damping, the damping force depends on the relative velocity of the damper components, as expressed in Equation (1)

f=c*v^a                  (1)

where c represents the damping coefficient, primarily determined by the damper’s design, while $v$ denotes the velocity of the damper. The exponent a can vary from 0.15 to 1.85 depending on the liquid flow passage geometry and mechanism. For a linear viscous damper in which damping force is proportional to velocity, the exponent a=1.

Energy dissipation,  along with the damping coefficient, is essential in sizing a viscous damper.  It is typically assessed by harmonically stroking the damper and calculating the contour integral (evaluating the area within the contour) of force vs. displacement over one cycle.

The contour plot of force versus displacement (also known as the hysteresis plot), along with the time traces of force f and harmonic displacement x, for a linear viscous damper (velocity exponent a=1) is shown in Figure 1.

Figure 1 Time traces of force f and displacement x as well as hysteresis plot of f vs. x of a linear viscous damper

Following the same format as that of Figure 2, the time traces of force and harmonic displacement, as well as the contour of force vs. displacement plotted over one cycle (the hysteresis plot) for a digressive viscous damper with the velocity exponent of a=0.3 is presented in Figure 2.  As illustrated in Figure 2, digressive dampers—with velocity exponents below 1—produce lower peak forces than linear dampers with equivalent energy dissipation.

Figure 2 Time traces of force f and displacement x as well as hysteresis plot of f vs. x for a digressive viscous damper

Digressive viscous dampers (with velocity exponent a<1) can be advantageous because they provide similar energy dissipation to equivalent linear dampers, while producing lower peak damper forces making them particularly advantageous for applications like earthquake mitigation that demand substantial cyclic energy dissipation.

Turbulent Flow (Shock Absorber Type) Viscous Damping Devices

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 achieved by the reciprocating motion of the piston forcing the damping fluid thru: a) the annular clearance between the piston and the cylinder wall, b) small orifices built internally within the piston, c) an external by-pass channel, or d) a combination of these paths— each creating significant pressure drops that results in energy dissipation.

Through specific design features in viscous dampers’ internal flow paths, they can behave as linearly (with velocity exponent a=1) or nonlinearly (digressive with a<1 and progressive with a>1). Figure 3 shows force-velocity relationship for a linear and a nonlinear digressive viscous dampers.  Contrary to linear viscous dampers in which damping force is proportional to the piston velocity, in digressive dampers damping force increases rapidly at low piston velocities but levels off at higher velocities.  As noted above digressive dampers produce lower peak forces than linear dampers.

Figure 3 Force-velocity relationship for linear (blue trace) and nonlinear digressive (red trace) viscous dampers

Shock absorber type viscous dampers are one-dimensional energy dissipating devices and can only provide damping along their axis of motion (cylinder axis). These 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) operate at atmospheric pressure and have a simple make-up consisting of a container, a highly viscous damping liquid, a plunger, and a core.  The multi-directional motion of the plunger inside the damping liquid, relative to the container, shears the damping liquid, dissipating energy in multiple directions.

The ample clearance between the plunger and the tank as well as operation in atmospheric pressure eliminate the need for seals (to prevent leaking), in dashpots.  Moreover, the lack of solid-to-solid contact and/or solid to rubber-seal rubbing ensures that no stiction (static friction) and other nonlinearities associated with such contacts are present in these damping devices.  The absence of such undesirable, nonlinear attributes result in uniformity of damping performance at low as well as high amplitudes of vibration.

The cut away view of a dashpot model shown in Figure 4 depicts the velocity field (from ‘computational fluid dynamics’ analysis) of the high viscosity damping liquid in a dashpot, with blue color representing zero and red color representing maximum velocities.  The motion of the plunger along with the high viscosity of the liquid produce large velocity gradients in the liquid which in turn lead to damping force and energy dissipation in the system.

Figure 4 The velocity field (a) and velocity distribution in a cross-section of a ‘laminar flow viscous damper’

The damping effectiveness of dashpots in terms of their damping coefficient and cyclic energy dissipation are evaluated via measurements. 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 5 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 dynamic stiffness coefficient (the elastic attribute of the dashpot).

Figure 5 The measured (blue trace) and identified (red trace) force vs. displacement of a dashpot

High‑viscosity silicone fluids flow easily and dissipate energy well at low frequencies, but as excitation speeds rise, their polymer chains can’t rearrange quickly enough, causing the material to store energy elastically and behave more like a soft solid. This shift occurs because the storage modulus increases faster than the loss modulus, while mild shear‑thinning reduces effective viscosity, weakening high‑frequency damping. The combined effect is the strong low‑frequency damping, reduced dissipation at higher frequencies along with increase in dynamic stiffness.

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 6 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 6 Typical frequency-dependent stiffness and damping coefficients of a dashpot

High‑viscosity silicone fluids—especially those above 10,000 cSt—flow easily and dissipate well at low frequencies, but as excitation speeds rise, their polymer chains can’t rearrange quickly enough, causing the material to store energy elastically and behave more like a soft solid. This shift occurs because the storage modulus increases faster than the loss modulus, while mild shear‑thinning reduces effective viscosity, weakening high‑frequency damping. The combined effect is a familiar pattern in real systems: strong low‑frequency damping, reduced dissipation at higher frequencies, and a marked increase in dynamic stiffness—an inherent consequence of how ultra‑thick polymeric fluids respond under oscillatory loading.

The Impact of Temperature Variation

As temperature increases in liquids, molecules gain more kinetic energy, reducing the intermolecular forces that resist flow. This makes the liquid less viscous.

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 Normalized viscosity of silicone fluid vs temperature