Viscous damping

In continuum mechanics, viscous damping is a formulation of the damping phenomena, in which the source of damping force is modeled as a function of the volume, shape, and velocity of an object traversing through a real fluid with viscosity.[1]

Typical examples of viscous damping in mechanical systems include:

• Fluid films between surfaces
• Fluid flow around a piston in a cylinder
• Fluid flow through an orifice
• Fluid flow within a journal bearing

Viscous damping also refers to damping devices. Most often they damp motion by providing a force or torque opposing motion proportional to the velocity. This may be affected by fluid flow or motion of magnetic structures. The intended effect is to improve the damping ratio.

• Shock absorbers in cars
• Seismic retrofitting with viscous dampers[2]
• Tuned mass dampers in tall buildings
• Deployment actuators in spacecraft

Single-degree-of-freedom system

In a single-degree-of-freedom system, viscous damping model relates force to velocity as shown below:

${\displaystyle f=c{\dot {x}}}$

Where ${\displaystyle c}$ is the viscous damping coefficient with SI units of ${\displaystyle N\cdot s/m}$. This model adequately describes the damping force on a body that is moving at a moderate speed through a fluid.[3] It is also the most common modeling choice for damping.[4]

See also

• Hysteresis
• Coulomb damping

References

1. Mechanical Vibrations, Rao, 5th ed.
2. Pollini, Nicolò; Lavan, Oren; Amir, Oded (2017). "Minimum-cost optimization of nonlinear fluid viscous dampers and their supporting members for seismic retrofitting". Earthquake Engineering & Structural Dynamics. 46 (12): 1941–1961. doi:10.1002/eqe.2888. ISSN 1096-9845. S2CID 114445524.
3. Tony L. Schmitz, K. Scott Smith. Mechanical Vibrations: Modeling and Measurement (2e). 2021. pp. 30, 51.
4. Tony L. Schmitz, K. Scott Smith. Mechanical Vibrations: Modeling and Measurement (2e). 2021. p. 52.