Structural Dynamics / module 18
Supplemental damping devices
Manufactured viscous dampers: velocity-dependent force, the velocity exponent and what it is for, brace geometry and the cos²θ penalty, damper placement, sizing and the analysis they require.
What you will understand
- State the damper force law and explain why the force peaks where the displacement is zero
- Explain what the velocity exponent does and why α < 1 is chosen
- Apply the cos²θ projection to a linear damper under horizontal storey motion
- Compute the damping ratio a linear damper adds to a mode
- Place dampers using the modal drift across each storey
- Say what analysis a damped structure needs and why a spectrum will not do
Lessons
How a viscous damper works
Velocity-dependent force, brace geometry and how the exponent affects device and connection demands.
Sizing and placing dampers
Where a damper earns its keep, how much damping it actually adds, and what analysis a damped structure needs.
Module summary
- A viscous damper force depends on velocity, not displacement
- For harmonic axial motion, ideal viscous force peaks at zero axial displacement
- Assess combined damper and structural forces through the actual load paths and response histories
- F = C|v|^α; an exponent below 1 slows force growth without imposing a finite cap
- For horizontal motion and a rigid diagonal, the linear coefficient scales as cos²θ; nonlinear horizontal force scales as cos^(1+α)θ
- Added modal damping goes as the SQUARE of the relative modal displacement across the damper
- A damper in a storey with little modal drift does almost nothing
- An ideal viscous element adds no elastic stiffness; assess the complete supporting assembly
- Concentrated linear damping can couple modes; nonlinear devices need a suitable nonlinear response method
Teaching basis and review status
These are educational models and exercises. Check their assumptions before using the results. The full technical content and every diagram have not yet been independently verified.
Concrete and steel calculations retain their stated first-generation Eurocode teaching basis. Use the standards and amendments specified for your project; do not mix generations without an appropriate design basis.
Read the lesson register and outstanding review notesCheck your understanding
Practice
A damper with C = 1 200 kN·(s/m)0.5 and α = 0.5 is driven at 0.50 m/s. What force does it deliver, in kN?
Practice
For equal linear damping coefficients and the same horizontal storey velocity, what fraction of a horizontal damper’s horizontal force is retained by a rigid diagonal at 45°?
Practice
A linear damper with C = 1.5 MN·s/m braced at 45° spans a storey with first-mode relative displacement 0.28. The mode has ω = 3.5 rad/s and modal mass 750 tonnes. What damping ratio does it add?
Check yourself
Why is conventional uncoupled response-spectrum analysis not an exact treatment of nonlinear viscous dampers?