Damper

Linear translational damper relating force to relative velocity.

This component represents an ideal linear translational mechanical damper. The force f generated by the damper is proportional to the relative velocity v_{rel} between its two mechanical flanges. The constant of proportionality is the translational damping coefficient d. The force always acts to oppose the relative motion between the flanges. The component also calculates the instantaneous power lossPower dissipated by the damping action. The defining equations are:

\[f = d \cdot v_{rel}\]

\[lossPower = f \cdot v_{rel} = d \cdot v_{rel}^2\]

This component extends from PartialCompliantWithRelativeStates

Usage

TranslationalComponents.Damper(d)

Parameters:

Connectors

• flange_a - This connector represents a mechanical flange with position and force as the potential and flow variables, respectively. (Flange)
• flange_b - This connector represents a mechanical flange with position and force as the potential and flow variables, respectively. (Flange)

Variables

Behavior

\[ \begin{align} \mathtt{s\_rel}\left( t \right) &= \mathtt{flange\_b.s}\left( t \right) - \mathtt{flange\_a.s}\left( t \right) \\ \mathtt{v\_rel}\left( t \right) &= \frac{\mathrm{d} \mathtt{s\_rel}\left( t \right)}{\mathrm{d}t} \\ \mathtt{flange\_b.f}\left( t \right) &= f\left( t \right) \\ \mathtt{flange\_a.f}\left( t \right) &= - f\left( t \right) \\ f\left( t \right) &= d \mathtt{v\_rel}\left( t \right) \\ \mathtt{lossPower}\left( t \right) &= \mathtt{v\_rel}\left( t \right) f\left( t \right) \end{align} \]

Source

# Linear translational damper relating force to relative velocity.
#
# This component represents an ideal linear translational mechanical damper.
# The force `f` generated by the damper is proportional to the relative velocity `v_{rel}` between its two mechanical flanges.
# The constant of proportionality is the translational damping coefficient `d`.
# The force always acts to oppose the relative motion between the flanges.
# The component also calculates the instantaneous power `lossPower` dissipated by the damping action.
# The defining equations are:
# ```math
# f = d \cdot v_{rel}
# ```
# ```math
# lossPower = f \cdot v_{rel} = d \cdot v_{rel}^2
# ```
component Damper
  extends PartialCompliantWithRelativeStates
  # Translational damping coefficient relating force to relative velocity
  parameter d::TranslationalDampingConstant
  # Instantaneous power dissipated by the damper
  variable lossPower::Power
relations
  f = d * v_rel
  lossPower = f * v_rel
metadata {"Dyad": {"icons": {"default": "dyad://TranslationalComponents/Damper.svg"}}}
end

# Linear translational damper relating force to relative velocity.
#
# This component represents an ideal linear translational mechanical damper.
# The force `f` generated by the damper is proportional to the relative velocity `v_{rel}` between its two mechanical flanges.
# The constant of proportionality is the translational damping coefficient `d`.
# The force always acts to oppose the relative motion between the flanges.
# The component also calculates the instantaneous power `lossPower` dissipated by the damping action.
# The defining equations are:
# ```math
# f = d \cdot v_{rel}
# ```
# ```math
# lossPower = f \cdot v_{rel} = d \cdot v_{rel}^2
# ```
component Damper
  # Port for the first mechanical translational flange.
  flange_a = Flange() [{"Dyad": {"placement": {"icon": {"x1": -50, "y1": 450, "x2": 50, "y2": 550}}}}]
  # Port for the second mechanical translational flange.
  flange_b = Flange() [{"Dyad": {"placement": {"icon": {"x1": 950, "y1": 450, "x2": 1050, "y2": 550}}}}]
  # Relative displacement between flange_b and flange_a (flange_b.s - flange_a.s).
  variable s_rel::Distance
  # Relative velocity between flange_b and flange_a, defined as der(s_rel).
  variable v_rel::Velocity
  # Internal force exerted by the compliant element between the flanges.
  variable f::Dyad.Force
  # Translational damping coefficient relating force to relative velocity
  parameter d::TranslationalDampingConstant
  # Instantaneous power dissipated by the damper
  variable lossPower::Power
relations
  s_rel = flange_b.s - flange_a.s
  v_rel = der(s_rel)
  flange_b.f = f
  flange_a.f = -f
  f = d * v_rel
  lossPower = f * v_rel
metadata {"Dyad": {"icons": {"default": "dyad://TranslationalComponents/Damper.svg"}}}
end

Test Cases

No test cases defined.

Related

• Examples
• Experiments
• Analyses
• Tests
  • MassDamperSpringFixedTest