PartialCompliantWithRelativeStates

Base model for a 1D translational compliant connection using relative displacement and relative velocity as states.

This partial component provides the foundational kinematics and force propagation for a compliant connection between two translational 1D mechanical flanges, flange_a and flange_b. It defines the relative displacement (s_rel) and relative velocity (v_rel) between these flanges. The relative velocity is explicitly defined as the time derivative of the relative displacement. An internal force f is declared, which is intended to be defined by an extending model (e.g., based on spring stiffness or damping coefficient). This internal force is then transmitted to flange_b and, with an opposite sign, to flange_a, satisfying Newton's third law. Since this is a partial model, it does not define the constitutive equation for the force f (i.e., how f depends on s_rel and v_rel). The key kinematic and force equations are:

$$s_{rel}=flang{e}_b.s-flang{e}_a.s$$$$v_{rel}=\frac{d(s_{rel})}{dt}$$$$flang{e}_b.f=f$$$$flang{e}_a.f=-f$$

Usage

PartialCompliantWithRelativeStates()

Connectors

• flange_a - (Flange)

• flange_b - (Flange)

Variables

Name	Description	Units
s_rel	Relative displacement between flange_b and flange_a (flange_b.s - flange_a.s).	m
v_rel	Relative velocity between flange_b and flange_a, defined as der(s_rel).	m/s
f	Internal force exerted by the compliant element between the flanges.	N

Source

# Base model for a 1D translational compliant connection using relative displacement and relative velocity as states.
#
# This partial component provides the foundational kinematics and force propagation for a compliant
# connection between two translational 1D mechanical flanges, `flange_a` and `flange_b`. It defines
# the relative displacement (`s_rel`) and relative velocity (`v_rel`) between these flanges. The
# relative velocity is explicitly defined as the time derivative of the relative displacement. An
# internal force `f` is declared, which is intended to be defined by an extending model (e.g., based
# on spring stiffness or damping coefficient). This internal force is then transmitted to `flange_b`
# and, with an opposite sign, to `flange_a`, satisfying Newton's third law. Since this is a `partial`
# model, it does not define the constitutive equation for the force `f` (i.e., how `f` depends on
# `s_rel` and `v_rel`). The key kinematic and force equations are:
# ```math
# s_{rel} = flange_b.s - flange_a.s
# ```
# ```math
# v_{rel} = \frac{d(s_{rel})}{dt}
# ```
# ```math
# flange_b.f = f
# ```
# ```math
# flange_a.f = -f
# ```
partial component PartialCompliantWithRelativeStates
  # 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
relations
  s_rel = flange_b.s-flange_a.s
  v_rel = der(s_rel)
  flange_b.f = f
  flange_a.f = -f
end

Flattened Source

# Base model for a 1D translational compliant connection using relative displacement and relative velocity as states.
#
# This partial component provides the foundational kinematics and force propagation for a compliant
# connection between two translational 1D mechanical flanges, `flange_a` and `flange_b`. It defines
# the relative displacement (`s_rel`) and relative velocity (`v_rel`) between these flanges. The
# relative velocity is explicitly defined as the time derivative of the relative displacement. An
# internal force `f` is declared, which is intended to be defined by an extending model (e.g., based
# on spring stiffness or damping coefficient). This internal force is then transmitted to `flange_b`
# and, with an opposite sign, to `flange_a`, satisfying Newton's third law. Since this is a `partial`
# model, it does not define the constitutive equation for the force `f` (i.e., how `f` depends on
# `s_rel` and `v_rel`). The key kinematic and force equations are:
# ```math
# s_{rel} = flange_b.s - flange_a.s
# ```
# ```math
# v_{rel} = \frac{d(s_{rel})}{dt}
# ```
# ```math
# flange_b.f = f
# ```
# ```math
# flange_a.f = -f
# ```
partial component PartialCompliantWithRelativeStates
  # 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
relations
  s_rel = flange_b.s-flange_a.s
  v_rel = der(s_rel)
  flange_b.f = f
  flange_a.f = -f
metadata {}
end

Test Cases

This is setup code, that must be run before each test case.

using TranslationalComponents
using ModelingToolkit, OrdinaryDiffEqDefault
using Plots
using CSV, DataFrames

snapshotsdir = joinpath(dirname(dirname(pathof(TranslationalComponents))), "test", "snapshots")

"/home/actions-runner-10/.julia/packages/TranslationalComponents/khJb7/test/snapshots"

Related

• Examples

• Experiments

• Analyses