You can view and download this file on Github: cartesianSpringDamperUserFunction.py
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details: Example with CartesianSpringDamper, using symbolic user function for definition of spring-damper force
#
# Model: Nonlinear oscillator with mass point and force user function
#
# Author: Johannes Gerstmayr
# Date: 2023-12-07
#
# Copyright:This file is part of Exudyn. Exudyn is free software. You can redistribute it and/or modify it under the terms of the Exudyn license. See 'LICENSE.txt' for more details.
#
# *clean example*
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
## import exudyn package and utilities, create system
import exudyn as exu
from exudyn.utilities import *
SC = exu.SystemContainer()
mbs = SC.AddSystem()
## set abbreviation for symbolic library
esym = exu.symbolic
## define parameters for linear spring-damper
L=0.5
mass = 1.6
k = 4000
omega0 = 50 # sqrt(4000/1.6)
dRel = 0.05
d = dRel * 2 * 80 #80=sqrt(1.6*4000)
u0=-0.08
v0=1
f = 80
## create ground object
objectGround = mbs.CreateGround(referencePosition = [0,0,0])
## create mass point with initial displacement and initial velocity
massPoint = mbs.CreateMassPoint(referencePosition=[L,0,0],
initialDisplacement=[u0,0,0],
initialVelocity=[v0,0,0],
physicsMass=mass)
## create spring damper between ground and mass point
csd = mbs.CreateCartesianSpringDamper(bodyList=[objectGround, massPoint],
stiffness = [k,k,k],
damping = [d,0,0],
offset = [L,0,0])
## add force on mass point
load = mbs.CreateForce(bodyNumber=massPoint, loadVector= [f,0,0])
## add sensor to measure mass point position
sMass = mbs.AddSensor(SensorBody(bodyNumber=massPoint, storeInternal=True,
outputVariableType=exu.OutputVariableType.Position))
## create user function for Cartesian spring damper (can be used as Python or as symbolic user function)
#force is just for demonstration and may not represent real behavior
def springForceUserFunction(mbs, t, itemNumber, u, v, k, d, offset):
return [0.5*u[0]**2 * k[0]+esym.sign(v[0])*10,
k[1]*u[1],
k[2]*u[2]]
CSDuserFunction = springForceUserFunction
doSymbolic = False
if doSymbolic:
## create symbolic user function (which can be used in the same way as the Python function)
CSDuserFunction = CreateSymbolicUserFunction(mbs, springForceUserFunction,
'springForceUserFunction', csd)
#check function:
print('user function:\n',CSDuserFunction)
mbs.SetObjectParameter(csd, 'springForceUserFunction', CSDuserFunction)
## assemble and create simulation settings
mbs.Assemble()
simulationSettings = exu.SimulationSettings()
tEnd = 0.2*10
steps = 200000
simulationSettings.timeIntegration.numberOfSteps = steps
simulationSettings.timeIntegration.endTime = tEnd
simulationSettings.timeIntegration.verboseMode = 1
#simulationSettings.solutionSettings.solutionWritePeriod = tEnd/steps
simulationSettings.solutionSettings.writeSolutionToFile = False
simulationSettings.solutionSettings.sensorsWritePeriod = 0.001
simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 1 #SHOULD work with 0.9 as well
## start renderer and solver; use explicit solver to account for switching in spring-damper
exu.StartRenderer()
mbs.SolveDynamic(simulationSettings,
solverType=exu.DynamicSolverType.ExplicitMidpoint)
# SC.WaitForRenderEngineStopFlag()
exu.StopRenderer() #safely close rendering window!
## evaluate solution
n1 = mbs.GetObject(massPoint)['nodeNumber']
u = mbs.GetNodeOutput(n1, exu.OutputVariableType.Position)
print('u=',u)
mbs.PlotSensor(sMass)