cartesianSpringDamperUserFunction.py
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1#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
2# This is an EXUDYN example
3#
4# Details: Example with CartesianSpringDamper, using symbolic user function for definition of spring-damper force
5#
6# Model: Nonlinear oscillator with mass point and force user function
7#
8# Author: Johannes Gerstmayr
9# Date: 2023-12-07
10#
11# 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.
12#
13# *clean example*
14#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
15
16## import exudyn package and utilities, create system
17import exudyn as exu
18from exudyn.utilities import *
19
20SC = exu.SystemContainer()
21mbs = SC.AddSystem()
22
23## set abbreviation for symbolic library
24esym = exu.symbolic
25
26
27## define parameters for linear spring-damper
28L=0.5
29mass = 1.6
30k = 4000
31omega0 = 50 # sqrt(4000/1.6)
32dRel = 0.05
33d = dRel * 2 * 80 #80=sqrt(1.6*4000)
34u0=-0.08
35v0=1
36f = 80
37
38## create ground object
39objectGround = mbs.CreateGround(referencePosition = [0,0,0])
40
41## create mass point with initial displacement and initial velocity
42massPoint = mbs.CreateMassPoint(referencePosition=[L,0,0],
43 initialDisplacement=[u0,0,0],
44 initialVelocity=[v0,0,0],
45 physicsMass=mass)
46
47## create spring damper between ground and mass point
48csd = mbs.CreateCartesianSpringDamper(bodyList=[objectGround, massPoint],
49 stiffness = [k,k,k],
50 damping = [d,0,0],
51 offset = [L,0,0])
52
53## add force on mass point
54load = mbs.CreateForce(bodyNumber=massPoint, loadVector= [f,0,0])
55
56## add sensor to measure mass point position
57sMass = mbs.AddSensor(SensorBody(bodyNumber=massPoint, storeInternal=True,
58 outputVariableType=exu.OutputVariableType.Position))
59
60## create user function for Cartesian spring damper (can be used as Python or as symbolic user function)
61#force is just for demonstration and may not represent real behavior
62def springForceUserFunction(mbs, t, itemNumber, u, v, k, d, offset):
63 return [0.5*u[0]**2 * k[0]+esym.sign(v[0])*10,
64 k[1]*u[1],
65 k[2]*u[2]]
66
67CSDuserFunction = springForceUserFunction
68doSymbolic = False
69if doSymbolic:
70 ## create symbolic user function (which can be used in the same way as the Python function)
71 CSDuserFunction = CreateSymbolicUserFunction(mbs, springForceUserFunction,
72 'springForceUserFunction', csd)
73 #check function:
74 print('user function:\n',CSDuserFunction)
75
76mbs.SetObjectParameter(csd, 'springForceUserFunction', CSDuserFunction)
77
78## assemble and create simulation settings
79mbs.Assemble()
80
81simulationSettings = exu.SimulationSettings()
82
83tEnd = 0.2*10
84steps = 200000
85simulationSettings.timeIntegration.numberOfSteps = steps
86simulationSettings.timeIntegration.endTime = tEnd
87simulationSettings.timeIntegration.verboseMode = 1
88#simulationSettings.solutionSettings.solutionWritePeriod = tEnd/steps
89simulationSettings.solutionSettings.writeSolutionToFile = False
90simulationSettings.solutionSettings.sensorsWritePeriod = 0.001
91
92simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 1 #SHOULD work with 0.9 as well
93
94## start renderer and solver; use explicit solver to account for switching in spring-damper
95exu.StartRenderer()
96mbs.SolveDynamic(simulationSettings,
97 solverType=exu.DynamicSolverType.ExplicitMidpoint)
98# SC.WaitForRenderEngineStopFlag()
99exu.StopRenderer() #safely close rendering window!
100
101## evaluate solution
102n1 = mbs.GetObject(massPoint)['nodeNumber']
103u = mbs.GetNodeOutput(n1, exu.OutputVariableType.Position)
104
105print('u=',u)
106
107mbs.PlotSensor(sMass)