You can view and download this file on Github: nMassOscillator.py
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
# This is an EXUDYN example
#
# Details: Nonlinear oscillations interactive simulation
#
# Author: Johannes Gerstmayr
# Date: 2020-01-16
#
# 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.
#
#+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
import exudyn as exu
from exudyn.itemInterface import *
from exudyn.utilities import * #includes itemInterface and rigidBodyUtilities
import exudyn.graphics as graphics #only import if it does not conflict
import matplotlib.pyplot as plt
from exudyn.interactive import InteractiveDialog
import numpy as np
from math import sin, cos, pi, sqrt
import time #for sleep()
SC = exu.SystemContainer()
mbs = SC.AddSystem()
#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#
N = 12; #number of masses
spring = 800; #stiffness [800]
mass = 1; #mass
damper = 2; #old:0.1; damping parameter
force = 1; #force amplitude
d0 = damper*spring/(2*sqrt(mass*spring)) #dimensionless damping for single mass
caseHarmonic = 1
#damper=2
#mode1:force=0.52
#mode2:force=2
#mode3:force=4
#mode12: force=100, damping=0.05, period=0.005
caseStep = 2
#damper=1
#force=20
mbs.variables['loadCase'] = caseHarmonic
mbs.variables['resetMotion'] = 0 #run
mbs.variables['forceAmplitude'] = force
eigenMode = 1
h = 0.002 #step size
deltaT = 0.01 #time period to be simulated between every update
# if (mode < 2) h=h*2; F=0.4*F; end
# if (mode < 5) h=h*2; F=0.4*F; end
# if (mode < 6) h=h*2.5; end
# if (mode == 6) F=F*2; end
# if (mode == 3) h=h*0.5; end
# if (mode > 16) F=2*F; end
# if (mode > 10) F=2*F; end
# if (N < 11) h=h/2; l_mass = 2*l_mass; r_mass=2*r_mass; F=0.5*F; end
# if (N < 6) h=h/2; l_mass = 2*l_mass; r_mass=2*r_mass; end
# om=sqrt(diag(ew))
#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#create model for linear and nonlinear oscillator:
# L=0.5
# load0 = 80
# omega0=np.sqrt(spring/mass)
# f0 = 0.*omega0/(2*np.pi)
# f1 = 1.*omega0/(2*np.pi)
# tEnd = 200 #end time of simulation
# steps = 20000 #number of steps
omegaInit = 3.55
omegaMax = 40 #for plots
mbs.variables['mode'] = 0 #0=linear, 1=cubic nonlinear
mbs.variables['omega'] = omegaInit #excitation frequency changed by user
#mbs.variables['omega'] = omegaInit #excitation, changed in simFunction
mbs.variables['phi'] = 0 #excitation phase, used to get smooth excitations
mbs.variables['stiffness'] = spring
mbs.variables['damping'] = damper
mbs.variables['dampingPrev'] = damper
# #user function for spring force
# def springForce(mbs, t, itemIndex, u, v, k, d, offset, mu, muPropZone):
# k=mbs.variables['stiffness']
# d=mbs.variables['damping']
# if mbs.variables['mode'] == 0:
# return k*u + v*d
# else:
# #return 0.1*k*u+k*u**3+v*d
# return k*u+1000*k*u**3+v*d #breaks down at 13.40Hz
# mode = 0 #0...forward, 1...backward
#user function for load
def userLoad(mbs, t, load):
f = mbs.variables['forceAmplitude']
fact = 1
if mbs.variables['loadCase']==caseHarmonic:
fact = sin(mbs.GetSensorValues(mbs.variables['sensorPhi']))
return f*fact
def userLoad3D(mbs,t, load):
f = mbs.variables['forceAmplitude']
fact = 10
# if mbs.variables['loadCase']==caseHarmonic:
# fact = sin(mbs.GetSensorValues(mbs.variables['sensorPhi']))
# mbs.SetLoadParameter(0,'loadVector',[fact,0,0])
return [f*fact,0,0]
#dummy user function for frequency
def userFrequency(mbs, t, load):
return mbs.variables['omega']
#user function used in GenericODE2 to integrate current omega
def UFintegrateOmega(mbs, t, itemIndex, q, q_t):
return [mbs.variables['omega']] #current frequency*2*pi is integrated into phi, return vector!
#ground node
nGround=mbs.AddNode(NodePointGround(referenceCoordinates = [0,0,0]))
#drawing parameters:
l_mass = 0.2 #spring length
r_mass = 0.030*2 #radius of mass
r_spring = r_mass*1.2
L0 = l_mass*1
L = N * l_mass + 4*l_mass
z=-r_mass-0.1
hy=0.25*L
hy1=2*hy - 4*r_mass
hy0=-4*r_mass
maxAmp0 = 0.1
maxAmpN = 0.1*N
background = [graphics.Quad([[-L0,hy0,z],[ L,hy0,z],[ L,hy1,z],[-L0,hy1,z]],
color=graphics.color.lightgrey)]
offCircleY = 1*hy
# for i in range(N):
# t=r_mass*0.5
# ox = l_mass*(i+1)
# oy = offCircleY
# line0 = {'type':'Line', 'data':[ox-t,oy+0,0, ox+t,oy+0,0], 'color':graphics.color.grey}
# line1 = {'type':'Line', 'data':[ox+0,oy-t,0, ox+0,oy+t,0], 'color':graphics.color.grey}
# background += [line0, line1]
oGround=mbs.AddObject(ObjectGround(visualization=VObjectGround(graphicsData=background)))
#marker for ground (=fixed):
groundMarker=mbs.AddMarker(MarkerNodeCoordinate(nodeNumber= nGround, coordinate = 0))
prevMarker = groundMarker
nMass = []
mbs.variables['springDamperList'] = []
for i in range(N):
#node for 3D mass point:
col = graphics.color.steelblue
if i==0:
col = graphics.color.green
elif i==N-1:
col = graphics.color.lightred
gSphere = graphics.Sphere(point=[0,0,0], radius=r_mass, color=col, nTiles=16)
node = mbs.AddNode(Node1D(referenceCoordinates = [l_mass*(1+len(nMass))],
initialCoordinates=[0.],
initialVelocities=[0.]))
massPoint = mbs.AddObject(Mass1D(nodeNumber = node, physicsMass=mass,
referencePosition=[0,0,0],
visualization=VMass1D(graphicsData=[gSphere])))
# gCircle = {'type':'Circle','position':[0,0,0],'radius':0.5*r_mass, 'color':col}
# massPoint2 = mbs.AddObject(Mass1D(nodeNumber = node, physicsMass=0,
# referencePosition=[l_mass*(len(nMass)+1),offCircleY-l_mass*(len(nMass)+1),0],
# referenceRotation=[[0,1,0],[1,0,0],[0,0,1]],
# visualization=VMass1D(graphicsData=[gCircle])))
# node = mbs.AddNode(Point(referenceCoordinates = [l_mass*(1+len(nMass)),0,0]))
# massPoint = mbs.AddObject(MassPoint(physicsMass = mass, nodeNumber = node,
# visualization=VMassPoint(graphicsData=[gSphere])))
nMass += [node]
#marker for springDamper for first (x-)coordinate:
nodeMarker =mbs.AddMarker(MarkerNodeCoordinate(nodeNumber= node, coordinate = 0))
#Spring-Damper between two marker coordinates
sd = mbs.AddObject(CoordinateSpringDamper(markerNumbers = [prevMarker, nodeMarker],
stiffness = spring, damping = damper,
#springForceUserFunction = springForce,
visualization=VCoordinateSpringDamper(drawSize=r_spring)))
mbs.variables['springDamperList'] += [sd]
prevMarker = nodeMarker
#add load to last mass:
if False: #scalar load
mbs.AddLoad(LoadCoordinate(markerNumber = nodeMarker,
load = 0, loadUserFunction=userLoad)) #load set in user function
else:
mMassN = mbs.AddMarker(MarkerBodyPosition(bodyNumber= massPoint, localPosition=[0,0,0]))
mbs.AddLoad(Force(markerNumber=mMassN, loadVector=[1,0,0],
loadVectorUserFunction=userLoad3D))
# #dummy load applied to ground marker, just to record/integrate frequency
lFreq = mbs.AddLoad(LoadCoordinate(markerNumber = groundMarker,
load = 0, loadUserFunction=userFrequency))
sensPos0 = mbs.AddSensor(SensorNode(nodeNumber=nMass[0], fileName='solution/nMassPos0.txt',
outputVariableType=exu.OutputVariableType.Coordinates))
sensPosN = mbs.AddSensor(SensorNode(nodeNumber=nMass[-1], fileName='solution/nMassPosN.txt',
outputVariableType=exu.OutputVariableType.Coordinates))
sensFreq = mbs.AddSensor(SensorLoad(loadNumber=lFreq, fileName='solution/nMassFreq.txt',
visualization=VSensorLoad(show=False)))
#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#compute eigenvalues
from exudyn.solver import ComputeODE2Eigenvalues
mbs.Assemble()
[values, vectors] = ComputeODE2Eigenvalues(mbs)
print('omegas (rad/s)=', np.sqrt(values))
#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#integrate omega: node used to integrate omega into phi for excitation function
nODE2=mbs.AddNode(NodeGenericODE2(referenceCoordinates=[0], initialCoordinates=[0],initialCoordinates_t=[0],
numberOfODE2Coordinates=1))
oODE2=mbs.AddObject(ObjectGenericODE2(nodeNumbers=[nODE2],massMatrix=np.eye(1),
forceUserFunction=UFintegrateOmega,
visualization=VObjectGenericODE2(show=False)))
#improved version, using integration of omega:
mbs.variables['sensorPhi'] = mbs.AddSensor(SensorNode(nodeNumber=nODE2, fileName='solution/nonlinearPhi.txt',
outputVariableType = exu.OutputVariableType.Coordinates_t,
visualization=VSensorNode(show=False)))
#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#finalize model and settings
mbs.Assemble()
SC.visualizationSettings.general.textSize = 12
SC.visualizationSettings.openGL.lineWidth = 2
SC.visualizationSettings.openGL.multiSampling = 4
SC.visualizationSettings.general.graphicsUpdateInterval = 0.005
#SC.visualizationSettings.window.renderWindowSize=[1024,900]
SC.visualizationSettings.window.renderWindowSize=[1600,1000]
SC.visualizationSettings.general.showSolverInformation = False
SC.visualizationSettings.general.drawCoordinateSystem = False
SC.visualizationSettings.loads.fixedLoadSize=0
SC.visualizationSettings.loads.loadSizeFactor=0.5
SC.visualizationSettings.loads.drawSimplified=False
SC.visualizationSettings.loads.defaultSize=1
SC.visualizationSettings.loads.defaultRadius=0.01
SC.visualizationSettings.general.autoFitScene = True #otherwise, renderState not accepted for zoom
#++++++++++++++++++++++++++++++++++++++++
#setup simulation settings and run interactive dialog:
simulationSettings = exu.SimulationSettings()
simulationSettings.timeIntegration.generalizedAlpha.spectralRadius = 1
simulationSettings.solutionSettings.writeSolutionToFile = True
simulationSettings.solutionSettings.solutionWritePeriod = 0.05 #data not used
simulationSettings.solutionSettings.sensorsWritePeriod = 0.1 #data not used
simulationSettings.solutionSettings.solutionInformation = 'n-mass-oscillatior'
simulationSettings.timeIntegration.verboseMode = 1 #turn off, because of lots of output
simulationSettings.timeIntegration.numberOfSteps = int(1000)
simulationSettings.timeIntegration.endTime = 5
simulationSettings.timeIntegration.newton.useModifiedNewton = True
simulationSettings.displayComputationTime = True
# simulationSettings.numberOfThreads = 1
#%%+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
#set up interactive window
mbs.SolveDynamic(simulationSettings=simulationSettings)
mbs.SolutionViewer()