Compare ElasticImpact and WP2

In the case of the impact of an elastic striker on a bar, compare the analytical result given by ElasticImpact and the numerical result computed with WP2.

import numpy as np
import matplotlib.pyplot as plt
from elwaspatid import WP2, BarSet, ElasticImpact

Define material parameters

E = 201e9  # Young modulus [Pa]
rho = 7800  # Density [kg/m3]
d1 = 0.02  # bar/stricker diameter [m]
d2 = 0.03  # bar/stricker diameter [m]
L = 1.  # length of the striker [m]
Vo = 5.  # intial striker velocity [m/s]

Analytical result with ElasticImpact

Three possible cases:

1. striker and bar have the same diameter

2. striker smaller than bar

3. striker larger than bar

time = np.linspace(-10e-6, 10e-3, num=1000)

EI = ElasticImpact(E, rho, d1, L, Vo)
EI.computeImpact(time)  # time array must be given to the method
EI.plotForce('compare', label='ds=db')

EJ = ElasticImpact(E, rho, d=[d1, d2])
EJ.computeImpact(time)
EJ.plotForce('compare', label='ds<db')

EK = ElasticImpact(E, rho, d=[d2, d1])
EK.computeImpact(time)
EK.plotForce('compare', label='ds>db')
_ = plt.legend()

EK.plotRn()  # plot amplitude of successive steps

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Out:

comment calculer l'eq. 35 pour un choc viscoelastique??
comment calculer l'eq. 35 pour un choc viscoelastique??
comment calculer l'eq. 35 pour un choc viscoelastique??

Numerical result with WP2

Bar configuration: one striker and one bar at rest

striker = BarSet([E, E], [rho, rho], [L, .2], [d2, d1], nmin=6)
testk = WP2(striker, nstep=400, left='free', right='infinite', Vinit=Vo)
testk.plot('striker')

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Out:

Setting initial velocity of first segment (Vo=5)

Get force at at impacted side of the bar

f1, v1, x1, ind1 = testk.getSignal(x=0, iseg=1, plot=True)

Compare analytical and numerical solutions

plt.figure()
plt.plot(testk.time, f1, '-', label='num')
plt.plot(time, -EK.force, '--', label='ana')
plt.legend()
plt.xlim(xmax=2.7e-3)

plt.show()