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| import pylab as pl
import numpy as np
import sympy as sy
from scipy import integrate
from scipy.integrate import quad
from scipy import integrate as intg
from sympy import *
L = 60
D = 5
e = 0.2
E = 25000
rho = 2400
ksi = 0.05
x = np.linspace(0, L, 30)
def moment_quad():
I = np.pi*((D)**4-(D-2*e)**4)/64
return I
def masse_cheminee():
S = np.pi*(((D/2)**2-(D/2-e)**2))
m = rho*S
return m
def fonction_deplacement(x):
psi = 1-np.cos(np.pi*x/(2*L))
return psi
def masse_generalisee(x):
m_tilde = (1-np.cos(np.pi*x/(2*L)))**2*m
return m_tilde
def rigidite_generalisee(x):
x = sy.symbols('x')
y = 1-sy.cos(sy.pi*x/(2*L))
yprime = sy.diff(y, x)
ysec = yprime.diff(x)
k_tilde = (ysec)**2*E*I
return k_tilde
def facteur_excitation(x):
gamma = (1-np.cos(np.pi*x/(2*L)))*m
return gamma
I = moment_quad()
m = masse_cheminee()
psi = fonction_deplacement(x)
m_tilde = masse_generalisee(x)
k_tilde = rigidite_generalisee(x)
gamma = facteur_excitation(x)
print("moment quadratique I = ", I, "m4")
print("masse lineaire ml = ", m, "kg/m")
print("raideur EI = ", E*I/(16*L**3))
i1 = intg.romberg(fonction_deplacement, 0, L)
i2 = intg.romberg(masse_generalisee, 0, L)
i3 = intg.romberg(rigidite_generalisee, 0, L)
i4 = intg.romberg(facteur_excitation, 0, L) |
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