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sci_tfem.py
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sci_tfem.py
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# -*- coding: utf-8 -*-
"""
Created on Tue Sep 11 00:22:39 2018
@author: cheyi
"""
import numpy as np
from scipy.integrate import quad as integrate
import pylab as py
# from numba import jit
from tqdm import tqdm
def phi(f, i, tj, w = False):
if f == 0:
phi1 = lambda x: 0
phi2 = lambda x: 0
phi3 = lambda x: 0
else:
if w:
phi1 = lambda x: f*(1 - 23*(x/tj)**2 + 66*(x/tj)**3 -68*(x/tj)**4 + 24*(x/tj)**5) * ((x/tj) - 1/2)
phi2 = lambda x: f*(16*(x/tj)**2 - 32*(x/tj)**3 + 16*(x/tj)**4) * ((x/tj) - 1/2)
phi3 = lambda x: f*(7*(x/tj)**2 - 34*(x/tj)**3 + 52*(x/tj)**4 - 24*(x/tj)**5) * ((x/tj) - 1/2)
else:
phi1 = lambda x: f*(1 - 23*(x/tj)**2 + 66*(x/tj)**3 -68*(x/tj)**4 + 24*(x/tj)**5)
phi2 = lambda x: f*(16*(x/tj)**2 - 32*(x/tj)**3 + 16*(x/tj)**4)
phi3 = lambda x: f*(7*(x/tj)**2 - 34*(x/tj)**3 + 52*(x/tj)**4 - 24*(x/tj)**5)
dic = {0:phi1, 1:phi2, 2:phi3}
return dic[i]
def dphi(f, i, tj, w = False):
if f == 0:
dphi1 = lambda x: 0
dphi2 = lambda x: 0
dphi3 = lambda x: 0
else:
if w:
dphi1 = lambda x: f*(-46*(x/tj)/tj + 66*3*(x/tj)**2/tj - 68*4*(x/tj)**3/tj + 24*5*(x/tj)**4/tj) * ((x/tj) - 1/2)
dphi2 = lambda x: f*(32*(x/tj)/tj - 32*3*(x/tj)**2/tj + 16*4*(x/tj)**3/tj) * ((x/tj) - 1/2)
dphi3 = lambda x: f*(14*(x/tj)/tj - 34*3*(x/tj)**2/tj + 52*4*(x/tj)**3/tj - 24*5*(x/tj)**4/tj) * ((x/tj) - 1/2)
else:
dphi1 = lambda x: f*(-46*(x/tj)/tj + 66*3*(x/tj)**2/tj - 68*4*(x/tj)**3/tj + 24*5*(x/tj)**4/tj)
dphi2 = lambda x: f*(32*(x/tj)/tj - 32*3*(x/tj)**2/tj + 16*4*(x/tj)**3/tj)
dphi3 = lambda x: f*(14*(x/tj)/tj - 34*3*(x/tj)**2/tj + 52*4*(x/tj)**3/tj - 24*5*(x/tj)**4/tj)
dic = {0:dphi1, 1:dphi2, 2:dphi3}
return dic[i]
# @jit
def matfun(m, n, a, b, ksi, w, wn, k):
ms = 5.3
tj = 1/a/m * 60
B = np.array([[0, 0],
[k*w*b/ms, 0]])
A = np.array([[0, 1],
[-(k*w*b/ms + wn**2), -2*ksi*wn]])
II = np.eye(n)
N = np.zeros([2,2])
P = np.zeros([2,2])
NN = np.zeros([4,6])
PP = np.zeros([4,6])
for i in range(2):
for j in range(2):
ff1 = dphi(II[i,j], 0, tj)
ff2 = phi(A[i,j], 0, tj)
N[i,j] = integrate(ff1, 0, tj)[0] - integrate(ff2, 0, tj)[0]
gg = phi(B[i,j], 0, tj)
P[i,j] = integrate(gg, 0, tj)[0]
NN[0:2,0:2] = N
PP[0:2,0:2] = P
for i in range(2):
for j in range(2):
ff1 = dphi(1, 1, tj)
ff2 = phi(A[i,j], 1, tj)
N[i,j] = integrate(ff1, 0, tj)[0] - integrate(ff2, 0, tj)[0]
gg = phi(B[i,j], 1, tj)
P[i,j] = integrate(gg, 0, tj)[0]
NN[0:2,2:4] = N
PP[0:2,2:4] = P
for i in range(2):
for j in range(2):
ff1 = dphi(II[i,j], 2, tj)
ff2 = phi(A[i,j], 2, tj)
N[i,j] = integrate(ff1, 0, tj)[0] - integrate(ff2, 0, tj)[0]
gg = phi(B[i,j], 2, tj)
P[i,j] = integrate(gg, 0, tj)[0]
NN[0:2,4:] = N
PP[0:2,4:] = P
for i in range(2):
for j in range(2):
ff1 = dphi(II[i,j], 0, tj, w = True)
ff2 = phi(A[i,j], 0, tj, w = True)
N[i,j] = integrate(ff1, 0, tj)[0] - integrate(ff2, 0, tj)[0]
gg = phi(B[i,j], 0, tj, w = True)
P[i,j] = integrate(gg, 0, tj)[0]
NN[2:4,0:2] = N
PP[2:4,0:2] = P
for i in range(2):
for j in range(2):
ff1 = dphi(II[i,j], 1, tj, w = True)
ff2 = phi(A[i,j], 1, tj, w = True)
N[i,j] = integrate(ff1, 0, tj)[0] - integrate(ff2, 0, tj)[0]
gg = phi(B[i,j], 1, tj, w = True)
P[i,j] = integrate(gg, 0, tj)[0]
NN[2:4,2:4] = N
PP[2:4,2:4] = P
for i in range(2):
for j in range(2):
ff1 = dphi(II[i,j], 2, tj, w = True)
ff2 = phi(A[i,j], 2, tj, w = True)
N[i,j] = integrate(ff1, 0, tj)[0] - integrate(ff2, 0, tj)[0]
gg = phi(B[i,j], 2, tj, w = True)
P[i,j] = integrate(gg, 0, tj)[0]
NN[2:4,4:] = N
PP[2:4,4:] = P
return NN, PP
# @jit
def tfem(a, b, ksi, w, wn, k):
delay = 1/a*60
m = 40 + np.int(np.ceil(150*delay))
n = 2
sz = m*4+2
H = np.zeros([sz,sz])
G = np.zeros([sz,sz])
H[0:2,0:2] = np.eye(n)
G[0:2,sz-2:] = np.eye(n)
NN, PP = matfun(m, n, a, b, ksi, w, wn, k)
for i in range(1,m+1):
H[2+(i-1)*4:6+(i-1)*4, (i-1)*4:6+(i-1)*4] = NN;
G[2+(i-1)*4:6+(i-1)*4, (i-1)*4:6+(i-1)*4] = PP;
V = np.linalg.solve(H,G)
lam = np.linalg.eigvals(V)
rho = np.max(np.real(np.log(lam)))/delay
return rho
if __name__ == '__main__':
py.rcParams['xtick.labelsize'] = 12
py.rcParams['ytick.labelsize'] = 12
py.rcParams['font.size'] = 15
py.rcParams["font.weight"] = 'bold'
py.rcParams["axes.labelweight"] = 'bold'
py.rcParams['axes.linewidth'] = 2
# parameters in the simulation
ksi = 0.02
k = 200*10**9
w = 50*10**(-3)
wn = 300*2*np.pi
# resolution
n = 100
# range of the simulation
alist = np.linspace(500, 4000, n)
blist = np.linspace(0, 26e-5, n)
rho = np.zeros([n,n])
#simulation start
for i in tqdm(range(len(alist))):
for j in range(len(blist)):
rho[i,j] = tfem(alist[i], blist[j], ksi, w, wn, k)
# rho = np.load('MC_mean_nor_2d.npy')
py.figure()
a = py.contourf(alist, blist, rho.T, 0, colors = ['w', 'grey'])
b = py.contour(a, levels = a.levels, colors = 'k', linewidths = 3)
# py.plot(2.5e3, 1e-4, 'go')
# py.plot(2.5e3, 2e-4, 'bo')
# py.plot(2.5e3, 1.485e-4, 'yo')
# py.xlabel(r'$\Omega$' + r' $(round/min)$')
# py.ylabel(r'$b$' + r' $(m)$')
py.xlabel(r'$x_2$' + r' $(round/min)$')
py.ylabel(r'$x_1$' + r' $(m)$')
py.ticklabel_format(style = 'sci', axis = 'x', scilimits = (0,0))
py.ticklabel_format(style = 'sci', axis = 'y', scilimits = (0,0))
py.subplots_adjust(left = 0.14, right=0.9, top = 0.88, bottom = 0.13)