def plot_twisting_errors(nodes, n=3):
print "\nEvaluating Twisting errors for {0} first modes:".format(n)
plt.figure("twisting_errors")
freqs_i = [[] for _ in range(n)]
for N in nodes:
beam = TwistingBeam(L, S, mat, BCs=[0], nodes=N)
for i, (freq, mode) in enumerate(beam.get_modes()[:n]):
freqs_i[i].append(freq)
modes = cantilever_twisting_modes(beam, n)
freqs = map(lambda x: x[0], modes)
for i, (f, f_i) in enumerate(zip(freqs, freqs_i)):
plt.plot(nodes, abs(f-f_i)/f*100, bstyles[i])
plt.legend(["$f = %.2f Hz$" % f for f in freqs])
plt.xlabel(r'Number of nodes')
plt.ylabel(r'Relative error $\epsilon = |f_n - f|/f*100$ (%)')
plt.grid()
def plot_twisting_modes(nodes, n=3):
print "\nPloting {0} first twisting modes:".format(n)
fig, axarr = plt.subplots(n, sharex=True)
fs = []
for j, N in enumerate(nodes):
beam = TwistingBeam(L, S, mat, BCs=[0], nodes=N)
modes = beam.get_modes()[:n]
print "\nN:", N
for i, (freq, mode) in enumerate(modes):
print "mode {0}, f = {1:.2f} Hz".format(i+1, freq)
axarr[i].plot(np.linspace(0, L, len(mode)), mode, styles[j % 3])
fs.append(map(lambda x: x[0], modes))
axarr[n-1].set_xlabel(r"Length of the beam ($y$ axis) in meters")
axarr[n/2].set_ylabel("Normalized angular deflection")
fi = []
modes = cantilever_twisting_modes(beam, n, points=20)
print "\nStatic:"
for i, (freq, mode) in enumerate(modes):
print "mode {0}, f = {1:.2f} Hz".format(i+1, freq)
fi.append(freq)
x = mode.T[0]
y = mode.T[1]
axarr[i].plot(x, y, styles[2])
axarr[i].grid()
axarr[n/2].legend(["N = 8", "N = 20", "static"],
loc='center right',
bbox_to_anchor=(1.3, 0.5))
plt.subplots_adjust(right=0.8)
fs = [fi] + fs
fs = np.array(fs).T
f0 = fs[:, 0:1] * np.ones((1, 2))
errs = np.abs(fs[:, 1:] - f0) / f0 * 100
with open("twisting.out", "w") as outfile:
for a, b in zip(fs, errs):
line = "\t".join(["%.2f" % p for p in np.hstack((a, b))])
outfile.writelines(line + "\n")
