def simulate(Theta, alpha, num_periods=10):
# Dimensionless model requires the following parameters:
from math import sin, pi
I = Theta
V = 0
m = 1
b = alpha
s = lambda u: sin(u)
F = lambda t: 0
damping = 'quadratic'
# Estimate T and dt from the small angle solution
P = 2*pi # One period (theta small, no drag)
dt = P/40 # 40 intervals per period
T = num_periods*P
theta, t = solver(I, V, m, b, s, F, dt, T, damping)
omega = np.zeros(theta.size)
omega[1:-1] = (theta[2:] - theta[:-2])/(2*dt)
omega[0] = (theta[1] - theta[0])/dt
omega[-1] = (theta[-1] - theta[-2])/dt
S = omega**2 + np.cos(theta)
D = alpha*np.abs(omega)*omega
return t, theta, S, D
def solve(self, t, terminate=None):
dt = t[1] - t[0] # assuming constant time step
T = t[-1]
I, V = self.U0
self.u, self.t = vib.solver(I,
V,
self.rhs.m,
self.rhs.b,
self.rhs.s,
self.rhs.F,
dt,
T,
damping=self.rhs.damping)
# Must compute v=u' and pack with u
self.v = np.zeros_like(self.u)
self.v[1:-1] = (self.u[2:] - self.u[:-2]) / (2 * dt)
self.v[0] = V
self.v[-1] = (self.u[-1] - self.u[-2]) / dt
self.r = np.zeros((self.u.size, 2))
self.r[:, 0] = self.u
self.r[:, 1] = self.v
if terminate is not None:
for i in range(len(self.t)):
if terminate(self.r, self.t, i):
return self.r[:i + 1], self.t[:i + 1]
return self.r, self.t
def simulate_forced_vibrations2():
# Scaling with u_c based on gamma=1
from vib import solver, visualize
from math import pi
delta = 0.5
delta = 0.99
alpha = 1
u, t = solver(I=alpha, V=0, m=1, b=0, s=lambda u: u, F=lambda t: cos(delta * t), dt=2 * pi / 160, T=2 * pi * 160)
visualize(u, t)
raw_input()
def simulate_forced_vibrations3():
# Scaling with u_c based on large delta
from vib import solver, visualize
from math import pi
delta = 10
alpha = 0.05*delta**2
u, t = solver(I=alpha, V=0, m=1, b=0, s=lambda u: delta**(-2)*u,
F=lambda t: cos(t),
dt=2*pi/160, T=2*pi*20)
visualize(u, t)
raw_input()
def simulate_forced_vibrations1():
# Scaling with u_c based on resonance amplitude
from vib import solver, visualize
from math import pi
delta = 0.99
alpha = 1 - delta**2
u, t = solver(I=alpha, V=0, m=1, b=0, s=lambda u: u,
F=lambda t: (1-delta**2)*cos(delta*t),
dt=2*pi/160, T=2*pi*160)
visualize(u, t)
raw_input()
def simulate_forced_vibrations3():
# Scaling with u_c based on large delta
from vib import solver, visualize
from math import pi
delta = 10
alpha = 0.05 * delta ** 2
u, t = solver(
I=alpha, V=0, m=1, b=0, s=lambda u: delta ** (-2) * u, F=lambda t: cos(t), dt=2 * pi / 160, T=2 * pi * 20
)
visualize(u, t)
raw_input()
def simulate_forced_vibrations2():
# Scaling with u_c based on gamma=1
from vib import solver, visualize
from math import pi
delta = 0.5
delta = 0.99
alpha = 1
u, t = solver(I=alpha, V=0, m=1, b=0, s=lambda u: u,
F=lambda t: cos(delta*t),
dt=2*pi/160, T=2*pi*160)
visualize(u, t)
raw_input()
def simulate_forced_vibrations1():
# Scaling with u_c based on resonance amplitude
from vib import solver, visualize
from math import pi
delta = 0.99
alpha = 1 - delta ** 2
u, t = solver(
I=alpha,
V=0,
m=1,
b=0,
s=lambda u: u,
F=lambda t: (1 - delta ** 2) * cos(delta * t),
dt=2 * pi / 160,
T=2 * pi * 160,
)
visualize(u, t)
raw_input()
def solve(self, t, terminate=None):
dt = t[1] - t[0] # assuming constant time step
T = t[-1]
I, V = self.U0
self.u, self.t = vib.solver(
I, V, self.rhs.m, self.rhs.b, self.rhs.s, self.rhs.F,
dt, T, damping=self.rhs.damping)
# Must compute v=u' and pack with u
self.v = np.zeros_like(self.u)
self.v[1:-1] = (self.u[2:] - self.u[:-2])/(2*dt)
self.v[0] = V
self.v[-1] = (self.u[-1] - self.u[-2])/dt
self.r = np.zeros((self.u.size, 2))
self.r[:,0] = self.u
self.r[:,1] = self.v
if terminate is not None:
for i in range(len(self.t)):
if terminate(self.r, self.t, i):
return self.r[:i+1], self.t[:i+1]
return self.r, self.t
import sys, os
sys.path.insert(0, os.path.join(os.pardir, 'src-vib'))
from vib import solver, visualize, plt
from math import pi, sin
import numpy as np
beta_values = [0.005, 0.05, 0.2]
beta_values = [0.00005]
gamma_values = [5, 1.5, 1.1, 1]
for i, beta in enumerate(beta_values):
for gamma in gamma_values:
u, t = solver(I=1,
V=0,
m=1,
b=2 * beta,
s=lambda u: u,
F=lambda t: sin(gamma * t),
dt=2 * pi / 60,
T=2 * pi * 20,
damping='quadratic')
visualize(u, t, title='gamma=%g' % gamma, filename='tmp_%s' % gamma)
print gamma, 'max u amplitude:', np.abs(u).max()
for ext in 'png', 'pdf':
cmd = 'doconce combine_images '
cmd += ' '.join(['tmp_%s.' % gamma + ext for gamma in gamma_values])
cmd += ' resonance%d.' % (i + 1) + ext
os.system(cmd)
raw_input()
import sys, os
sys.path.insert(0, os.path.join(os.pardir, 'src-vib'))
from vib import solver, visualize, plt
from math import pi, sin
import numpy as np
beta_values = [0.005, 0.05, 0.2]
beta_values = [0.00005]
gamma_values = [5, 1.5, 1.1, 1]
for i, beta in enumerate(beta_values):
for gamma in gamma_values:
u, t = solver(I=1, V=0, m=1, b=2*beta, s=lambda u: u,
F=lambda t: sin(gamma*t), dt=2*pi/60,
T=2*pi*20, damping='quadratic')
visualize(u, t, title='gamma=%g' %
gamma, filename='tmp_%s' % gamma)
print gamma, 'max u amplitude:', np.abs(u).max()
for ext in 'png', 'pdf':
cmd = 'doconce combine_images '
cmd += ' '.join(['tmp_%s.' % gamma + ext for gamma in gamma_values])
cmd += ' resonance%d.' % (i+1) + ext
os.system(cmd)
raw_input()
