def steady_state_response_i(zs=(0, 1.0, 0.1),
rmin=(0, 1, .1),
rmax=(1., 2.0, 0.1)):
"""Interactive phase plot of steady state response of
single degree of freedom system.
``steady_state_response`` is only functional in a
`Jupyter notebook <http://jupyter.org>`_.
Parameters
----------
zs: array
Array with the damping values
rmin, rmax: floats
Minimum and maximum frequency ratio
Returns
-------
r: Array
Array containing the values for the frequency ratio
A: Array
Array containing the values for anmplitude
Plot with steady state magnitude and phase
"""
if in_ipynb():
w = interactive(steady_state_response, zs=zs, rmin=rmin, rmax=rmax)
display(w)
else:
print('steady_state_response_i can only be used in an iPython\
notebook.')
def time_plot_i(max_time=(1.0, 100.0),
x0=(-100, 100),
v0=(-100, 100),
m=(1.0, 100.0),
c=(0.0, 100.0),
k=(1.0, 100.0)):
'''Interactive single degree of freedom free reponse plot in iPython
``time_plot_i`` is only functional in a
`Jupyter notebook <http://jupyter.org>`_.
Parameters
----------
m, c, k : floats, optional
mass, damping coefficient, stiffness
x0, v0: floats, optional
initial displacement, initial velocity
max_time: float, optional
end time for :math:`x(t)`
'''
if in_ipynb():
w = interactive(time_plot,
max_time=max_time,
v0=v0,
m=m,
c=c,
x0=x0,
k=k)
display(w)
else:
print('time_plot_i can only be used in an iPython notebook.')
'''
def transmissibility_i(zs=(0, 1.0, 0.1), rmin=0, rmax=2.0):
"""Interactive phase plot of transmissibility of
single degree of freedom system.
``transmissibility_i`` is only functional in a
`Jupyter notebook <http://jupyter.org>`_.
Parameters
----------
zs: array
Array with the damping values
rmin, rmax: float
Minimum and maximum frequency ratio
Returns
-------
r: Array
Array containing the values for the frequency ratio
D: Array
Array containing the values for displacement
F: Array
Array containing the values for force
Plot with Displacement transmissibility ratio
and force transmissibility ratio
"""
if in_ipynb():
w = interactive(transmissibility, zs=zs, rmin=rmin, rmax=rmax)
display(w)
else:
print('transmissibility_i can only be used in an iPython notebook.')
def phase_plot_i(max_time=(1.0, 200.0),
v0=(-100, 100, 1.0),
m=(1.0, 100.0, 1.0),
c=(0.0, 1.0, 0.1),
x0=(-100, 100, 1),
k=(1.0, 100.0, 1.0)):
"""Interactive phase plot of free response of single degree of freedom system.
``phase_plot_i`` is only functional in a
`Jupyter notebook <http://jupyter.org>`_.
Parameters
----------
m, c, k: floats, optional
mass, damping coefficient, stiffness
x0, v0: floats, optional
initial displacement, initial velocity
max_time: float, optional
end time for :math:`x(t)`
"""
if in_ipynb():
w = interactive(phase_plot,
max_time=max_time,
v0=v0,
m=m,
c=c,
x0=x0,
k=k)
plt.show()
display(w)
else:
print('phase_plot_i can only be used in an iPython notebook.')
def phase_plot_i(max_time=(1.0, 200.0), v0=(-100, 100, 1.0), m=(1.0, 100.0, 1.0),
c=(0.0, 1.0, 0.1), x0=(-100, 100, 1), k=(1.0, 100.0, 1.0)):
'''Interactive phase plot of free response of single degree of freedom system.
For information on variables see ``free_response``'''
w = interactive(phase_plot, max_time=max_time, v0=v0, m=m,
c=c, x0=x0, k=k)
display(w)
def time_plot_i(max_time=(1.0, 100.0), v0=(-100, 100), m=(1.0, 100.0),
c=(0.0, 100.0), x0=(-100, 100), k=(1.0, 100.0)):
w = interactive(time_plot, max_time=max_time, v0=v0, m=m,
c=c, x0=x0, k=k)
# I'd like to get the sliders to be side by side to take less vertical space
# cont = widgets.HBox(children = w)
# print(help(w))
display(w)
from IPython.display import display
from ipywidgets.widgets.interaction import interactive
def f(a, b):
display(a + b)
return a + b
w = interactive(f, a=10, b=20)
print(type(w))
display(w)
def duff_bif_phase(k = 0.012):
plt.subplot(1,2,1)
mu = 0.01; alpha = .2; sigma = 0.05; amax = 1.0
phase_plot(duf_bif_deriv, max_time=100.0, numx = 7, numv = 7, span = (0.01,1.2,-0.5,4), args = (mu, k, alpha, sigma))
plt.xlabel('a')
plt.ylabel('$\gamma$')
plt.subplot(1,2,2)
a, gamma = duff_bif_diag(mu = 0.01, k_int = k, alpha = alpha, sigma = sigma, amax = amax)
plt.title('')
plt.subplot(1,2,1)
sp.reshape(a,(3,1))
plt.plot(sp.reshape(a,(1,3)),sp.reshape(gamma,(1,3)),'*')
plt.tight_layout(w_pad=1.5)
# This little bit makes the prior function interactive with 'ipcd.display(duff_interact_jump)'
duff_interact_jump = interactive(duff_bif_phase, k = (0.0070,0.017,.0004))
def duff_amp_solve(mu = 0.01, k = 0.013, alpha = .2, sigma = (-0.5,.5)):
sigma = sp.linspace(sigma[0],sigma[1],1000)
#print(sigma.size)
#print(sigma)
a = sp.zeros((sigma.size,3))*1j
first = 1
#print(a)
for idx, sig in enumerate(sigma):
#print(idx)
p = sp.array([alpha**2, 0, -16./3.*alpha*sig, 0, 64./9.*(mu**2 + sig**2),0,-64./9.*k**2])
soln = sp.roots(p)
#print('original soln')
def duff_bif_phase(k = 0.012):
plt.subplot(1,2,1)
mu = 0.01; alpha = .2; sigma = 0.05; amax = 1.0
phase_plot(duf_bif_deriv, max_time=100.0, numx = 7, numv = 7, span = (0.01,1.2,-0.5,4), args = (mu, k, alpha, sigma))
plt.xlabel('a')
plt.ylabel('$\gamma$')
plt.subplot(1,2,2)
a, gamma = duff_bif_diag(mu = 0.01, k_int = k, alpha = alpha, sigma = sigma, amax = amax)
plt.title('')
plt.subplot(1,2,1)
sp.reshape(a,(3,1))
plt.plot(sp.reshape(a,(1,3)),sp.reshape(gamma,(1,3)),'*')
plt.tight_layout(w_pad=1.5)
# This little bit makes the prior function interactive with 'ipcd.display(duff_interact_jump)'
duff_interact_jump = interactive(duff_bif_phase, k = (0.0070,0.017,.0004))
def duff_amp_solve(mu = 0.01, k = 0.013, alpha = .2, sigma = (-0.5,.5)):
sigma = sp.linspace(sigma[0],sigma[1],1000)
#print(sigma.size)
#print(sigma)
a = sp.zeros((sigma.size,3))*1j
first = 1
#print(a)
for idx, sig in enumerate(sigma):
#print(idx)
p = sp.array([alpha**2, 0, -16./3.*alpha*sig, 0, 64./9.*(mu**2 + sig**2),0,-64./9.*k**2])
soln = sp.roots(p)
#print('original soln')