def RHS(X, t=0.0):
x1, x2 = X
gs.wedge(theta=x1, thetaDot=x2)
[Fx, Fy, Mz] = aero.calcLoad()
x1dot = x2
x2dot = -100*x1 + Mz
return [x1dot, x2dot]
def RHS(X, t=0.0):
x1, x2 = X
gs.wedge(theta=x1, thetaDot=x2)
[Fx, Fy, Mz] = aero.calcLoad()
x1dot = x2
x2dot = -100 * x1 + Mz
return [x1dot, x2dot]
def residual(x):
T = x[-1]
x = x[:-1]
omega0 = 2*np.pi / T
Omega = omega0 * n
t = np.linspace(0, T, N+1)
t = t[0:-1]
# # Check derivatives
a = 0.1
x_ = np.sin(a*t)
dxdt_ = a*np.cos(a*t)
X_ = np.fft.fft(x_)
DxDt_ = np.fft.ifft(1j * np.multiply(Omega, X_))
X = np.fft.fft(x)
dx = np.fft.ifft(np.multiply(1j * Omega, X))
ddx = np.fft.ifft(np.multiply(-Omega**2, X))
f = np.zeros(N)
for ix in range(0, len(x)):
if np.imag(x[ix]) > 1e-3 or np.imag(dx[ix]) > 1e-3:
np.disp('You have a problem with imaginary numbers!')
np.disp([np.imag(x[ix]), np.imag(dx[ix])])
gs.wedge(theta=np.real(x[ix]), thetaDot=np.real(dx[ix]))
[Fx, Fy, Mz] = aero.calcLoad()
f[ix] = Mz
Residual = ddx + 100 * x - Mz
Residual = Residual
Residual = np.sum(np.abs((Residual**2)))
# Residual = np.sum(np.abs((Residual**1)))
# return Residual + np.max(np.abs(np.real(DxDt_ - dxdt_)))
return Residual
def residual(x):
T = x[-1]
x = x[:-1]
omega0 = 2 * np.pi / T
Omega = omega0 * n
t = np.linspace(0, T, N + 1)
t = t[0:-1]
# # Check derivatives
a = 0.1
x_ = np.sin(a * t)
dxdt_ = a * np.cos(a * t)
X_ = np.fft.fft(x_)
DxDt_ = np.fft.ifft(1j * np.multiply(Omega, X_))
X = np.fft.fft(x)
dx = np.fft.ifft(np.multiply(1j * Omega, X))
ddx = np.fft.ifft(np.multiply(-Omega**2, X))
f = np.zeros(N)
for ix in range(0, len(x)):
if np.imag(x[ix]) > 1e-3 or np.imag(dx[ix]) > 1e-3:
np.disp('You have a problem with imaginary numbers!')
np.disp([np.imag(x[ix]), np.imag(dx[ix])])
gs.wedge(theta=np.real(x[ix]), thetaDot=np.real(dx[ix]))
[Fx, Fy, Mz] = aero.calcLoad()
f[ix] = Mz
Residual = ddx + 100 * x - Mz
Residual = Residual
Residual = np.sum(np.abs((Residual**2)))
# Residual = np.sum(np.abs((Residual**1)))
# return Residual + np.max(np.abs(np.real(DxDt_ - dxdt_)))
return Residual
def residual(x):
X = np.fft.fft(x)
dx = np.fft.ifft(np.multiply(1j * Omega, X))
ddx = np.fft.ifft(np.multiply(-Omega**2, X))
f = np.zeros(N)
for ix in range(0, len(x)):
if np.imag(x[ix]) > 1e-3 or np.imag(dx[ix]) > 1e-3:
np.disp('You have a problem with imaginary numbers!')
np.disp([np.imag(x[ix]), np.imag(dx[ix])])
gs.wedge(theta=np.real(x[ix]), thetaDot=np.real(dx[ix]))
[Fx, Fy, Mz] = aero.calcLoad()
f[ix] = Mz
Residual = ddx + 100 * x - Mz
Residual = np.sum(np.abs((Residual**2)))
return Residual
def residual(x):
X = np.fft.fft(x)
dx = np.fft.ifft(np.multiply(1j * Omega, X))
ddx = np.fft.ifft(np.multiply(-Omega**2, X))
f = np.zeros(N)
for ix in range(0, len(x)):
if np.imag(x[ix]) > 1e-3 or np.imag(dx[ix]) > 1e-3:
np.disp('You have a problem with imaginary numbers!')
np.disp([np.imag(x[ix]), np.imag(dx[ix])])
gs.wedge(theta=np.real(x[ix]), thetaDot=np.real(dx[ix]))
[Fx, Fy, Mz] = aero.calcLoad()
f[ix] = Mz
Residual = ddx + 100 * x - Mz
Residual = np.sum(np.abs((Residual**2)))
return Residual
# Author: Koorosh Gobal
# Python code for 3.5
# Main file for flutter analysis
# -----------------------------------
import getShape as gs
import aerodynamic as aero
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import minimize
from scipy.integrate import odeint
# -----------------------------------
gs.wedge(theta = 0, thetaDot = 5)
[Fx, Fy, Mz] = aero.calcLoad()
N = 9
T = 1*2*np.pi
t = np.linspace(0, T, N+1)
t = t[0:-1]
Omega = np.fft.fftfreq(N, T/(2*np.pi*N))
x0 = np.zeros(N)
def residual(x):
X = np.fft.fft(x)
dx = np.fft.ifft(np.multiply(1j * Omega, X))
ddx = np.fft.ifft(np.multiply(-Omega**2, X))
f = np.zeros(N)
for ix in range(0, len(x)):
if np.imag(x[ix]) > 1e-3 or np.imag(dx[ix]) > 1e-3:
np.disp('You have a problem with imaginary numbers!')
np.disp([np.imag(x[ix]), np.imag(dx[ix])])
gs.wedge(theta=np.real(x[ix]), thetaDot=np.real(dx[ix]))
# Author: Koorosh Gobal
# Python code for 3.5
# Main file for flutter analysis
# This file calls 'aerodynamics' and 'getShape' functions. Please make sure that
# you have them is the same directory.
# -----------------------------------
import getShape as gs
import aerodynamic as aero
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import minimize
from scipy.integrate import odeint
# -----------------------------------
gs.wedge(theta=0, thetaDot=5)
[Fx, Fy, Mz] = aero.calcLoad()
N = 9
T = 1 * 2 * np.pi
t = np.linspace(0, T, N + 1)
t = t[0:-1]
Omega = np.fft.fftfreq(N, T / (2 * np.pi * N))
x0 = np.zeros(N)
def residual(x):
X = np.fft.fft(x)
dx = np.fft.ifft(np.multiply(1j * Omega, X))
ddx = np.fft.ifft(np.multiply(-Omega**2, X))
f = np.zeros(N)
for ix in range(0, len(x)):
if np.imag(x[ix]) > 1e-3 or np.imag(dx[ix]) > 1e-3: