circular_membrane.py

from __future__ import division
from numpy import pi, sin, cos, mgrid
from scipy.special import jn, jn_zeros
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import matplotlib.animation as animation
from matplotlib import rcParams


# In Windows the next line should provide the full path to convert.exe
# since convert is a Windows command
rcParams['animation.convert_path'] = "C:\Program Files\ImageMagick-6.9.3\convert.exe"
rcParams['savefig.transparent'] = True
plot_args = {'rstride': 1, 'cstride': 1, 'cmap':"RdYlBu",
             'linewidth': 0.2, 'antialiased': True, 'color': '#1e1e1e',
             'shade': True, 'alpha': 1.0, 'vmin': -1, 'vmax':1}


def data_gen(num, m, n):
    ax.cla()
    lam = jn_zeros(m, n)[-1]
    dt = 2*pi/(30*lam)
    z = cos(m*t)*jn(m, lam*r)*sin(lam*num*dt)
    surf = ax.plot_surface(x, y, z, **plot_args)
    ax.view_init(elev=30, azim=45)
    ax.set_xlim(-0.6, 0.6)
    ax.set_ylim(-0.6, 0.6)
    ax.set_zlim(-1, 1)    
    plt.axis("off")
    return surf


r, t = mgrid[0:1:20j, 0:2*pi:40j]
x, y = r*cos(t), r*sin(t)
for m in range(0, 3):
    for n in range(1, 4):
        fig = plt.figure(dpi=600, facecolor=None)
        ax = fig.add_subplot(111, projection='3d')
        ani = animation.FuncAnimation(fig, data_gen, range(30), blit=False,
                              fargs=(m, n))
#        ani.save("Drum vibration mode01.gif", writer='imagemagick')
        ani.save("Drum vibration mode%i%i.avi" % (m, n), writer='ffmpeg')
#        plt.show()

membrane-3-2.mp4

membrane_ani.py

import numpy as np
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
import matplotlib.animation as animation

# In Windows the next line should provide the full path to convert.exe
# since convert is a Windows command
#rcParams['animation.convert_path'] = "C:\Program Files\ImageMagick-6.9.3\convert.exe"


fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
plot_args = {'rstride': 1, 'cstride': 1, 'cmap':"Spectral",
             'linewidth': 0.1, 'antialiased': True, 'edgecolor': '#1e1e1e',
             'shade': True, 'alpha': 1.0, 'vmin': -1, 'vmax':1}
x, y = np.mgrid[0:1:31j, 0:1:31j]


def data_gen(num):
    ax.cla()
    z = np.sin(3*np.pi*x)*np.sin(2*np.pi*y)*np.sin(0.1*np.pi*num)
    surf = ax.plot_surface(x, y, z, **plot_args)
    ax.view_init(elev=35, azim=45)
    ax.set_xlim(0, 1)
    ax.set_ylim(0, 1)
    ax.set_zlim(-1, 1)
    ax.set_xlabel(r"$x$")
    ax.set_ylabel(r"$y$")
    ax.set_zlabel(r"$z$")
    ax.set_zticks([-1, -0.5, 0, 0.5, 1])
    return surf


ani = animation.FuncAnimation(fig, data_gen, range(30), blit=False)
ani.save("membrane-3-2.mp4")
plt.show()

plots.py

import numpy as np
import matplotlib.pyplot as plt
from matplotlib import rcParams

rcParams['font.family'] = 'serif'
rcParams['font.size'] = 16

x = np.pi*np.linspace(-1, 1, 200)
y = np.sin(x)
plt.figure(figsize=(8,6))
plt.plot(x/np.pi,np.pi*y)
plt.grid(True, color="blue", alpha=0.3)
plt.xlabel(r"$x/\pi$", size=18)
plt.ylabel(r"$\pi y$", size=18)

x = np.pi*np.linspace(-1, 1, 200)
y = np.pi*np.linspace(-1, 1, 200)
X,Y = np.meshgrid(x,y)
Z = np.sin(np.sqrt(X**2 + Y**2))/np.sqrt(X**2 + Y**2)
plt.figure(figsize=(8,8))
plt.contourf(X,Y,Z, cmap="RdBu")
plt.xlabel(r"$x$", size=18)
plt.ylabel(r"$y$", size=18)

plt.show()

square_membrane.py

# -*- coding: utf-8 -*-
"""
Animation of a rectangular membrane with initial conditions

    0.02*(x - x**2)*(y - 2*y**2)
    
in the domain [0, 1] x [0, 0.5]

@author: Nicolas Guarin-Zapata
"""
from __future__ import division
from numpy import mgrid, sin, pi, sqrt, cos
import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.animation as animation


plot_args = {'rstride': 1, 'cstride': 1, 'cmap':"Spectral",
             'linewidth': 0.1, 'antialiased': True, 'edgecolor': '#1e1e1e',
             'shade': True, 'alpha': 1, 'vmin': -6e-4, 'vmax':6e-4}


def data_gen(num, Nx, Ny, dt):
    ax.cla()
    z = np.zeros_like(x)
    t = num * dt
    for m in range(1, Nx + 1, 2):
        for n in range(1, Ny + 1, 2):
            k = sqrt(m**2 + 4*n**2)
            z += sin(m*pi*x) * sin(2*n*pi*y)*cos(20*pi*k*t)/(m*n)**3
    z = 0.64*z/pi**6
    surf = ax.plot_surface(x, y, z, **plot_args)
    ax.set_zlim(-6e-4, 6e-4)    
    return surf


Nx = 50
Ny = 50
dt = 0.001
y, x = mgrid[0:0.5:21j, 0:1:21j]
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ani = animation.FuncAnimation(fig, data_gen, range(200), blit=False,
                              fargs=(Nx, Ny, dt))
plt.show()