Datasets:
File size: 3,287 Bytes
92f32a3 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 | """Driven string + free-end ring standalone script."""
import numpy as np
import matplotlib.pyplot as plt
import matplotlib.animation as animation
from matplotlib.patches import Arc, Circle
L = 3.6274365689555736
mu = 0.061816546826749114
T = 4.683184571657916
A = 0.12558062153730848
f_drive = 1.9342617572984468
gamma_w = 1.0881157607858623
N = 200
n_per_frame = 16
duration = 12
fps = 30
omega = 2*np.pi*f_drive
c = np.sqrt(T/mu)
dx = L/N
x_grid = np.linspace(0.0, L, N+1)
dt = 1.0/(fps*n_per_frame)
factor = (c*dt/dx)**2
damp_n = 1.0/(1.0+gamma_w*dt)
damp_p = 1.0 - gamma_w*dt
assert factor < 1.0, f"CFL violated: factor={factor:.3f}"
u_curr = np.zeros(N+1); u_prev = np.zeros(N+1)
n_frames = int(duration*fps)+1
U_frames = np.zeros((n_frames, N+1))
U_frames[0] = u_curr.copy()
for frame in range(1, n_frames):
for sub in range(n_per_frame):
t_curr = (frame-1)/fps + (sub+1)*dt
u_next = np.empty_like(u_curr)
lap_int = u_curr[2:] - 2*u_curr[1:-1] + u_curr[:-2]
u_next[1:-1] = damp_n*(2*u_curr[1:-1] - damp_p*u_prev[1:-1] + factor*lap_int)
lap_right = 2*(u_curr[-2] - u_curr[-1])
u_next[-1] = damp_n*(2*u_curr[-1] - damp_p*u_prev[-1] + factor*lap_right)
u_next[0] = A*np.sin(omega*t_curr)
u_prev, u_curr = u_curr, u_next
U_frames[frame] = u_curr.copy()
fig_w, fig_h = 12.0, 4.0
fig_aspect = fig_w/fig_h
x_lo_d, x_hi_d = -0.40, L+0.40
y_lo_d, y_hi_d = -4.5*A, 4.5*A
dx_d, dy_d = x_hi_d-x_lo_d, y_hi_d-y_lo_d
if dx_d/dy_d < fig_aspect:
extra = (fig_aspect*dy_d - dx_d)/2.0
x_lo, x_hi = x_lo_d-extra, x_hi_d+extra
y_lo, y_hi = y_lo_d, y_hi_d
else:
extra = (dx_d/fig_aspect - dy_d)/2.0
x_lo, x_hi = x_lo_d, x_hi_d
y_lo, y_hi = y_lo_d-extra, y_hi_d+extra
fig = plt.figure(figsize=(fig_w,fig_h), facecolor="#1a1a2e")
ax = fig.add_axes([0,0,1,1]); ax.set_facecolor("#16213e")
ax.set_xlim(x_lo,x_hi); ax.set_ylim(y_lo,y_hi)
ax.set_aspect("equal"); ax.axis("off")
ax.axhline(0.0, color="#3a4357", lw=1, ls="--", zorder=0)
ax.plot([0,0],[y_lo,y_hi], color="#4a4e69", lw=1.5, ls=":", zorder=1)
driver_dot = Circle((0,0), 0.04, facecolor="#e63946",
edgecolor="#adb5bd", lw=1.0, zorder=5)
ax.add_patch(driver_dot)
r_x = 0.22; r_y = 0.11
back_arc = Arc((L,0), 2*r_x, 2*r_y, theta1=0, theta2=180,
edgecolor="#e63946", lw=10, zorder=2)
ax.add_patch(back_arc)
ax.plot([L,L],[y_lo,y_hi], color="#adb5bd", lw=14, solid_capstyle="butt", zorder=3)
front_arc = Arc((L,0), 2*r_x, 2*r_y, theta1=180, theta2=360,
edgecolor="#e63946", lw=10, zorder=5)
ax.add_patch(front_arc)
n_cut = int(round(r_x/dx))
n_inside = (N+1) - n_cut
str_x_plot = x_grid[:n_inside]
str_line, = ax.plot([],[], color="#a8dadc", lw=2.4, zorder=4)
def update(f):
u = U_frames[f]; yy = u[-1]
str_y = u[:n_inside].copy(); str_y[-1] = yy
str_line.set_data(str_x_plot, str_y)
driver_dot.center = (0, u[0])
back_arc.set_center((L, yy))
front_arc.set_center((L, yy))
return str_line, driver_dot, back_arc, front_arc
ani = animation.FuncAnimation(fig, update, frames=n_frames,
interval=1000.0/fps, blit=False)
ani.save("video.mp4", writer=animation.FFMpegWriter(fps=fps, bitrate=1800), dpi=120)
plt.close()
print("Saved video.mp4")
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