model checkpoint

scripts/string_model_de.py

@@ -100,3 +100,69 @@ import math
 # eq 23: temporal boundary conditions
 # y(-1, n) = -y(1, n)
 # y(N + 1, n) = -y(N - 1, n)
+
+# string parameters
+E = 1 # youngs modulus
+mu = 1 # linear mass density
+kappa = 1 # radius of gyration
+L = 1 # string length
+M_S = mu*L # string mass
+S = 1 # string cross sectional area
+T = 1 # string tension
+c = math.sqrt(T/mu) # transverse wave velocity
+stiffness = 1 # string stiffness parameter
+sigma = 1 # decay rate
+tau = 1/sigma # decay time
+omega = 1 # angular frequency
+
+# hammer parameters
+M_H = 1 # hammer mass
+HSMR = M_H/M_S # hammer-mass string ratio
+V_H_0 = 1 # initial hammer velocity at t=0
+x_0 = 1 # distance of hammer from agraffe
+alpha = x_0 / L # relative hammer striking position
+
+# simulation parameters
+f1 = 440 # fundamental frequency
+f_e = 44100 # sampling frequency
+N = 100 # number of string segments
+delta_t = 1/f_e # time step
+delta_x = L/N # spatial step
+H = f_e * 10 # length of simulation in time
+
+# empirical constants
+b_1 = 1 # some constant
+b_3 = 1 # some constant 
+K = 1 # hammer stiffness
+p = 1 # stiffness nonlinear exponent
+
+# derived components
+D = 1 + b_1*delta_t + 2*b_3/delta_t
+r = c*delta_t/delta_x
+a_1 = (2 - 2*r**2 + b_1/delta_t - 6*stiffness*N**2*r**2)/D
+a_2 = (-1 + b_1*delta_t + 2*b_3/delta_t)/D
+a_3 = (r**2*(1 + 4*stiffness*N**2))/D
+a_4 = (b_3/delta_t - stiffness*N**2*r**2)/D
+a_5 = (-b_3/delta_t)/D
+
+
+x = [0] * N # current string position
+last_x1 = [0] * N # string position from last timestep
+last_x2 = [0] * N # string position from two timesteps ago
+x_next = [0] * N # buffer for next string position
+
+x_out = np.zeros(H) # taking this as the sound output at some artibraty point along the string
+t = np.arange(0, H/f_e, delta_t)
+
+for n in range(H): # time
+
+    for i in range(N): # space
+        x_out[n] = math.sin(n/10000)
+
+# plotting
+plt.plot(t, x_out)
+plt.title("Step Response")
+plt.xlabel("t")
+plt.ylabel("y")
+plt.grid()
+plt.show()