homeburger/sonobulus
1
0
Fork 0
Code Issues Pull Requests Actions Packages Projects Releases Wiki Activity

sync

Browse Source
This commit is contained in:
Bliblank
2026-06-19 13:50:49 -05:00
parent 2bad7d66d8
commit a2df345216
2 changed files with 40 additions and 24 deletions
Download Patch File Download Diff File Expand all files Collapse all files

53
scripts/string_model_de.py
View File

@@ -2,6 +2,7 @@
import matplotlib.pyplot as plt import matplotlib.pyplot as plt
import numpy as np import numpy as np
import math import math
import sounddevice as sd
# https://people.cs.uchicago.edu/~ridg/stabil/pianostring.pdf # https://people.cs.uchicago.edu/~ridg/stabil/pianostring.pdf
# a differential equations model for a piano string # a differential equations model for a piano string
@@ -104,23 +105,26 @@ import math
# simulation parameters # simulation parameters
f1 = 50 # fundamental frequency f1 = 50 # fundamental frequency
f_e = 44100 # sampling frequency f_e = 44100 # sampling frequency
N = 50 # number of string segments N = 200 # number of string segments
delta_t = 1/f_e # time step delta_t = 1/f_e # time step
L = 0.5 # string length, meters L = 0.5 # string length, meters
delta_x = L/N # spatial step delta_x = L/N # spatial step
H = int(f_e * 0.1) # length of simulation in time H = int(f_e * 2) # length of simulation in time
# string parameters # string parameters
E = 200 * 10**9 # youngs modulus, steel = 200GPa E = 100 * 10**9 # youngs modulus, steel = 200GPa
rho = 8000 # density, steel, kg/m^3 rho = 8000 # density, steel, kg/m^3
radius = 0.002 # meters radius = 0.005 # meters
kappa = radius/2 # radius of gyration, r/2 for a circular string kappa = radius/2 # radius of gyration, r/2 for a circular string
S = math.pi*radius**2 # string cross sectional area, assuming circular S = math.pi*radius**2 # string cross sectional area, assuming circular
mu = S*rho # linear mass density mu = S*rho # linear mass density
M_S = mu*L # string mass M_S = mu*L # string mass
T = 10000 # string tension, N T = 500 # string tension, N
c = math.sqrt(T/mu) # transverse wave velocity c = math.sqrt(T/mu) # transverse wave velocity
stiffness = kappa**2 * delta_t**2 / delta_x**4 # string stiffness parameter I = math.pi*radius**4 / 4
k = math.sqrt(E*I/(rho*S))
# stiffness = k**2 * delta_t**2 / delta_x**4 # string stiffness parameter
stiffness = 0
sigma = 1 # decay rate sigma = 1 # decay rate
tau = 1/sigma # decay time tau = 1/sigma # decay time
omega = 1/f1 # angular frequency omega = 1/f1 # angular frequency
@@ -128,14 +132,14 @@ omega = 1/f1 # angular frequency
# hammer parameters # hammer parameters
M_H = 0.5 # hammer mass, kg M_H = 0.5 # hammer mass, kg
HSMR = M_H/M_S # hammer-mass string ratio HSMR = M_H/M_S # hammer-mass string ratio
V_H_0 = 10 # initial hammer velocity at t=0, m/s V_H_0 = 10000000000 # initial hammer velocity at t=0, m/s
x_0 = L/2 # distance of hammer from agraffe x_0 = L/2 # distance of hammer from agraffe
alpha = x_0 / L # relative hammer striking position alpha = x_0 / L # relative hammer striking position
# empirical constants # empirical constants
b_1 = 1 # some constant b_1 = 0 # some constant
b_3 = 0.001 # some constant b_3 = 0 # some constant
K = 10 # hammer stiffness K = 1 # hammer stiffness
p = 1 # stiffness nonlinear exponent p = 1 # stiffness nonlinear exponent
# derived components # derived components
@@ -152,7 +156,7 @@ x = [0] * N # current string position
x_initial = [0] * N # assuming string at rest x_initial = [0] * N # assuming string at rest
last_x1 = [0] * N # string position from last timestep last_x1 = [0] * N # string position from last timestep
last_x2 = [0] * N # string position from two timesteps ago last_x2 = [0] * N # string position from two timesteps ago
x_sample = int(alpha*N) # location where we sample the string position for signal x_sample = int(0.8*N) # location where we sample the string position for signal
# hammer # hammer
F_H_current = 0 # current force exterted by hammer F_H_current = 0 # current force exterted by hammer
@@ -175,7 +179,7 @@ def plot_current():
def spatial_window(i): def spatial_window(i):
if(i < x_hammer+i_H/2 and i > x_hammer-i_H/2): if(i < x_hammer+i_H/2 and i > x_hammer-i_H/2):
return 1 return abs(i-x_hammer-i_H/2)
else: else:
return 0 return 0
@@ -196,8 +200,6 @@ eta_current = eta_next
for i in range(1, N-1): for i in range(1, N-1):
x[i] = last_x1[i+1] + last_x1[i-1] - x_initial[i] + ((delta_t**2)*N*F_H_current*spatial_window(i))/M_S x[i] = last_x1[i+1] + last_x1[i-1] - x_initial[i] + ((delta_t**2)*N*F_H_current*spatial_window(i))/M_S
plot_current()
last_x2 = last_x1.copy() last_x2 = last_x1.copy()
last_x1 = x.copy() last_x1 = x.copy()
F_H_current = K * abs(eta_current - x[x_hammer])**p F_H_current = K * abs(eta_current - x[x_hammer])**p
@@ -217,25 +219,29 @@ for n in range(H): # time
F_H_current = K * abs(push)**p F_H_current = K * abs(push)**p
else: else:
F_H_current = 0 F_H_current = 0
F_H_current = 0
next_x = [0] * N next_x = [0] * N
for i in range(2, N-2): # space for i in range(2, N-2): # space
term_1 = a_1*x[i] + a_2*last_x1[i] # term_1 = a_1*x[i] + a_2*last_x1[i]
term_2 = a_3*(x[i+1] + x[i-1]) + a_4*(x[i+2] + x[i-2]) # term_2 = a_3*(x[i+1] + x[i-1]) + a_4*(x[i+2] + x[i-2])
term_3 = a_5*(last_x1[i+1] + last_x1[i-1] + last_x2[i]) # term_3 = a_5*(last_x1[i+1] + last_x1[i-1] + last_x2[i])
term_4 = (delta_t**2 * N*F_H_current * spatial_window(i))/M_S # term_4 = (delta_t**2 * N*F_H_current * spatial_window(i))/M_S
next_x[i] = term_1 + term_2 + term_3 + term_4 # next_x[i] = term_1 + term_2 + term_3 + term_4
next_x[i] = 2*(1-r**2)*x[i] + r**2 * (x[i+1] + x[i-1]) - last_x1[i]
x[0] = 0
x[1] = 0
x[N-2] = 0
x[N-1] = 0
last_x2 = last_x1.copy() last_x2 = last_x1.copy()
last_x1 = x.copy() last_x1 = x.copy()
x = next_x.copy() x = next_x.copy()
if(n == 30):
plot_current()
x_out[n] = x[x_sample] x_out[n] = x[x_sample]
# plotting # plotting
@@ -245,3 +251,6 @@ plt.xlabel("t")
plt.ylabel("x(t, x_sample)") plt.ylabel("x(t, x_sample)")
plt.grid() plt.grid()
plt.show() plt.show()
sd.play(x_out, f_e)
sd.wait()

11
scripts/string_model_ss.py
View File

@@ -2,6 +2,7 @@
import scipy.signal as sig import scipy.signal as sig
import matplotlib.pyplot as plt import matplotlib.pyplot as plt
import numpy as np import numpy as np
import sounddevice as sd
import math import math
# simple first order step response simulation # simple first order step response simulation
@@ -32,8 +33,11 @@ import math
f_1 = 440 # fundamental frequency f_1 = 440 # fundamental frequency
def f_n(n): def f_n(n):
return f_1 * n return f_1 * n
omega_1 = 2*math.pi*f_1
b = 0.01
def omega_n(n): def omega_n(n):
return 2*math.pi*f_n(n) # a cooler option would be omega_n = c*n*omega_1*sqrt(1+B*n^2) to factor in string stiffness to its vibration mode # return 2*math.pi*f_n(n) # a cooler option would be omega_n = c*n*omega_1*sqrt(1+B*n^2) to factor in string stiffness to its vibration mode
return 1.001*omega_1*math.sqrt(1+b*n**2)
# x = [ q1, q1dot, q2, q2dot, q3, q3dot ]^T < --state vector # x = [ q1, q1dot, q2, q2dot, q3, q3dot ]^T < --state vector
omega_1 = omega_n(1) omega_1 = omega_n(1)
@@ -52,7 +56,7 @@ A = [
] # isnt this formatting gorgeous ] # isnt this formatting gorgeous
B = [ [0], [0.707], [0], [0], [0], [-0.707] ] B = [ [0], [0.707], [0], [0], [0], [-0.707] ]
c_1 = 0.001 c_1 = 0.0001
c_2 = c_1 / 2 c_2 = c_1 / 2
c_3 = c_1 / 3 c_3 = c_1 / 3
C = [[-c_1*omega_1**2, -2*c_1*zeta_1*omega_1, -c_2*omega_2**2, -2*c_2*zeta_2*omega_2, -c_3*omega_3**2, -2*c_3*zeta_3*omega_3]] C = [[-c_1*omega_1**2, -2*c_1*zeta_1*omega_1, -c_2*omega_2**2, -2*c_2*zeta_2*omega_2, -c_3*omega_3**2, -2*c_3*zeta_3*omega_3]]
@@ -80,3 +84,6 @@ plt.xlabel("t")
plt.ylabel("y") plt.ylabel("y")
plt.grid() plt.grid()
plt.show() plt.show()
sd.play(y, 44100)
sd.wait()