138 lines
3.1 KiB
Markdown
138 lines
3.1 KiB
Markdown
```python
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import math
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import numpy as np
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from pint import UnitRegistry
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unit = UnitRegistry()
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unit.formatter.default_format = "~"
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# Parameters
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spring_constant = 1.1 * 4 * unit.N / unit.mm
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spring_length_resting = 112 * unit.mm
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weight_total = 14 * unit.kg
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dampening = 1 * unit.N / (unit.m / unit.s)
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def spring_length_at(weight):
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return (weight * unit.standard_gravity / spring_constant + spring_length_resting).to(unit.mm)
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def resonant_freq_at(weight):
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return (1 / (2 * math.pi) * np.sqrt(spring_constant / weight)).to(unit.Hz)
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spring_length = spring_length_at(weight_total)
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f0 = resonant_freq_at(weight_total)
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print(f"Length: {spring_length:~.1f}")
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print(f"Freq: {f0:~.3f}")
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```
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Length: 143.2 mm
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Freq: 2.822 Hz
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```python
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def lehr_dampening_factor(d, k, m):
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return d / (2 * np.sqrt(m * k))
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lehr_dampening = lehr_dampening_factor(dampening, spring_constant, weight_total)
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lehr_dampening.ito_reduced_units()
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lehr_dampening
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```
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0.00201455741006345
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```python
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def amplitude_ratio(lehr, f0, f):
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eta = f / f0
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return 1 / np.sqrt((1 - eta**2)**2 + (2 * eta * lehr)**2)
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f_in = np.geomspace(0.5, 90, 100) * unit.Hz
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ratio = amplitude_ratio(lehr_dampening, f0, f_in)
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import matplotlib.pyplot as plt
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plt.plot(f_in, ratio)
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def transmissibility_plot_setup(plt):
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plt.xscale('log')
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xticks = [1, 3, 10, 50]
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plt.xticks(xticks, [f"{t} Hz" for t in xticks], minor=False)
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plt.xlabel("Excitation Frequency")
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plt.ylim(0.001, 10)
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plt.yscale('log')
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plt.ylabel("Transmissibility Ratio")
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plt.grid(True, "both")
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transmissibility_plot_setup(plt)
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```
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/usr/lib/python3.13/site-packages/matplotlib/cbook.py:1355: UnitStrippedWarning: The unit of the quantity is stripped when downcasting to ndarray.
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return np.asarray(x, float)
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```python
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def ratio_for_dkm(d, k, m, f_in):
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f0 = (1 / (2 * math.pi) * np.sqrt(k / m)).to(unit.Hz)
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lehr = lehr_dampening_factor(d, k, m)
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return amplitude_ratio(lehr, f0, f_in)
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d = dampening
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k = [
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spring_constant,
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spring_constant / 4,
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]
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m = [
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weight_total,
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24 * unit.kg,
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]
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import matplotlib.pyplot as plt
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for k_ in k:
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m_ = m[0]
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plt.plot(f_in, ratio_for_dkm(d, k_, m_, f_in), label=f"{k_:~.1f}, {m_:~.1f}")
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for m_ in m[1:]:
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k_ = k[0]
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plt.plot(f_in, ratio_for_dkm(d, k_, m_, f_in), label=f"{k_:~.1f}, {m_:~.1f}")
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ref_thorlabs_f = [3, 4, 4.42, 5, 6, 7, 8, 9, 10, 40]
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ref_thorlabs_r = [2, 5, 15.0, 4, 1.5, 0.7, 0.5, 0.35, 0.28, 0.018]
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plt.plot(ref_thorlabs_f, ref_thorlabs_r, label="Thorlabs PTP702 (Passive)")
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ref_thorlabs_f = [1, 1.35, 2, 3, 5, 9, 20, 27, 30]
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ref_thorlabs_r = [2, 3, 0.9, 0.3, 0.1, 0.02, 0.009, 0.007, 0.0023]
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plt.plot(ref_thorlabs_f, ref_thorlabs_r, label="Thorlabs PTS601 (Active)")
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plt.legend(loc="upper right")
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transmissibility_plot_setup(plt)
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```
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/usr/lib/python3.13/site-packages/matplotlib/cbook.py:1355: UnitStrippedWarning: The unit of the quantity is stripped when downcasting to ndarray.
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return np.asarray(x, float)
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```python
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```
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