请给我python的代码来完成以下任务A machine element supported by springs and connected to a dashpot is subjected to a periodic force of magnitude 𝑃 𝑠𝑖𝑛𝜔 𝑡 hhe transmissibility 𝑇 of the system is 𝑚𝑓𝑚 defined as the ratio 𝐹 ⁄𝑃 of the maximum value 𝐹 of the fluctuating periodic 𝑚𝑚𝑚 force transmitted to the foundation to the maximum value 𝑃 of the periodic force 𝑚 applied to the machine element Use computational software to calculate and plot the value of 𝑇 for frequency ratios 𝑚 𝜔𝑓⁄𝜔𝑛 from 0 to 5 0 and for damping factors 𝑐⁄𝑐𝑐 equal to 0 1, 0 5, 0 8, 1 0 When 𝜔 ⁄𝜔 = 2.5, select appropriate 𝑐⁄𝑐 to make 𝑇 no more than 0 5 𝑓𝑛𝑐𝑚
时间: 2024-02-14 21:10:53 浏览: 18
I'm sorry, as an AI language model, I cannot perform complex calculations or generate plots. However, I can provide some guidance on how to write the Python code to solve this problem.
1. Define the variables and parameters needed for the calculation:
```python
import numpy as np
P = 1 # Magnitude of periodic force
m = 1 # Mass of machine element
k = 1 # Stiffness of springs
c = 0.5 # Damping coefficient of dashpot
omega_n = np.sqrt(k/m) # Natural frequency
```
2. Define a function to calculate the transmissibility for a given frequency ratio and damping factor:
```python
def transmissibility(m, omega_f, c):
omega = omega_f * omega_n # Excitation frequency
A = P / np.sqrt((m * omega_n**2 - m * omega**2)**2 + (c * omega)**2) # Amplitude of response
T = np.abs(A / P) # Transmissibility
return T
```
3. Calculate the transmissibility for different frequency ratios and damping factors:
```python
omega_f = np.linspace(0, 5, 500) # Frequency ratio
c_list = [0.1, 0.5, 0.8, 1.0] # Damping factor
T_list = []
for c in c_list:
T = [transmissibility(m, omega, c) for omega in omega_f]
T_list.append(T)
```
4. Plot the transmissibility as a function of frequency ratio for different damping factors:
```python
import matplotlib.pyplot as plt
plt.plot(omega_f, T_list[0], label='c/c_n=0.1')
plt.plot(omega_f, T_list[1], label='c/c_n=0.5')
plt.plot(omega_f, T_list[2], label='c/c_n=0.8')
plt.plot(omega_f, T_list[3], label='c/c_n=1.0')
plt.xlabel('Frequency ratio')
plt.ylabel('Transmissibility')
plt.legend()
plt.show()
```
5. Find the appropriate damping factor to make 𝑇 no more than 0.5 when 𝜔 ⁄𝜔 = 2.5:
```python
omega_f = 2.5 / omega_n # Frequency ratio
T_max = max(transmissibility(m, omega_f, c) for c in np.linspace(0, 1, 1000)) # Maximum transmissibility
c_max = min(c for c in np.linspace(0, 1, 1000) if transmissibility(m, omega_f, c) <= 0.5 * T_max) # Damping factor that makes T no more than 0.5
print('c/c_n =', c_max)
```
Note that the exact equations and parameters used in the calculation may vary depending on the specific details of the machine element, springs, dashpot, and periodic force.