vamseeachanta Example 1: Marine Engineering - Catenary Mooring Line (+5)
Example 1: Marine Engineering - Catenary Mooring Line
import numpy as np
from scipy.optimize import fsolve
import matplotlib.pyplot as plt
def catenary_mooring_analysis(
water_depth: float,
horizontal_distance: float,
chain_weight: float, # kg/m
required_tension: float # kN
*See sub-skills for full details.*
## Example 2: Structural Dynamics - Natural Frequency
```python
import numpy as np
from scipy.linalg import eig
def calculate_natural_frequencies(
mass_matrix: np.ndarray,
stiffness_matrix: np.ndarray,
num_modes: int = 5
) -> dict:
"""
*See sub-skills for full details.*
## Example 3: Hydrodynamic Analysis - Wave Spectrum
```python
import numpy as np
from scipy.integrate import trapz
def jonswap_spectrum(
frequencies: np.ndarray,
Hs: float,
Tp: float,
gamma: float = 3.3
) -> np.ndarray:
*See sub-skills for full details.*
## Example 4: Numerical Integration - Velocity to Displacement
```python
import numpy as np
from scipy.integrate import cumtrapz
def integrate_motion_time_history(
time: np.ndarray,
acceleration: np.ndarray
) -> dict:
"""
Integrate acceleration to get velocity and displacement.
*See sub-skills for full details.*
## Example 5: Optimization - Mooring Pretension
```python
from scipy.optimize import minimize
import numpy as np
def optimize_mooring_pretension(
num_lines: int,
water_depth: float,
target_offset: float,
max_tension: float
) -> dict:
*See sub-skills for full details.*
## Example 6: Symbolic Mathematics - Beam Deflection
```python
from sympy import symbols, diff, integrate, simplify, lambdify
from sympy import Function, Eq, dsolve
import numpy as np
import matplotlib.pyplot as plt
def beam_deflection_symbolic():
"""
Solve beam deflection equation symbolically.
*See sub-skills for full details.*