Explicit space-time excitation¶

This executable example shows the complete contract: the caller defines both axes, a load generates a field, and the beam solver projects it.

In [1]:

import matplotlib.pyplot as plt
import numpy as np

import dynaresp as dr

time = np.arange(600, dtype=float) / 200.0
positions = np.linspace(0.0, 5.0, 101)
beam = dr.systems.Beam(
    length=5.0,
    material="steel",
    section=("rectangular", 0.10, 0.02),
    n_elements=20,
    n_modes=5,
)

import matplotlib.pyplot as plt import numpy as np import dynaresp as dr time = np.arange(600, dtype=float) / 200.0 positions = np.linspace(0.0, 5.0, 101) beam = dr.systems.Beam( length=5.0, material="steel", section=("rectangular", 0.10, 0.02), n_elements=20, n_modes=5, )

/home/runner/work/DynaResp/DynaResp/.venv/lib/python3.13/site-packages/tqdm/auto.py:21: TqdmWarning: IProgress not found. Please update jupyter and ipywidgets. See https://ipywidgets.readthedocs.io/en/stable/user_install.html
  from .autonotebook import tqdm as notebook_tqdm

In [2]:

vehicle = dr.loads.TwoWheelLoad(
    front_load=-4000.0, rear_load=-3500.0, speed=2.5, wheel_spacing=1.25
)
history = vehicle.generate(time, positions)
assert history.values.shape == (positions.size, time.size)
assert np.max(np.count_nonzero(history.values, axis=0)) <= 2
plt.pcolormesh(time, positions, history.values, shading="auto")
plt.xlabel("Time [s]")
plt.ylabel("Position [m]")
plt.colorbar(label="Force [N]")
plt.show()

vehicle = dr.loads.TwoWheelLoad( front_load=-4000.0, rear_load=-3500.0, speed=2.5, wheel_spacing=1.25 ) history = vehicle.generate(time, positions) assert history.values.shape == (positions.size, time.size) assert np.max(np.count_nonzero(history.values, axis=0)) <= 2 plt.pcolormesh(time, positions, history.values, shading="auto") plt.xlabel("Time [s]") plt.ylabel("Position [m]") plt.colorbar(label="Force [N]") plt.show()

In [3]:

spec = dr.SimulationSpec(
    system=beam,
    load=vehicle,
    sensors=(dr.sensors.Accelerometer(position=2.5),),
    time=time,
    positions=positions,
)
result = dr.run_simulation(spec, seed=42)
plt.plot(result.time, result.signal[0])
plt.xlabel("Time [s]")
plt.ylabel("Acceleration")
plt.show()

spec = dr.SimulationSpec( system=beam, load=vehicle, sensors=(dr.sensors.Accelerometer(position=2.5),), time=time, positions=positions, ) result = dr.run_simulation(spec, seed=42) plt.plot(result.time, result.signal[0]) plt.xlabel("Time [s]") plt.ylabel("Acceleration") plt.show()

result.positions is the supplied physical axis, result.load_values is the original field, and result.force is its modal projection. No beam grid is requested by the load.