Solve harmonic problem (with damping) using matrix inverse

This example shows how to create a harmonic (over frequencies) fields container for an analysis with damping. This fields container is then used to solve the problem Ma+Dv+Ku=F by inverting the matrix

Note

This example requires the Premium ServerContext. For more information, see Server context.

import math

from ansys.dpf import core as dpf
from ansys.dpf.core import operators as ops


dpf.set_default_server_context(dpf.AvailableServerContexts.premium)

Create 2D (x,y) matrix fields for inertia, damping, and stiffness.

freq = [25, 50, 100, 200, 400]
dim = 2  # dimension of matrix

fM0 = dpf.fields_factory.create_matrix_field(1, dim, dim)
fM0.append([0.0, 1.0, 2.0, 3.0], 1)
fK0 = dpf.fields_factory.create_matrix_field(1, dim, dim)
fK0.append([4.0, 8.0, 0.0, 1.0], 1)
fC0 = dpf.fields_factory.create_matrix_field(1, dim, dim)
fC0.append([7.0, 5.0, 9.0, 1.0], 1)

Create a fields container for real and imaginary parts for each frequency.

reals = {}
ims = {}
for k, f in enumerate(freq):
    omega = 2.0 * math.pi * f
    omega2 = omega**2
    real = fK0 + fM0 * omega2
    imag = fC0 * omega
    reals[f] = real.outputs.field()
    ims[f] = imag.outputs.field()

cplx_fc = dpf.fields_container_factory.over_time_freq_complex_fields_container(
    reals, ims, time_freq_unit="Hz"
)

Use DPF operators to inverse the matrix and then compute the amplitude and the phase.

inverse = ops.math.matrix_inverse(cplx_fc)
component = ops.logic.component_selector_fc(inverse, 0)
amp = ops.math.amplitude_fc(component)
phase = ops.math.phase_fc(component)

Get the phase and amplitude and then plot it over frequencies.

amp_over_frequency = amp.outputs.fields_container()
phase_over_frequency = phase.outputs.fields_container()
time_freq_support = amp_over_frequency.time_freq_support

amp_array = []
phase_array = []
for f in amp_over_frequency:
    amp_array.append(f.data)

for f in phase_over_frequency:
    phase_array.append(f.data * 180.0 / math.pi)

import matplotlib.pyplot as plt

plt.figure()
plt.plot(time_freq_support.time_frequencies.data, amp_array, "r", label="amplitude")
plt.xlabel("Frequency (Hz)")
plt.ylabel("Displacement ampliude (m)")
plt.legend()
plt.show()

plt.figure()
plt.plot(time_freq_support.time_frequencies.data, phase_array, "r", label="phase")
plt.xlabel("Frequency (Hz)")
plt.ylabel("Displacement phase (deg)")
plt.legend()
plt.show()

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