pystran/tutorials/10_truss_5_vibration_tut.py at main · PetrKryslUCSD/pystran · GitHub

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"""
pystran - Python package for structural analysis with trusses and beams

(C) 2025, Petr Krysl, pkrysl@ucsd.edu

# Statically-determinate truss vibration

## Problem description:

A simple truss is analyzed for free vibration. The truss is statically determinate.

The frequencies are compared to the reference values.

## References

MECHANICAL VIBRATIONS THEORY AND APPLICATION TO STRUCTURAL
DYNAMICS, ThirdEdition, by Michel Géradin and Daniel J. Rixen

Example from Section 5.3.2: 2D Truss Analysis
"""

from math import pi, sqrt
from numpy.linalg import norm
import context
from pystran import model
from pystran import section
from pystran import freedoms
from pystran import plots

# The material properties and the geometry of the truss are assumed here at
# these values. The frequencies are compared in normalized form, which removes
# the direct dependency on the adopted numbers.
E = 30000000.0
rho = 1.0
L = 5.0
A = 0.0155


# Table 5.4 in the reference book gives the normalized frequencies.
reference_values = [0.03428, 0.05810, 0.08901, 0.1215, 0.1947, 0.2342]


# The normalized frequency is given by the formula:
def normalized_analyt(om2):
    return sqrt(om2) / 2 / pi * sqrt(rho / E) * L


# The geometry is given in Figure 5.15 of the reference book.
m = model.create(2)

model.add_joint(m, 1, [0.0, 0.0])
model.add_joint(m, 2, [1 * L, 0.0])
model.add_joint(m, 3, [2 * L, 0.0])
model.add_joint(m, 4, [3 * L, 0.0])
model.add_joint(m, 5, [1 * L, L])
model.add_joint(m, 6, [2 * L, L])

s1 = section.truss_section("s1", E, A, rho)

model.add_truss_member(m, 1, [1, 2], s1)
model.add_truss_member(m, 2, [2, 3], s1)
model.add_truss_member(m, 3, [3, 4], s1)
model.add_truss_member(m, 4, [1, 5], s1)
model.add_truss_member(m, 5, [5, 6], s1)
model.add_truss_member(m, 6, [6, 4], s1)
model.add_truss_member(m, 7, [2, 5], s1)
model.add_truss_member(m, 8, [2, 6], s1)
model.add_truss_member(m, 9, [3, 6], s1)

model.add_support(m["joints"][1], freedoms.U1)
model.add_support(m["joints"][1], freedoms.U2)
model.add_support(m["joints"][4], freedoms.U2)

# The free vibration problem is solved.

model.number_dofs(m)
model.solve_free_vibration(m)

# The frequencies are printed and compared to the reference values.
# In particular, the normalized frequencies are compared.
# The mode shapes are also plotted.
for mode in range(0, 6):
    print(f"Mode {mode}: ", m["frequencies"][mode])
    print(f"  Normalized frequency: ", normalized_analyt(m["eigvals"][mode]))
    if (
        abs(
            (reference_values[mode] - normalized_analyt(m["eigvals"][mode]))
            / reference_values[mode]
        )
        > 1.0e-3
    ):
        raise ValueError("Error in the normalized frequency")
    ax = plots.setup(m)
    plots.plot_members(m)
    model.set_solution(m, m["eigvecs"][:, mode])
    plots.plot_deformations(m, 0.25)
    ax.set_title(f"Mode {mode}, frequency = {m['frequencies'][mode]:.2f} Hz")
    plots.show(m)