107 lines
3.3 KiB
Python
Executable File
107 lines
3.3 KiB
Python
Executable File
#!/usr/bin/env python
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# -*- coding: utf-8 -*-
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"""\
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Beam
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"""
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from __future__ import absolute_import, division, print_function, unicode_literals
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from math import sqrt, pi
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__author__ = "Daniel Weschke"
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__copyright__ = "Copyright 2020 Daniel Weschke"
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__credits__ = ["Daniel Weschke"]
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__license__ = "MIT"
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__version__ = "2020.10.21"
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__maintainer__ = "Daniel Weschke"
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__email__ = "daniel.weschke@directbox.de"
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__status__ = "Production" # "Prototype", "Development", "Production"
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VERSION = """\
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%(prog)s version {version} {copyright}
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For Unicode characters check the file encoding that the console is using.
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Windows user may execute the command "chcp 65001".""".format(
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version=__version__, copyright=__copyright__)
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EPILOG = """\
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"""
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def eigen_frequency_fixed_free(n, E, I, rho, A, L):
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"""\
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Dynamic beam equation, the Euler-Lagrange equation, of an
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Euler-Bernoulli beam.
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Free vibration of a cantilever beam (fixed-free support).
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Returns the natural frequencies of vibration.
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!!! Currently only the first four frequencies can be calculated.
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n Mode number (1 for first mode, ...)
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E Elastic modulus / Young's modulus
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I Second moment of area of the beam's cross-section
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rho Density
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A Cross-section
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L Length
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beta_n := ((mu*omega_n^2)/(E*I))^(1/4)
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omega_n = beta_n^2*sqrt(E*I/mu)
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β_n can be solved numerically
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β1 L/π = 0.59686..., β2 L/π = 1.49418..., β3 L/π = 2.50025...,
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β4 L/π = 3.49999..., ...
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"""
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# mu Mass per unit length
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beta = [0.59686, 1.49418, 2.50025, 3.49999]
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beta_n = beta[n-1]*pi/L if n < len(beta) else 0
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mu = rho * A
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return beta_n**2*sqrt(E*I/mu)/(2*pi)
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def main():
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"""\
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Main function
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"""
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import argparse
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parser = argparse.ArgumentParser(
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description=__doc__, prefix_chars='-', epilog=EPILOG,
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#usage="%(prog)s [OPTION]... NAME",
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formatter_class=argparse.RawTextHelpFormatter,
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)
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parser.add_argument('-v', '--verbose', action="store_true", help="Verbose output")
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parser.add_argument('-V', '--version', action='version', version=VERSION)
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parser.add_argument('-D', '--debug', dest='debug', action='store_true', help=argparse.SUPPRESS)
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subparsers = parser.add_subparsers(help='', dest='case')
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parser_a = subparsers.add_parser(
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'frequency', help="eigen frequencies", prefix_chars='-',
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description=r"""Eigen frequencies of an Euler-Bernoulli beam.
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βₙ² ⎛E I⎞¹/₂ π
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fₙ = --- ⎜---⎟ with βₙ = -- aₙ
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2π ⎝ρ A⎠ L
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aₙ is a numerically solved value.
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!!! Currently only the first four frequencies can be calculated.
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""",
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formatter_class=argparse.RawTextHelpFormatter)
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parser_a.add_argument('N', type=int, help='Mode number')
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parser_a.add_argument('E', type=float, help='Young\'s modulus')
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parser_a.add_argument('I', type=float, help='Second moment of area')
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parser_a.add_argument('RHO', type=float, help='Density')
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parser_a.add_argument('A', type=float, help='Area')
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parser_a.add_argument('L', type=float, help='Length')
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args = parser.parse_args()
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if args.debug:
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print(args)
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if args.case == 'frequency':
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f_n = eigen_frequency_fixed_free(args.N, args.E, args.I,
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args.RHO, args.A, args.L)
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print("f_" + str(args.N) + " =", f_n)
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return 0
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if __name__ == "__main__":
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import sys
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sys.exit(main())
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