add beam

src/beam.py

@@ -0,0 +1,96 @@
+#!/usr/bin/env python
+# -*- coding: utf-8 -*-
+"""\
+Beam
+"""
+from __future__ import absolute_import, division, print_function, unicode_literals
+from math import sqrt, pi
+
+__author__ = "Daniel Weschke"
+__copyright__ = "Copyright 2020 Daniel Weschke"
+__credits__ = ["Daniel Weschke"]
+__license__ = "MIT"
+__version__ = "2020.10.21"
+__maintainer__ = "Daniel Weschke"
+__email__ = "daniel.weschke@directbox.de"
+__status__ = "Production"  # "Prototype", "Development", "Production"
+
+VERSION = """\
+%(prog)s version {version} {copyright}
+
+For Unicode characters check the file encoding that the console is using.
+Windows user may execute the command "chcp 65001".""".format(
+  version=__version__, copyright=__copyright__)
+
+EPILOG = """\
+"""
+
+def eigen_frequency_fixed_free(n, E, I, rho, A, L):
+  """\
+  Dynamic beam equation, the Euler-Lagrange equation, of an 
+  Euler-Bernoulli beam.
+  Free vibration of a cantilever beam (fixed-free support).
+  Returns the natural frequencies of vibration.
+  !!! Currently only the first four frequencies can be calculated.
+
+  n    Mode number (1 for first mode, ...)
+  E    Elastic modulus / Young's modulus
+  I    Second moment of area of the beam's cross-section
+  rho  Density
+  A    Cross-section
+  L    Length
+
+  beta_n := ((mu*omega_n^2)/(E*I))^(1/4)
+  omega_n = beta_n^2*sqrt(E*I/mu)
+
+  β_n can be solved numerically
+  β1 L/π = 0.59686..., β2 L/π = 1.49418..., β3 L/π = 2.50025...,
+  β4 L/π = 3.49999..., ... 
+  """
+  # mu  Mass per unit length
+  beta = [0.59686, 1.49418, 2.50025, 3.49999]
+  beta_n = beta[n-1]*pi/L if n < len(beta) else 0
+  mu = rho * A
+  return beta_n**2*sqrt(E*I/mu)/(2*pi)
+
+def main():
+  """\
+  Main function
+  """
+  import argparse
+
+  parser = argparse.ArgumentParser(
+    description=__doc__, prefix_chars='-', epilog=EPILOG,
+    #usage="%(prog)s [OPTION]... NAME",
+    formatter_class=argparse.RawTextHelpFormatter,
+  )
+  parser.add_argument('-v', '--verbose', action="store_true", help="Verbose output")
+  parser.add_argument('-V', '--version', action='version', version=VERSION)
+  parser.add_argument('-D', '--debug', dest='debug', action='store_true', help=argparse.SUPPRESS)
+  subparsers = parser.add_subparsers(help='', dest='case')
+
+  parser_a = subparsers.add_parser(
+    'frequency', help="eigen frequencies", prefix_chars='-',
+    description="Eigen frequenccies of an Euler-Bernoulli beam.")
+  parser_a.add_argument('N', type=int, help='Mode number')
+  parser_a.add_argument('E', type=float, help='Young\'s modulus')
+  parser_a.add_argument('I', type=float, help='Second moment of area')
+  parser_a.add_argument('RHO', type=float, help='Density')
+  parser_a.add_argument('A', type=float, help='Area')
+  parser_a.add_argument('L', type=float, help='Length')
+
+  args = parser.parse_args()
+
+  if args.debug:
+    print(args)
+
+  if args.case == 'frequency':
+    f_n = eigen_frequency_fixed_free(args.N, args.E, args.I,
+                                     args.RHO, args.A, args.L)
+    print("f_" + str(args.N) + " =", f_n)
+
+  return 0
+
+if __name__ == "__main__":
+  import sys
+  sys.exit(main())