#!/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=r"""Eigen frequencies of an Euler-Bernoulli beam.

     βₙ² ⎛E I⎞¹/₂           π
fₙ = --- ⎜---⎟    with βₙ = -- aₙ
     2π  ⎝ρ A⎠              L

aₙ is a numerically solved value.

!!! Currently only the first four frequencies can be calculated.
""",
    formatter_class=argparse.RawTextHelpFormatter)
  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())