def antisymmetric_disp_multiple(omega, k, thickness, num_points, rho, lamb,
mu):
"""
Parameters
----------
omega: Type, float or complex array
DESCRIPTION. Frequency multiplied by 2*pi {rad/s}
k: Type, complex array
DESCRIPTION. wavenumber {rad/m}
thickness: Type, float
DESCRIPTION. thickness of the plate waveguide. {m}
num_points: Type, float
DESCRIPTION. number of points along thickness.
rho: Type, float
DESCRIPTION. density of the plate waveguide. {kg/m^3}
lamb: Type, float
DESCRIPTION. frequency value at which roots are solved at. {default: 1e6 Hz}
mu: Type, float
DESCRIPTION. frequency value at which roots are solved at. {default: 1e6 Hz}
Returns
-------
antisymmetric Lamb wave displacement profiles for a given omega and k are arranged in a row: UX, UY
"""
omega.shape = (len(omega), 1) # formatting shape
k.shape = (len(k), 1) # formatting shape
cL, cT = es.wave_speed_calculator(rho=rho, lamb=lamb, mu=mu)
h = thickness / 2
q = np.sqrt(omega**2 / (cT**2) - k**2) # rad/m
p = np.sqrt(omega**2 / (cL**2) - k**2) # rad/m
thick_vect = np.linspace(start=-h,
stop=h,
num=num_points,
dtype=np.complex128)
thick_vect.shape = (1, len(thick_vect)) # formatting shape
A1 = -(k**2 - q**2) * np.cos(q * h) / (2 * 1j * k * p * np.cos(p * h))
UX = 1j * k * np.sin(p * thick_vect) * A1 - q * np.sin(q * thick_vect)
UY = p * np.cos(p * thick_vect) * A1 - 1j * k * np.cos(q * thick_vect)
thick_array = np.tile(thick_vect, (len(omega), 1))
return np.hstack((thick_array, UX, UY))
@author: Christopher Hakoda
[email protected]
"""
import numpy as np
import time
import matplotlib.pyplot as plt
import multiprocessing as mp
from functools import partial
import matplotlib as mpl
import elasticity as es
# Setting Global Parameters
thickness = 0.001
cL, cT = es.wave_speed_calculator(rho=2700, lamb=5.697675e10, mu=2.5947e10)
# phase velocity range of interest for the dispersion curves
cmin = 200 # m/s; approx. min phase velocity
cmax = 10000 # m/s; approx. max phase velocity
# frequency range of interest for the dispersion curves
fmin = 1 # Hz; linspace used so this isn't the real min
fmax = 20e6 # Hz; maximum frequency
error_threshold = 0.01 # rad/m; max variation
def main():
# Note to self: make sure num_points is high enough otherwise some solutions will not be found. This is easier to find
# when sweeping from low frequency to higher frequencies because, generally, num_points has to be higher for higher
# frequencies.