Thesis
PROPAGACIÓN DE ONDAS EN UN MEDIO FLUIDO INMERSO EN UN SÓLIDO ELÁSTICO AGRIETADO, UTILIZANDO EL MÉTODO DE DIFERENCIAS FINITAS
Autor
CRUZ MEDINA, JOSUÉ DAVID
Institución
Resumen
The presence of irregularities (cracks) in elastic materials leads to dispersion and
diffraction during propagation of waves. This diffracted field produced during the
propagation of waves provides valuable information for the detection and
characterization of cracks or other heterogenetys.
It is study the propagation of elastic waves in a 2D configuration. These are produced by
a sonic source (Ricker pulse) in a fluid, in contact with an elastic solid. The solution of
the equations of motion are obtained in the time domain using the finite difference
method.
The formulations are based on the equations of motion and equilibrium of the system,
then get to the wave equation, using finite difference schemes are achieved in terms of
speed and stresses to reduce the degree of differential equations. In formulating the
spectral pseudo derivatives with respect to spatial variables are done with the fast
Fourier transform.
To have a clearer accuracy of the derived type mesh was used staggered. The crack
was introduced in the configuration, to observe and study the propagation of waves we
have with these formations.
Through language Fortran calculations were obtained pressure and movement, and
propagation is modeled by taking the Matlab program as a tool. It was the simulation of
four cases: primary formation of propagation, slow formation (velocity of shear wave of
solid is less), rapid formation and propagation of waves in half cracked.
The formulations are stable numerical method, which are presented and discussed
possible future work with more complex cases in geometry and materials.
This work implemented a technique for solving problems associated with the
propagation of waves in 2D, in systems with discontinuities of the finite difference
method.