Weak formulation of the Green's function for elastic wave propagation with mixed boundary problems
Terumi Touhei (Tokyo University of Science), Kojiro Masada (Tokyo University of Science)
Characterization and Imaging of Structural and Material Imperfections
Mon 4:20 - 5:40
Barus-Holley 191
Recently, a number of structures and infrastructures need to be assessed carefully for their durability. The severity of fatigue and deterioration of structure is not homogeneous but localized inside the structures since the severity of fatigue and deterioration is significantly affected by the usage of the structures and external conditions. In order to resolve the above problems non-destructive testing by means of elastic wave propagation has been developed and applied to investigate the structural integrity and detect the existence of flaw, crack, void and among others. This research aims to establish a mathematical formulation of wave propagation analysis which is applicable to mesh free numerical calculation. The explicit form of the Green's function for a rigidly fixed bi-embedded beam is introduced in this paper. On the surface, it seems that the deriving the Green's function is not very difficult. The conventional method based on the Fourier series expansion, however, encounters a difficulty of the mixed boundary value problem for elastic wave propagation. In this paper, a weak formulation instead of the conventional method is employed to overcome the difficulty. The process of deriving the Green's function is carefully provided in this paper. The explicit form of Green's function obtained from the weak formulation is similar to the spectral representation, which is found to be applicable to a mesh free method. Several numerical calculations are performed to examine the wave propagation properties of the beam.