ELASTIC WAVE SCATTERING FROM FLAWS IN AN INFINITE ISOTROPIC PLATE.

摘要

The scattering of plate modes (Lamb and SH waves) from flaws embedded in an infinite isotropic plate with stress-free boundary conditions on the plate surface, is investigated. Using a normal mode expansion of the Green's function for the infinite plate, an integral equation for the particle displacement field on the flaw is obtained. The variational principle of Levine and Schwinger is used to obtain approximate values for the reflection coefficient of a fundamental Lamb mode incident on an infinitely long (2-D) crack. The solutions to the corresponding elastostatic (zero frequency) problems were used as the approximate trial solutions in the variational expressions. The numerical results predict a resonance in the reflection coefficient of a Lamb mode incident on a pair of symmetrical edge cracks. This was experimentally verified using a heterodyne laser probe to measure the standing wave pattern produced on a polished plate surface by a Lamb mode incident on a pair of machined slots. Results using a generalized transmission line representation of the propagation of plate modes are given. In this case an equivalent circuit characterizing the flaw is obtained. Again, variational techniques are used to obtain approximate values for the circuit elements.; Extensions to the case of 3-D cracks in plates is given. Here, the Green's function is constructed by using an angular spectrum of plate modes. Difficulties in the implementation of the Levine-Schwinger variational principle for the case of 3-D cracks are resolved. In particular, a method is given to separate the Green's function into a singular and a nonsingular part; with the singular part being the Green's function for the infinite medium. Several useful scattering formulae obtained from reciprocity are derived. Also, the exact analogue of the Optical Theorem in Electromagnetism is derived for the case of plate mode scattering. This shows that the time averaged scattered power depends only on the value of the forward scattered amplitude of the incident plate mode.