Vibrational Characteristics of Cracked Cantilever Plates.

摘要

An analytical solution to the vibrational characteristics of a rectangular cantilever plate with a discontinuous boundary condition (crack) at the root is presented. Mechanical damping which may exist as a result of the contact between the crack's free surfaces during vibration has been eliminated by assuming the crack surface to be a free boundary. The approach to solution involves the use of the method of Ritz applied to Hamilton's Law of Varying Action. A comparison is made to the solution as obtained from conventional finite element theory (NASTRAN). No exact solution is available for comparison. The assumptions which underlie both theories are outlined. A comparison is made to the experimental results for a cantilever plate with a narrow slot of varying lengths at the root. Indications are that significant frequency deterioration and nodal pattern variations occur with increasing crack length. Further work on the effect of cracks/flaws on plate response is warranted.