Power reflection and transmission in beam structures containing a semi-infinite crack

ABSTRACTWave reflection and transmission in a beam containing a semi-infinite crack are studied analytically based on Timoshenko beam theory. Two kinds of crack surface conditions: non-contact (open) and fully contact (closed) cracks, are considered respectively for an isotropic beam. The analytical solution of reflection and transmission coefficients for a semi-infinite crack is obtained. The power reflection and transmission ratios depend on both the frequency and the position of the crack. Numerical results show the conservation of power transport. The transmitted energy among various wave modes is also investigated. A finite element method is used to verify the validity of the analytical results.