Vibration Analysis of Cracked Stepped Laminated Composite Beams

The free vibration of piecewise uniform defective laminated composite beams is investigated. The governing differential equations of motion are coupled both in torsional and bending deformations. A Dynamic Finite Cracked Element (DFCE) is developed and is applied to slender beams, characterized by an offset between inertial and bending axes. The hybrid DFCE is a combination of the conventional Finite Element Method (FEM) formulation and frequencydependent interpolation functions stemmed from the exact Dynamic Stiffness Matrix (DSM) method. The defect, a through-thickness edge crack, is then represented by a set of stiffness terms evaluated from the beam compliance matrix at the crack location. A number of stepped beam configurations are investigated by reducing the base, thickness, or both. The natural frequencies and modes of free vibration of the beams are examined for single through-thickness edge crack configurations.