Vibration of beams with double delaminations

The vibration of beams with double delaminations has been solved analytically without resorting to numerical approximation. The beam is analyzed as five interconnected beams using the delaminations as their boundaries. The continuity and boundary conditions are satisfied between adjoining beams. Classical beam theory is applied to each of the beams. A new slenderness ratio specific for vibration is introduced, which is shown to dominate the vibration behavior of the beam. Global, mixed and local vibration modes occur depending upon the slenderness ratios of the delaminated beams. Different vibration behaviors emerge for different sizes, depths, spanwise locations and relative slenderness ratios of the delaminations.