Vibrations of multiple delaminated beams

The free vibrations of beams with two enveloping delaminations have been solved analytically without resorting to numerical approximation. The multiple delaminated beam is analyzed as several interconnected Euler–Bernoulli beams. The differential stretching and the bending–extension coupling are considered in the formulation. The influence of the sizes and locations of the delaminations on the primary and secondary frequencies and mode shapes of a beam are investigated. For clamped–clamped beams, the primary frequency shows a high sensitivity for the long delamination but a low sensitivity for the second short delamination, while for the secondary frequency, the sensitivity is high for both delaminations. For cantilever beams, the primary and secondary frequencies show a high sensitivity for the long delamination but low sensitivity for the second short delamination. Results are compared with the analytical and experimental data reported in the literature to verify the validity of the present model.