Forced Vibrations of Multi-Cracked Shear Deformable Beams by Means of Extended Modal Analysis

Shear deformable beams modelled in accordance with the first order Timoshenko theory in presence of multiple cracks are the object of this study. The contribution provided by this work consists, first, in the derivation of the “extended” mode shapes explicitly formulated, by means of a distributional approach, to include the effect of multiple cracks. Then, it is proved that the orthogonality property of the proposed mode shapes embedding the effect of multiple cracks is preserved. On this ground, forced vibrations of the multi-cracked beam are analysed by making use of extended modal superposition by exploiting explicit expressions of the impulse response functions.