Free and forced vibration modelling of a delaminated beam structure using a Green's function method

This work proposes an analytical modelling method for free and forced vibration analyses of a delaminated beam structure based on the Green's function method, which considers the connection among sub-beams to generate a general model of a beam with different delaminations. This analytical modelling allows the investigation on the dynamic response of a delaminated beam under frequency-varying excitations. Two models have been developed, the 'free mode' and 'constrained mode' models, for simulating the dynamic response of a delaminated beam with its solution obtained from utilizing the Green's functions on multiple segments of the beam structure. The accuracy of the proposed models is verified by comparisons of results from the finite element models and the previous works that utilized the classical beam theory, demonstrating consistent dynamic characteristics of a delaminated beam structure. It is found that the delamination location has dominant influences on the deformation of the beam and its natural frequencies, compared to the delamination size and depth, with the higher frequency excitation generally has more influences on beam deformation compared to the low frequency excitation for a particular delamination configuration. The results demonstrated the effectiveness of the proposed modelling method for free and forced vibration analyses of a beam with delamination.