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Analytical method for vibration analysis of multi-cracked Timoshenko beam structures with elastic foundations
Received date: 2024-02-02
Revised date: 2024-03-28
Accepted date: 2024-05-30
Online published: 2024-06-14
This study proposes a novel analytical method for vibration analysis of arbitrary multi-crack Timoshenko damping beam structures with elastic foundations based on the Distributed Transfer Function Method （DTFM）. A two-parameter continuous spring model considering shear and rotational deformation is adopted for the elastic foundation. For local cracks on the beam structure， a local additional compliance matrix induced by the crack is employed， and the governing equation of the multi-cracked Timoshenko damping beam with an elastic foundation established. Using the augmented distributed transfer function method， we establish the local boundary matrices of the non-cracked and cracked beam components， respectively， and then obtain the global boundary equation in the global coordinate system. Finally， a closed-form analytical solution is derived in integral form， and the natural frequencies， mode shapes， and frequency responses of the cracked beam structures can be derived. In numerical examples， the results from previous papers and the Finite Element Method （FEM） are employed to validate the correctness of the proposed method， and the effect of the cracks and the elastic foundations on dynamic behaviors investigated. With higher computational accuracy and efficiency than the FEM for mid-to-high frequency dynamic responses， the proposed method can be used for crack detection of elastic foundation beams.
Ke WU , Qibo PENG , Xinfeng WU , Pengbo LIU , Yajun KOU . Analytical method for vibration analysis of multi-cracked Timoshenko beam structures with elastic foundations[J]. ACTA AERONAUTICAET ASTRONAUTICA SINICA, 2024 , 45(22) : 230280 -230280 . DOI: 10.7527/S1000-6893.2024.30280
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