GREEN'S FUNCTION FOR FORCED VIBRATION OF MULTI-CRACKED EULER-BERNOULLI CURVED BEAM WITH DAMPING^1)

This paper derives analytical solutions of the steady-state forced vibration of the multi-cracked Euler-Bernoulli curved beam (ECB) with damping effects by means of Green's functions. Separate variable method, Laplace transform method and matrix transfer method are successively used to obtain the Green's functions for the ECB equation. The results show that the curved beam can be approximated by the straight beam by setting the radius to infinity. The present analytical solutions are verified by comparing the numerical calculations of the present solution and those available in the literature. The effects of geometric and physical parameters on the vibration response and the interaction between cracks are investigated also.