Abstract:
Analysis of free vibration of cracked members has been under active study in the last three
decades.In these studies the member is divided into several segments with a crack in between each two.
Using the general solution for each segment, the boundary conditions and the compatibility equations
at cracked points the problem reduces to the solution of a system of equations. The order of the
system depends on the number of cracks. As a result only members with few cracks were considered.
In this paper a single governing equation for each multi-cracked member is developed. The derived
governing equation is a simple ordinary differential equation and is solved using the finite element
formulation which is developed for this study. Since the effects of cracks appeared within the mass
matrices of the formulated numerical problem, modelling the singularities due to cracks was not
needed. The computation of mass matrices is much easier than that of the stiffness of members with
singularity, hence resulting in reduction computational time and effort. The proposed formulation
is implemented in an at home software. Using this software several examples were analyzed.
Comparison of the results with that of commercial software verified the work.