Abstract
The problem of free vibration of uniform beams containing a local material damage has been studied with the aim of arriving at accurate closed form analytical expressions for the natural frequency for various homogeneous boundary conditions. Elementary beam theory is used, with the local material damage modelled as an effective reduction in Young's modulus, and the exact solution of the transcendental equations for the frequency parameter is obtained for various symmetric and unsymmetric boundary conditions in terms of the identified damage parameters. The numerical results for the natural frequency show that it is possible to arrive at a simple polynomial type of representation which is the same for various boundary conditions and mode numbers. The results also show that the nature of changes in frequency with respect to the damage location is of the same type as the local curvature in the undamaged beams. Finally, the study demonstrates that the analytical expressions derived for representing the damage dependence can also be used, with slight modification, in situations where there is local stiffening.
Published Version
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