Free vibration analysis of non-rotating and rotating Timoshenko beams with damaged boundaries using the Chebyshev collocation method

This paper proposes a new numerical technique for the free vibration analysis of non-rotating and rotating Timoshenko beams with damaged boundaries. For this purpose, the Chebyshev collocation method is applied to obtain the natural frequencies and mode shapes. The damaged boundaries of the Timoshenko beam are represented by distributed translational and torsional springs. In the present study the boundary conditions are coupled with the governing equation to formulate the eigenvalue problem.

► Chebyshev collocation method is applied to the free vibration problem of static and rotating Timoshenko beam.
► Damaged boundary is represented by a translational and rotational spring.
► The Kronecker product operator is used in the discretization of the governing equations and the boundary conditions.
► The eigenvalue problem is solved to obtain the natural frequencies.