Random Vibrations of Timoshenko Beams with Generalized Boundary Conditions
A new method which includes the effect of shear deformations and rotatory inertia is presented to obtain the response of beams. The equations of motion are written in the state vector form. The response is expressed as a linear combination of the eigenfunctions of the homogeneous boundary value problem which can be solved for any arbitrary boundary conditions. The eigenfunctions are obtained as a solution of a nested eigenvalue problem. To define the time dependent initial value problem for the principal coordinates, the adjoint eigenvalue problem is used. Numerical results for the natural frequencies, bending moment response variance and zero crossing rates are obtained for beams with several boundary conditions and the effect of shear deformation and rotatory inertia on these responses is evaluated.
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