Analytical approach to free and forced vibrations of axially loaded cracked Timoshenko beams

Wave vibration analysis of an axially loaded cracked Timoshenko beam is presented in this paper. It includes the effects of axial loading, shear deformation and rotary inertia. From wave standpoint, vibrations propagate, reflect and transmit in a structure. The transmission and reflection matrices for various discontinuities on an axially loaded Timoshenko beam are derived. Such discontinuities include cracks, boundaries and changes in section. The matrix relations between the injected waves and externally applied forces and moments are also derived. These matrices are combined to provide a concise and systematic approach to both free and forced vibration analyses of complex axially loaded Timoshenko beams with discontinuities such as cracks and sectional changes. The systematic approach is illustrated using several numerical examples.