A simple and efficient analytical approach is presented to determine the vibrational
frequencies and mode shape functions of axially-loaded Timoshenko beams with an arbitrary
number of cracks. The local compliance induced by a crack is described by a
massless rotational spring model. A set of boundary conditions are used as initial parameters
to define the mode shape of the segment of the beam before the first crack.
Using this, the remaining set of boundary conditions and recurrence formula developed
in the study, the mode shape function of vibration of the beam containing multiple cracks
can be easily determined. Four different classical boundary conditions (pinned-pinned,
clamped-pinned, clamped-free, and clamped-clamped) are considered. Elasticallyrestrained
support condition with concentrated masses is also considered. Three crack
depths and five axial force levels representing the conditions under service loads are
used. A parametric study is carried out for each case of support conditions to investigate
the effect of crack and axial load on the vibrational properties of cracked Timoshenko
beams. The influence of crack on the buckling load of the beam is also studied statically.
Part of the results obtained is checked against the published values. The study concludes
that the crack location, crack severity, and axial force level strongly affect the