Crack is a damage usually happened in structural members
but dangerous for safety of structure if it is not early detected.
However, cracks are often difficult to identify by visual
inspection as they occurred at the unfeasible locations.
Therefore, cracks could be indirectly detected from measured
total dynamical characteristics of structures such as natural
frequencies, mode shapes and frequency or time history
response. In order to identify location and size of a crack in a
structure the problem of analysis of the crack’s effect on the
dynamic properties is of great importance. It could give also
useful tool for crack localization and size evaluation. On the
other hand, beams are frequently used as structural member in
the practice of structural engineering. So, crack detection for
beam-like structures gets to be an important problem. Crack
detection problem of beam with uniform cross section is
thoroughly studied, but vibration of cracked beam with varying
cross section presents a difficult problem. It is because vibration
of such the structure is described by differential equations with
varying coefficients that are nowadays not generally solved.
The beam with piecewise uniform beam, acknowledged as
stepped beam is the simplest model of beam with varying cross
section. Although, vibration analysis and crack detection for
stepped beam have been studied in some publications,
developing more efficient methods for solving the problems of
various types of stepped beams is really demanded
