An analytical method for free-vibration analysis of multistep nonuniform cracked beam is presented. Special solutions for five different types of nonuniform beams are given first. The procedure for determining the fundamental solutions that satisfy the normalization conditions is proposed. The problem of free vibration of a multistep beam, each step beam being nonuniform and having an arbitrary number of cracks and concentrated masses, can be conveniently solved based on th fundamental solutions and recurrence formulas developed in this paper. The eigenvalue equation of such a multistep cracked beam with any kind of two end supports can be established from a determinant of order 2.
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