Nonlinear Features in the Dynamic Response of a Cracked Beam Under Harmonic Forcing

Abstract

Detection of damage in beam structures is usually pursued by means of methods based on the measured variations of modal quantities, like frequencies and eigenmodes. The drawback of these methods is the small sensitivity of modal quantities to concentrated damage. Since a crack introduces nonlinearities in the system, the use of nonlinear techniques of damage detection merits to be investigated. With this aim the present paper is devoted to analyze the peculiar features of the nonlinear response of a cracked beam. The problem of a cantilever beam with an asymmetric edge crack subjected to a harmonic forcing at the tip is considered as a plane problem and is solved by using two-dimensional finite element model; the behaviour of the breathing crack is simulated as a frictionless contact problem. The modification of the response with respect to the linear one is outlined: in particular, excitation of sub- and super-harmonics, period doubling, quasi-impulsive behaviour at crack interfaces are the main achievements. These response characteristics can be used in nonlinear techniques of damage identification.