Affiliations: EMBRAER: Empresa Brasileira de Aeronáutica S.A.,
Structural Engineering Division, Structural Analysis Section, Avenida
Brigadeiro Faria Lima, 2170, São José dos Campos, SP, 12227-901,
Brazil. Tel.: +55 12 3927 6139; Fax: +55 12 3927 6600 ext. 2651; E-mail:
[email protected]
Abstract: This paper addresses the situation in which some form of damage is
induced by cyclic mechanical stresses yielded by the vibratory motion of a
system whose dynamical behaviour is, in turn, affected by the evolution of the
damage. It is assumed that both phenomena, vibration and damage propagation,
can be modeled by means of time depended equations of motion whose coupled
solution is sought. A brief discussion about the damage tolerant design
philosophy for aircraft structures is presented at the introduction,
emphasizing the importance of the accurate definition of inspection intervals
and, for this sake, the need of a representative damage propagation model
accounting for the actual loading environment in which a structure may operate.
For the purpose of illustration, the finite element model of a cantilever beam
is formulated, providing that the stiffness matrix can be updated as long as a
crack of an assumed initial length spreads in a given location of the beam
according to a proper propagation model. This way, it is possible to track how
the mechanical vibration, through its varying amplitude stress field, activates
and develops the fatigue failure mechanism. Conversely, it is also possible to
address how the effect of the fatigue induced stiffness degradation influences
the motion of the beam, closing the loop for the analysis of a coupled
vibration-degradation dynamical phenomenon. In the possession of this working
model, stochastic simulation of the beam behaviour is developed, aiming at the
identification of the most influential parameters and at the characterization
of the probability distributions of the relevant responses of interest. The
knowledge of the parameters and responses allows for the formulation of
optimization problems aiming at the improvement of the beam robustness with
respect to the fatigue induced stiffness degradation. The overall results are
presented and analyzed, conducting to the conclusions and outline of future
investigation.
