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Nonlinear dynamics of a rotating shaft with a breathing crack (Annals of Sol. Stru. Mech.)

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In this paper, the effects of a breathing crack on the vibratory characteris-

tics of a rotating shaft are investigated. A new, simple and robust model composed of

two rigid bars connected with a nonlinear flexural spring is proposed. The nonlinear

spring, located at the cracked transverse section position, concentrates the global stiff-

ness of the cracked shaft. The breathing mechanism of the crack is described by a more

realistic periodic variation of the global stiffness depending not only but substantially

on the system vibratory response. It is based on an energy formulation of the problem

of 3D elasticity with unilateral contact conditions on the crack lips. A possible partial

opening and closing of the crack is considered which makes the approach more appro-

priate for deep cracks modeling. The harmonic balance method, direct time-integration

schemes and nonlinear dynamics tools are used to characterize the global dynamics of

the system. The effects of the crack depth and rotating frequency have been metic-

ulously examined and it was found that the cracked shaft never exhibits chaotic or

quasi-periodic vibratory response.

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