Damage detection in an uncertain nonlinear beam

Luis Gustavo Villani (1) , Samuel da Silva (1) , Americo Cunha Jr (2)

1 UNESP - Universidade Estadual Paulista Júlio de Mesquita Filho = São Paulo State University
2 UERJ - Universidade do Estado do Rio de Janeiro [Brasil] = Rio de Janeiro State University [Brazil] = Université d'État de Rio de Janeiro [Brésil]

The present paper proposes the use of discrete time Volterra series expanded with Kautz filters for predicting the experimental response of a nonlinear beam, taking into account uncertainties that are inherent to the system. Nonlinear behavior is simulated considering large amplitude of vibration in a clamped-free beam, with a magnet near the free end to cause cubic stiffness effect. The Volterra kernels and Kautz functions are estimated in a stochastic way, where the limits of confidence are established to the system response and used as a reference model to detect damage. The detection approach is based on a nonlinear stochastic index and hypothesis test, considering different levels of simulated damage, associated with loss of mass. The results have shown that considering the uncertainties when identifying the model is very important in the process of damage detection and the nonlinear metric proved to be more appropriated to describe the system response with better results mainly in the nonlinear regime of motion.

Mots clés: Nonlinear dynamics; Volterra series; Uncertainties quantification; SHM

Domaines: Vibrations [physics.class-ph]; Probabilités [math.PR]; Statistiques [math.ST]; Mécanique des structures [physics.class-ph]; Mécanique des solides [physics.class-ph]; Génie mécanique [physics.class-ph]

Luis Gustavo Villani, Samuel da Silva, Americo Cunha Jr. Damage detection in an uncertain nonlinear beam. Procedia Engineering, 2017, 199, pp.2090-2095. ⟨10.1016/j.proeng.2017.09.480⟩. ⟨hal-01590669⟩