Abstract
The presence of a crack in a structure affects its dynamic behaviour under working conditions. Cracks introduce nonlinearities into the system; the use of such nonlinearities for damage detection should be investigated. A model of a one-dimensional cracked cantilever bar subjected to longitudinal harmonic excitation is used to analyse a vibro-impact response as a way to monitor structural health. The effect of contact nonlinearity due to crack's faces interaction is considered. This nonlinear information is obtained based on a combination of the analytical technique and the Matlab-Simulink computation. The procedure uses a numerical approximation for dynamic compliance operators and a nonlinear model of contact faces interaction implemented numerically as a nonlinear feedback. Nonlinear resonant phenomena due to vibro-impact interaction in the cracked bar are obtained and analysed. A distribution of the higher harmonics along the bar length, generated due to the nonlinear response of the crack, is revealed as a function of the distance from the crack. Recommendations on structural health monitoring of cracked bars due to contact nonlinearity are presented
Highlights
Crack monitoring in critical structures is becoming more important to prevent failures occurring under operating conditions
Several researchers have addressed the problem of a beam with the breathing cracks using the finite element method and validated the results obtained through experimental analysis
The important aspect of this paper is to use the concept of dynamics compliance operator along with the theory of modal analysis to develop the Matlab-Simulimk model of the cracked bar
Summary
Crack monitoring in critical structures is becoming more important to prevent failures occurring under operating conditions. The discontinuous element in continuous structure is modelled using a special mathematical technique for proper matching of local and distributed elements of the resulting structure This is effectively implemented using the force characteristics of contact interaction for the discontinuous elements and Green’s function in the contact areas for the media [15]. Effective numerical simulation of such structures with Matlab-Simulink software requires implementation of realistic models for contact phenomena and transformation of the transcendental operators of dynamic compliances into rational functions of complex variable. This is made with the help of modal representation for the dynamic compliances. This produces a convenient calculation scheme for accurate estimation
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