Nonlinear Dynamic Structures with Developing Discontinuity

AbstractDiscontinuity is one of the most important nonlinear factors challenging both methods of nonlinear analysis and its applications. The problem becomes more complicated when the discontinuity is developing under the influence of dynamic processes in the structures. This paper presents the methodology for analysis and simulation of the systems with the developing discontinuity. It is based on the combination of analytical technique using nonlinear integral equations and the Matlab-Simulink computation. This methodology is applied to analysis of nonlinear dynamics of the cracked bar. Some new nonlinear phenomena have been revealed and validated

Vibro-Impact Response of a Cracked Bar

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 presente