Dynamic Stability Analysis of a Cracked Beam using a Lumped Parameter Model
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Abstract
Vibration based condition monitoring is one of the predictive maintenance strategies applied for structures and rotating machinery. Detection and identification of fatigue crack in structures has been a widely discussed problem in the literature of condition monitoring. This paper discusses the numerical results that have been obtained from the study of bending vibration of a cracked beam. The crack is primarily modelled as an opening/ closing crack resulting in a periodic variation in stiffness. The mathematical model considered for the cracked beam is a lumped single degree of freedom system. The resulting system equation of motion has the canonical form of a Mathieu equation. For obtaining the system response, the equation is written in a state-space form and then solved using fourth order Runge-Kutta numerical integration. The time and frequency domain responses are obtained for a specific harmonic excitation. Further, the stability of the cracked beam is discussed with respect to the variation in stiffness, by numerical analysis, using a Vander Pol and Strutt stability chart diagram.
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