Attractor Based Analysis of Centrally Cracked Plate Subjected to Chaotic Excitation

The presence of part-through cracks with limited length is one of the prevalent defects in the plate structures. Due to the slight effect of this type of damages on the frequency response of the plates, conventional vibration-based damage assessment could be a challenging task. In this study for the first time, a recently developed state-space method which is based on the chaotic excitation is implemented and nonlinear prediction error (NPE) is proposed as a geometrical feature to analyze the chaotic attractor of a centrally cracked plate. For this purpose using line spring method (LSM) a nonlinear multi-degree of freedom model of part through cracked rectangular plate is developed. Tuning of Lorenz type chaotic signal is conducted by crossing of the Lyapunov exponents’ spectrums of nonlinear model of the plate and chaotic signal and in the next step by varying the tuning parameter to find a span in which a tangible sensitivity in the NPE could be observable. Damage characteristics such as length, depth and angle of crack are altered and variation of proposed feature is scrutinized. Results show that by implementation of the tuned chaotic signal, tangible sensitivity and also near to monotonic behavior of NPE versus damage intensity are achievable. Finally, the superiority of the proposed method is examined through the comparison with the frequency-based method.

Keywords:

Crack , chaotic , nonlinear dynamics , plate , prediction error