Statistical Analysis of Nonlinear Response of Rectangular Cracked Plate Subjected to Chaotic Interrogation

Abstract

The presence of part-through cracks with limited length is one of the prevalent defects in plate structures. The vibrational response of plates can be used to investigate the effect of crack presence. In this paper the modified line spring method (MLSM) is used to develop a nonlinear multi degree of freedom model of part-through cracked rectangular plate. After a convergence study in time series domain, tuning of the chaotic signal is conducted in two steps: (i) crossing of the Lyapunov exponents’ spectrums for the nonlinear model of the plate and the chaotic signal which assures the effectiveness of the model filter on the Lyapunov dimension of chaotic signal and (ii) varying the tuning parameter of chaotic signal to find a span in which tangible sensitivity in statistical parameters can be observed. Standard deviation, skewness and kurtosis are proposed as features to analyze the time series response of cracked plate. Damage characteristics such as: length, angle, location and depth of crack are considered as parameters to be varied in order to scrutinize the response of plates. Results show that by implementation of a tuned chaotic interrogator signal, tangible sensitivity and also near to monotonic behavior of statistical parameters versus damage characteristics are achievable.