Medium frequency vibration modeling of cracked plates using hierarchical trigonometric functions

Abstract

A modeling tool is proposed to describe the vibration behavior of pristine and damaged plates in the medium frequency range (below 10 kHz). This tool is intended to provide a platform for the development and assessment of damage detection algorithms for aircraft structural health monitoring applications. The proposed analytical model employs a Hierarchical Trigonometric Function Set (HTFS) to characterize homogeneous plates with through cracks. This approach takes advantage of the very high order of stability of the HTFS [O. Beslin and J. Nicolas, J. Sound Vib. 202, 633–655 (1997)] to approximate the effects of a small crack in a plate for all combinations of classical boundary conditions (e.g., CFSC, CCFF, FSFS). The model is first presented and then assessed for healthy and cracked CCCC plates with eigenvalues and eigenmodes presented in the literature. For a healthy square plate, numerical results provide good agreement up to the 1000th mode while, for a cracked rectangular plate, good agreement is obtained up to the 3rd mode, corresponding to the highest mode order available in the literature. Wave propagation simulation obtained from HTFS shows the scattering around the cracks in the plates. Experimental validation of the model is conducted both in frequency and time domains for healthy and cracked plates. [Work supported by the Consortium for Research and Innovation in Aerospace in Quebec (CRIAQ) and Defence R&D Canada.]

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“…Lower frequencies, used in modal techniques, need less signal processing but are less sensitive to small damage [8]. Finally, a medium frequency range seems to be a good compromise since it has already been used in the past to localize damages in large plates using wave propagation approaches [9][10][11] or using the variation of frequency response in a damaged riveted structure [12].…”

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“…The aim of this paper is to present a method of detection of cracks in structures executing flexural oscillations by using piezoelectric sensors and actuators bonded to these structures. This work is a part of a cooperative effort to develop smart technologies for structural health monitoring of aerospace structures, which included the development of modeling tools simulating the effect of cracks on the dynamic behavior of structures at low and medium frequencies, and of several damage detection strategies based on modal analysis, time-frequency approach and flexural wave propagation analysis using piezoelectric sensors and actuators and shape-memory alloys [8][9].…”