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Nonlinear Modeling of Cracked Beams for Impedance Based Structural Health Monitoring

[+] Author Affiliations
Naserodin Sepehry, Firooz Bakhtiari-Nejad, Mahnaz Shamshirsaz

Amirkabir University of Technology, Tehran, Iran

Weidong Zhu

University of Maryland at Baltimore County, Baltimore, MD

Paper No. IMECE2017-70808, pp. V04BT05A034; 8 pages
  • ASME 2017 International Mechanical Engineering Congress and Exposition
  • Volume 4B: Dynamics, Vibration, and Control
  • Tampa, Florida, USA, November 3–9, 2017
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-5838-7
  • Copyright © 2017 by ASME


One of the main objectives of the structural health monitoring by piezoelectric wafer active sensor (PWAS) using electromechanical impedance method is continuously damage detection applications. In present work impedance method of beam structure is considered and the effect of early crack using breathing crack modeling is studied. In order to model the effect of a crack in beam, the beam is connected with a rotational spring in crack location. The Rayleigh–Ritz method is used to generate ordinary differential equation of cracked beam. Firstly, only open crack is considered that this is leads to linear system equation. In linear system, time domain system equations are converted to frequency domain, and then impedance of PWAS in frequency domain is calculated. Secondly, the breathing crack is modeled to be fully open or fully closed. This phenomenon leads to the nonlinear system equations. These nonlinear equations are solved using pseudo-arc length continuation scheme and collocation method for any harmonic voltage applied to actuator. Then impedance of PWAS is calculated. Two methods are used to detect early crack using breathing crack modeling on PWAS impedance. At the first, frequency response of breathing crack in the frequency range with its sub-harmonics is calculated. Second, only frequency response of one harmonic is computed with its super-harmonics. Finally, the detection method of linear is compared with nonlinear model.

Copyright © 2017 by ASME



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