Vibration based damage detection in composite beams under temperature variations using Poincaré maps

Abstract In this work numerical and experimental study of the vibration of laminated beams with damage, subjected to dynamic loading and temperature variations is presented. The goal of the study is to check the applicability of the damage detection technique based on an analysis of the Poincare maps of the beam response. The geometrically nonlinear version of the Timoshenko beam theory is used to model the beam behavior. The damage is represented as a reduction of the effective elastic modulus of the beam material in a small area of the structure. The beams are subjected to a harmonic loading, leading to large amplitude vibrations and to temperature changes. The main results are focused on establishing the influence of the damage on the vibration response of heated or unheated structures and the change in the time-history diagrams and the Poincare maps, caused by a damage and elevated temperature. The damage detection criterion formulated earlier for nonheated plates, based on analysing of the Poincare maps of the damaged and healthy plate, is modified and tested for the case of beams additionally subjected to elevated temperatures. The importance of taking into account the actual temperature in the process of damage detection is shown. Performed experimental tests (by an optical method) confirm the applicability and sensitivity of the proposed method.

[1]  Rune Brincker,et al.  Vibration Based Inspection of Civil Engineering Structures , 1993 .

[2]  Bogdan I. Epureanu,et al.  Exploiting Chaotic Dynamics for Detecting Parametric Variations in Aeroelastic Systems , 2004 .

[3]  Daniel J. Inman,et al.  TIME DOMAIN ANALYSIS FOR DAMAGE DETECTION IN SMART STRUCTURES , 1997 .

[4]  Ugo Andreaus,et al.  Fatigue crack growth, free vibrations, and breathing crack detection of aluminium alloy and steel beams , 2009 .

[5]  Irina Trendafilova,et al.  Large amplitude vibrations and damage detection of rectangular plates , 2008 .

[6]  Irina Trendafilova,et al.  Vibration-based damage detection in plates by using time series analysis , 2008 .

[7]  Hoon Sohn,et al.  Structural Health Monitoring Using Statistical Process Control , 2000 .

[8]  Daniel J. Inman,et al.  An experimentally validated damage detection theory in smart structures , 1996 .

[9]  Nikos A. Aspragathos,et al.  Identification of crack location and magnitude in a cantilever beam from the vibration modes , 1990 .

[10]  Z. Qin,et al.  Damage Detection in Plate Structures Based on Space-time Autoregressive Moving Average Processes , 2011 .

[11]  Anant R. Kukreti,et al.  Dynamic analysis of nonlinear structures by pseudo-normal mode superposition method , 1984 .

[12]  P. Ribeiro,et al.  The effect of temperature on the large amplitude vibrations of curved beams , 2005 .

[13]  E. Manoach.  Dynamic large deflection analysis of elastic-plastic Mindlin circular plates , 1994 .

[14]  Marco Amabili,et al.  Thermal effects on geometrically nonlinear vibrations of rectangular plates with fixed edges , 2009 .

[15]  Grant P. Steven,et al.  VIBRATION-BASED MODEL-DEPENDENT DAMAGE (DELAMINATION) IDENTIFICATION AND HEALTH MONITORING FOR COMPOSITE STRUCTURES — A REVIEW , 2000 .

[16]  Dahsin Liu,et al.  An Assessment of Damping Measurement in the Evaluation of Integrity of Composite Beams , 1987 .

[17]  K. Law,et al.  Time series-based damage detection and localization algorithm with application to the ASCE benchmark structure , 2006 .

[18]  Fabrizio Vestroni,et al.  Frequency reduction in elastic beams due to a stable crack: numerical results compared with measured test data. , 2003 .

[19]  Pedro Ribeiro,et al.  Coupled, thermoelastic, large amplitude vibrations of Timoshenko beams , 2004 .

[20]  E. Parloo,et al.  AUTONOMOUS STRUCTURAL HEALTH MONITORING—PART II: VIBRATION-BASED IN-OPERATION DAMAGE ASSESSMENT , 2002 .

[21]  C. W. Yap,et al.  Analytical and numerical studies on the buckling of delaminated composite beams , 2007 .

[22]  S. L. Tsyfansky,et al.  NON-LINEAR VIBRATION METHOD FOR DETECTION OF FATIGUE CRACKS IN AIRCRAFT WINGS , 2000 .

[23]  Michael D. Todd,et al.  A multivariate, attractor-based approach to structural health monitoring , 2005 .

[24]  Charles R. Farrar,et al.  Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: A literature review , 1996 .

[25]  P. Casini,et al.  Non-linear dynamics of a cracked cantilever beam under harmonic excitation , 2007 .

[26]  Ugo Andreaus,et al.  Cracked beam identification by numerically analysing the nonlinear behaviour of the harmonically forced response , 2011 .

[27]  P. Ribeiro.  Thermally induced transitions to chaos in plate vibrations , 2007 .

[28]  Roberts Joffe,et al.  Analytical modeling of stiffness reduction in symmetric and balanced laminates due to cracks in 90° layers , 1999 .

[29]  J. Reddy.  Mechanics of laminated composite plates and shells : theory and analysis , 1996 .

[30]  E. Manoach,et al.  Dynamic response of thick elastic-plastic beams , 1993 .

[31]  E. Parloo,et al.  AUTONOMOUS STRUCTURAL HEALTH MONITORING—PART I: MODAL PARAMETER ESTIMATION AND TRACKING , 2002 .

[32]  L. Pecora,et al.  Vibration-based damage assessment utilizing state space geometry changes: local attractor variance ratio , 2001 .