Identification of the nonlinear behaviour of a cracked RC beam through the statistical analysis of the dynamic response

SUMMARY This study investigates a new identification procedure suitable to deal with nonlinear systems. The proposed approach is made up of three main parts: system excitation with a band-limited white noise, solution of the Fokker–Planck equation that describes the motion of the structure in a parametric form and identification of the unknown system parameters by minimizing a suitable functional. The new procedure is able, for instance, to assess the severity of cracking caused by the shrinkage or by the overcoming of the concrete tensile strength in reinforced concrete (RC) structures. Cracked RC elements, in fact, exhibit a nonlinear behaviour due to different values of the flexural stiffness that depends on the opening of the cracks. Some numerical simulations allowed verifying the applicability of the procedure. Copyright # 2008 John Wiley & Sons, Ltd.

[1]  John S. Owen,et al.  The application of auto–regressive time series modelling for the time–frequency analysis of civil engineering structures , 2001 .

[2]  P. D. McFadden,et al.  Nonlinear Vibration Characteristics of Damaged Concrete Beams , 2003 .

[3]  A. L. Materazzi M. Breccolotti.  Reliability of the dynamic methods for evaluating structural concrete bridge integrity , 2004 .

[4]  M. Fogli,et al.  An original approximate method for estimating the invariant probability distribution of a large class of multi-dimensional nonlinear stochastic oscillators , 2003 .

[5]  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 .

[6]  R. Clough,et al.  Dynamics Of Structures , 1975 .

[7]  Rune Brincker,et al.  Identification and level I damage detection of the Z24 highway bridge , 2001 .

[8]  H. K. Hilsdorf,et al.  Code-type formulation of fracture mechanics concepts for concrete , 1991 .

[9]  Nicholas I. M. Gould,et al.  A globally convergent Lagrangian barrier algorithm for optimization with general inequality constraints and simple bounds , 1997, Math. Comput..

[10]  L Frýba,et al.  Load tests and modal analysis of bridges , 2001 .

[11]  Pierfrancesco Cacciola,et al.  Crack detection and location in a damaged beam vibrating under white noise , 2003 .

[12]  Hoon Sohn,et al.  A review of structural health monitoring literature 1996-2001 , 2002 .

[13]  P. Toint,et al.  A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds , 1991 .

[14]  Surendra P. Shah,et al.  Fracture Mechanics of Concrete: Applications of Fracture Mechanics to Concrete, Rock and Other Quasi-Brittle Materials , 1995 .

[15]  C. F. Beards,et al.  Random Vibration of Mechanical Systems , 1986 .

[16]  A. Rotem,et al.  Determination of Reinforcement Unbonding of Composites by a Vibration Technique , 1969 .

[17]  O. S. Salawu,et al.  Damage Location Using Vibration Mode Shapes , 1994 .

[18]  Lawrence A. Bergman,et al.  Application of multi-scale finite element methods to the solution of the Fokker–Planck equation , 2005 .

[19]  M. Shinozuka,et al.  Digital simulation of random processes and its applications , 1972 .

[20]  A. Hillerborg,et al.  Analysis of crack formation and crack growth in concrete by means of fracture mechanics and finite elements , 1976 .

[21]  Pierfrancesco Cacciola,et al.  Dynamic response of a rectangular beam with a known non-propagating crack of certain or uncertain depth , 2002 .

[22]  P. N. Saavedra,et al.  Crack detection and vibration behavior of cracked beams , 2001 .

[23]  Wilfried B. Krätzig,et al.  Compliance-based structural damage measure and its sensitivity to uncertainties , 2005 .

[24]  Yu-Kweng Michael Lin.  Probabilistic Theory of Structural Dynamics , 1976 .

[25]  J. Z. Zhu,et al.  The finite element method , 1977 .