Health assessment of beams - Theoretical formulation and analytical verification

Theoretical aspects and analytical verification of a novel non-destructive structural health assessment procedure being developed by a research team at the University of Arizona are presented in this paper. The experimental verification of the procedure is discussed in the companion paper. The health assessments of fixed ended and simply supported beams are specifically addressed. The basic procedure is a finite element-based linear time domain system identification technique where input excitation information is not required. Beams are represented by finite elements. By tracking the changes in the moduli of rigidities of the elements, the current health of the beams can be assessed. Rayleigh damping is used in the dynamic formulation to reduce the size of the identification problem. How to establish the optimal number of finite elements is first discussed. Defects, in terms of two notches, are introduced in an element in fixed ended and simply supported beams. Analytical responses of defect-free and defective beams excited by sinusoidal loadings are evaluated by using a computer programme. Using analytical response information only and completely ignoring the input excitation information, the health of the beams is successfully predicted in all cases. When defects were present, the method also identified the location of the defective element. The beams were then experimentally tested to verify conclusively the proposed method, as discussed in the companion paper.