A spectral approach for damage quantification in stochastic dynamic systems

Intrinsic to all real structures, parameter uncertainty can be found in material properties and geometries. Many structural parameters, such as, elastic modulus, Poisson's rate, thickness, density, etc., are spatially distributed by nature. The Karhunen-Loeve expansion is a method used to model the random field expanded in a spectral decomposition. Once many structural parameters can not be modelled as a Gaussian distribution the memoryless nonlinear transformation is used to translate a Gaussian random field in a non-Gaussian. Thus, stochastic methods have been used to include these uncertainties in the structural model. The Spectral Element Method (SEM) is a wave-based numerical approach used to model structures. It is also developed to express parameters as spatially correlated random field in its formulation. In this paper, the problem of structural damage detection under the presence of spatially distributed random parameter is addressed. Explicit equations to localize and assess damage are proposed based on the SEM formulation. Numerical examples in an axially vibrating undamaged and damaged structure with distributed parameters are analysed.