Crack detection in beams and spinning beams: solution of the inverse problem via a power series algorithm

MARTA B. ROSALES; CARLOS P. FILIPICH

Rio de Janeiro, Brasil

Congreso; 6th. Word Congress of Structural and Multidisciplinary Optimization; 2005

ISSMO, AIAA, ABCM

Many methods are based in studying changes in parameters of a cracked structural elements such as the mass, stiffness, modulus of elasticity and modal parameters. The use of measured frequencies as a crack detection criterion has been extensively applied in the last decades since its experimental determination for a given cracked element is rather straightforward. However the inverse problem of determination of the crack parameters (location and depth) for a given set of measured frequencies is not simple. An efficient numerical technique has to be employed so as to obtain acceptable results. The crack is modeled through the introduction of an intermediate rotational spring in a Bernoulli-Euler beam without and with a constant spinning velocity. The spinning beam may have different principal moment of inertia of the cross section, i.e. two springs are assumed corresponding to each principal plane. The beam-spring analytical model is first stated and the power series method employed to obtain the solution for a given set of data (direct method). A systematization of the well-known power series technique already used by the authors in other problems, leads to an efficient numerical method. The input data for the inverse algorithm is obtained at this stage from a computational experiment (FEM model). When dealing with the spinning beam, an analytical solution, previously developed by the authors, is employed to solve a three-span stepped beam that is used as the numerical experiment. Two numerical examples are presented with an evaluation of the errors in the results. The simplicity and systematization of the methodology as well as the results are encouraging.