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This paper seeks to present a new solution algorithm for updating of finite element models in structural dynamics. A random search method is applied to improving the correlation between the numerical simulation and the measured experimental data

Abstract:The objective of this work is to use natural frequencies for the localization and quantification of cracks in beams. First, to study the effect of the crack on natural frequencies, a finite element model of Euler-Bernoulli is presented. Concerning the damaged element, the stiffness matrix is calculated by the theory of fracture mechanics, by inverting the flexibility matrix. Then, in order to detect damage, we are going to show that the shape given by the change in the natural frequencies is as function of the damage position only. Thus, the crack is located by the correlation between the shape of the measured frequencies and those obtained by the finite elements, where the position that gives the calculated shape which is the most similar to the measured one, indicates the crack position. After the localization, an inverse method will be applied to quantify the damage. Finally, an experimental application is presented to show the real applicability of the method, in which the crack is introduced by using an Electrical Discharge Machining. The results confirm the applicability of the method for the localization and the quantification of cracks.

Finite element (FE) model updating technique belongs to the class of inverse problems in classical mechanics. According to the continuum damage mechanics, damage is represented by a reduction factor of the element stiffness and mass. The objective of the optimization problem is to minimize the difference between measured and numerical FE vibration data. In this study a new method is presented for structural damage detection called Improved Modified Accelerated Random Search algorithm (IMARS). The algorithm uses model updating procedure to detect damages in a decoupled fashion. First, detecting the location and the number of damaged elements is evaluated by multi-run process. Knowing damage number, the quantification step is then applied using simple computing procedure. The effectiveness of the algorithm is first tested on mathematical benchmark functions. The algorithm is then applied in damage detection of 2D beam structure and 2D truss structure. These two cases have different boundary conditions and different damage scenarios. The simulated experimental modal data have been taken as reference values. A real cantilever beam with experimental modal parameters is used to validate the proposed method for real single and double damages. Results show that the proposed method is accurate and robust in structural damage identification.