Análisis de modelos de vibraciones en lajas y placas

Abstract

This paper is related with the development of mathematical models aimed to simulate the dynamic input and output of experimental nondestructive tests in order to detect structural imperfections. The structures to be considered are composed by steel plates of thin thickness. The imperfections in these cases are cracks and they can penetrate either a significant part of the plate thickness or be micro cracks or superficial imperfections. They first class of cracks is related with structural safety and the second one is more connected to the structural protection to the environment. particularly if protective paintings can be deteriorated. Two mathematical groups of models have been developed. The first group tries to locate the position and extension of the imperfection on the first class, i.e. crack. Bending Kirchoff thin plate models belong to this first group and they are used to this respect. The another group of models is dealt with membrane structures under the superficial Rayleigh waves excitation. With group of models the micro cracks detection is intended. In the application of the first group of models to the detection of cracks, it has been observed that the differences between the natural frequencies of the non cracked and the cracked structures are very small. Also modes vectors comparison using different norms are not reliable tools to detect structural imperfections, because this comparison may depends on the crack position and the excited mode. However, geometry and crack position can be identified quite accurately if this comparison is carried out between first derivatives (mode rotations) of the natural modes are used instead. Finally. in relation with the analysis of the superficial crack existence the use of Rayleigh waves is very promising. The geometry and the penetration of the micro crack can be detected very accurately. The mathematical and numerical treatment of the generation of these Rayleigh waves present, however serious complexities. particularly due to the dispersion problems appearing during the analysis by finite differences along the time domain and the computation of the larger number of finite elements on the spatial coordinates needed in this model.