Damage Identification by Dynamic Load Monitoring

Abstract

A damage in an elastic material can have different causes, such as a crack, a hole or a delamination in case of a layered material. All of these defects alter the dynamic behaviour of the structure, which means that a wave, which propagates along the structure, is affected in a certain way. The method, that is being outlined in this chapter, relies on the idea that the difference of the wave propagation in the undamaged structure and in the damaged structure is caused by a (virtual) external force which is interpreted as the cause of altered wave properties such as reflections, attenuation or mode conversions. Computing the origin of this external volume force then enables us to locate the damage. Since we use time-dependent data, this method is called dynamic load monitoring and works as follows. First we simulate the wave propagation in an undamaged structure, e.g. a plate, by solving a corresponding initial boundary value problem, that is based on the equations of linear elastodynamics. Evaluating the solution u _R at the observed boundary values leads to a reference measurement Qu _R , where Q denotes the so-called observation operator. This observation operator must be seen as the mathematical model of the specific data acquisition. Having the outcome Qu _D of the same measurements of a damaged plate at hand we subtract the reference data from the measured ones. In this way all sources e.g. gravitation is removed from the signal, since the underlying PDE is linear, and the remaining sources therefore can be interpreted as caused by defects. This is the key idea of our method. Besides proving existence and uniqueness of a solution of the underlying initial boundary value problem, we precisely describe the implementation of our method and show its numerical performance when applied to a transversely isotropic material.