Unbalanced Force Mapping Method

In the present work a method is developed that, using the vibration data gathered from the surface measurement of displacements or velocities, is able to analyze them and to assess the position and length of the structural anoma- lies of a beam or shell layered structure. The key idea is to use a standard linear Finite Element Model (hereafter FEM) of the structure to reproduce the balance e¿ect between the inertial and elastic forces in the free vibrating area of the structure. The linear matrix application, representing the FEM, will map the vector space of the measured nodal displacements to the vector space of the applied external nodal forces. From a theoretical point of view the resultant forces must be zero in the nodes under free vibration condition and as a consequence the applied external nodal force vector must be a null vector. A gap between the mathematical model and the real physical model in an homogeneous structure will anyway be present and will results in a force vector di¿erent from zero with a constant in space mean error distribution. This non-zero value represents the unbalanced forces between the inertial and elastic component due to the model uncertainty.