The reduced model can be rewritten as: S m S m mf M x K x . (9) where the mass and stiffness matrices are: 1 , 2 , 1 , , r mgen T S mgen T S S mgen T S mgen T S S diag Ȧ ĭ ĭ K T K T ĭ ĭ M T MT . (10) and 2 rȦ is the eigenvalues vector. MODAL-PROPERTIES COMPARISON The comparison of the two approach of sensor location are proposed with different targets: x distribution in space of the selected nodes; x modal identification results from experimental tests and comparison with respect to FE models; x sensitivity of identified modal properties and robustness of reduced models from numerical or experimental data. The comparison is carried on an engine component, it is the crankshaft of a 4 cylinder / 4 strokes diesel engine that is characterized by the following properties: x it could be considered in a very simplified approach as a mono-dimensional (1D) object, as in the analytical method used for studying the torsional behaviour; so a basic idea of selecting very few nodes is to linearly distribute them along its axis, but master nodes selection outside axis is not so trivial for taking into account the bending behaviour; x from a manufacturing point of view, it is obtained through casting and following turning and milling processes, it presents a plane of symmetry that could be slightly deformed by holes for lubricants and static balancing requirements; x it has numerous bending modes in two different planes, interposed between several torsional and axial modes; rich dynamic properties are due to close modes effects in a quite reduced frequency area. In Figure 2 and 3 the actual component and the corresponding model are shown. Figure 2 – Actual crankshaft component. Figure 3 – Finite element model. The FE model has been experimentally validated, through roving hammer impulse tests and MIMO (Multi Input Multi Output) modal identification technique in frequency domain [2]. The experimental tests are conducted for the case of free-free boundary conditions. In Figure 4 the experimental test rig for the crankshaft case is shown. The FE models of the components are described in Table 1. 286
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