Proposal of a modal-geometrical-based master nodes selection criterion in modal analysis

Dynamic condensation techniques, used to simplify the dynamic representation of complex mechanical systems, and experimental modal identifications, in terms of number of sensors and their location, are deeply influenced by the selection of the degrees of freedom.The paper deals with a methodology for selecting physical nodes involved in model reduction or in experimental sensor location, named modal-geometrical selection criterion (MoGeSeC). It is based on the geometrical properties of the structure and on mode shape displacements, evaluated through finite element models or measured data set.By means of the well-known system equivalent reduction expansion process (SEREP) approach applied with MoGeSeC methodology, the ill conditioning of mass and stiffness matrices of the reduced model is minimized with a very low computational cost.In order to test MoGeSeC performance, some optimal nodes placement techniques, based on the maximization of the independence of modal properties or on energetic approaches, have been investigated. Finally, by means of a tailored iterative procedure, the best and the worst master node selections are performed on a particular model.Modal properties and ill conditioning of mass and stiffness matrices of reduced models are computed for several cases of different kind (1D-beam, 2D-shell, and 3D-solid elements). Finally an FE model of an exhaust pipeline, characterised by different constraint conditions, is considered and experimentally tested in order to validate the proposed methodology.