A Modal-Geometrical Selection Criterion for Master Nodes: Numerical and Experimental Testing Elvio Bonisoli, Cristiana Delprete and Carlo Rosso Politecnico di Torino, Corso Duca degli Abruzzi, 24 - 10129, Torino, Italy ABSTRACT Usually, the problem of master nodes selection characterizes both computational or experimental modal analyses and defines the numerical properties of reduced models that possess equivalent dynamic properties. Methodologies based on experience are normally used or heavy time-consuming numerical algorithms can be applied. In that paper, the Modal-Geometrical Selection Criterion (MoGeSeC) is applied to a crankshaft, both for an EMA (experimental modal analysis) and for a reduction procedure applied on progressive numerical models. Then the results are compared with other literature criteria and algorithms. The nodes suggested by MoGeSeC and other criteria are used for identification tools of the dynamic behaviour of the crankshaft. In that way MoGeSeC proves to be a very quick and accurate method because the nodes it selects depicts very well modal features of the tested component. The proposed criterion is also applied to the component in order to evaluate the reduced inertia and stiffness matrices and their numerical ill-conditioning is measured. Also in that case MoGeSeC provides the analyzer with a good instrument for identification processes. NOMENCLATURE jk A accelerance function in node j, due to a dynamic force acting in node k k F0, amplitude of acting force in node k j imaginary operator ki weight coefficients m order of the reduced model n number of degrees of freedom (dofs) of the starting model r number of considered modes in term mW max O , min O maximum and minimum eigenvalue i[ damping factor of mode i Z frequency of the acting force iZ natural frequency of mode i i i ix y z , , geometrical grid coordinates of node i f t generalized forces set vector q modal coordinates vector x t , mx , sx respectively generalized coordinates vector, master and slave subset W weight function of the modal-geometrical selection criterion gW geometric term of the weight function mW modal term of the weight function M,K respectively mass and stiffness matrix rM , rK respectively mass and stiffness matrix of the reduced model Q Fisher information matrix J covariance matrix of error with truncated modal displacement base T. Proulx (ed.), Linking Models and Experiments, Volume 2, Conference Proceedings of the Society for Experimental Mechanics Series 5, 281 DOI 10.1007/978-1-4419-9305-2_20, © The Society for Experimental Mechanics, Inc. 2011
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