A Test-analysis-matrix (tam) with Improved Dynamic Characteristics

Whenever experimentally derived (Test) modal vectors are compared to the analytically obtained (Analysis) modal vectors, for purpose of model verification or model updating, a transformation matrix must be utilized to expand/reduce the degrees offreedom, DOF, so that the spatial dimension of the two sets of modal vectors is the same. The measured set of DOF seldom match the analytical set of DOF in dimension. Several Test A_nalysis &&M.x (TAM) approaches such as the Guyan reduction, Improved Reduced System, System Equivalent Reduction/Expansion Process and the Hybrid TAM have been developed to achieve such a transformation. One of the simplest examples of utilizing such a TAM is the computation of n cross orthogonaliry matrix involving the modal test vectors, the analytical mass matrix and the analytical vectors. An important requirement of this correlation is that the reduced matrices of man and sti&ess represent the xame dynamics as the actual physical structure. Again the TAMS need to incorporate the target mode dynamics and the equally important residual dynamics. The present investigarion aims at developing a new transformation mapping that reduces/expands the analytical vectors to the required size of the experimental DOFfor such an orthogonalitj check with effective residualflexibili~. The residual subspace used in this mapping has, as its basis. modes derived using the residual flexibiliry matrix that carry with them the effect of all of the residual set of normal modes. Simulated test-analysis correlation results are represented by FE.44 target modes with noise modeled ns a random linear combination of all FE.44 modes. Nomenclature Introduction M,K,C,G : mass, stiffness, damping and flexibility matrices of analytical model. T, P : Transformation and Projector matrices. Y : modal matrix of modes stacked as columns. ” : displacement vector. X(w), F(w) : displacement and force vectors. ;t : modal coordinates. : modal frequency. 0, “I : damping factor and natural frequency. Accurate analytical models of structures are required for a variety of reasons. These may be for model verification/updating, failure analysis, control system design or design modification requirement. The analytical model is usually based upon a Finite Element Model, FEM. Accuracy is often assessed by comparing the modal characteristics extracted using vibration test data with the corresponding modal properties predicted by the analytical model. a, 0, n : active, omitted and total DOFs. Test and analysis frequencies can be compared directly if t-1 : subscripts representing target and residual the corresponding modal vectors can be identified. modes. However modal vectors cannot be readily compared because of the large difference in the number of analytical