Modal synthesis using accelerated modal summations

摘要

In view of impedance coupling applications, a new method of characterization of residual modal terms, termed "the method of orthocomplement", has been proposed in a recent paper [1]. Modified closed-form modal formulae were obtained in that way, including static or inertia relief terms, and "accelerated" modal series. More than limitating truncation effects, which can be achieved through a great number of existing methods, such formulae were seen to make the control of errors possible. It is proposed here to show how the modified modal formulae, considered as general expressions of inverse dynamical operators, can be used in the discussion of various techniques of model reduction. Interesting closed form expressions of mass and stiffness equivalent matrices are obtained in that way. Results should now be applied to the analysis and benchmarking of effective numerical methods (see, by example, ([2]-[10])), but this last part of the work remains to be done. At the present stage of investigation, interesting observations can however be made about (1) the possible divergence of Craig-Brampton reductions through "algebraic truncation"; (2) the specificity of Mac Neal reductions of free-floating components.