Linear substructure synthesis via Lyapunov stable penalty methods
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Component mode synthesis theories in structural dynamics are comprised of two fundamental steps: (1) substructure order reduction and (2) synthesis of the reduced order substructure models to achieve approximate full order response. The most common criticism of component mode synthesis procedures in general is that they require heuristic decision based upon physical insight of the analyst to insure accurate results. This paper introduces a novel approach for the problem of coupling reduced order models based upon recent work by the authors in nonlinear multibody dynamics. It is attractive in its simplicity, and in the fact that some theoretical results regarding the accuracy of the coupling procedure have been derived. The method enforces constraints between substructures by approximating the constrained governing system of differential-algebraic equations by a penalty-parameterized system of ordinary differential equations. The resulting formulation has several advantages: (i) Explicit time-domain constraint violation bounds are available for the approximate full order system. (ii) Under relatively mild sufficient conditions, the approximate governing equations are guaranteed to be Lyapunov (asymptotically) stable. (iii) The approximate method is equivalent to a linear quadratic feedback control formulation to minimize the constraint work. (iv) The method retains a high degree of sparsity in the full order, approximate system. (v) The approach is simple to implement compared to many other alternative techniques of substructure coupling. 1991.