INCLUSION PRINCIPLE FOR THE RAYLEIGH-RITZ BASED SUBSTRUCTURE SYNTHESIS

This paper is concerned with the convergence characteristics of a Rayleigh-Ritz based substructure synthesis developed earlier by these authors. According to this substructure synthesis, the motion of every substructure is modeled in terms of quasicomparison functions, which are linear combinations of admissible functions capable of satisfying all the boundary conditions. A consistent kinematical procedure permits the aggregation of the various substructures and it ensures compatibility without the need of imposing constraints. The substructure synthesis is characterized by the fact that the mass and stiffness matrices of the model possess the embedding property, which implies that the matrices defining the (n + 1)-order approximation are obtained by simply adding one row and one column to the matrices defining the n-order approximation. As a result, the computed eigenvalues satisfy the inclusion principle, which in turn can be used to demonstrate uniform convergence of the approximate solution. A numerical example illustrates the inclusion principle.