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This approach uses a flexible fixture in the experimental substructure to improve the modal basis of the substructure; thus, providing a higher quality substructure.
The transmission simulator method avoids the need to measure connection point rotations, facilitates substructuring for systems with continuous connections and enriches the modal basis of the substructure model.
We derive a reduced order model by projecting the governing partial differential equations along the linear modal basis of the Timoshenko beam.
The modal basis of uncoupled-subsystems that can be estimated by the finite element method in the mid-frequency range is used as input data.
The corresponding modal basis of the transmission simulator is described by the fixed-interface modes, rather than free modes that were used in the original approach.
In order to validate these abilities, an experimental modal analysis, considered as the reference, is compared first with a numerical calculation and then with an analytical modeling of the modal basis of the same soundboard.
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By expressing this projection in terms of the modal basis, the number of significant modes in the analysis decreases drastically, and the computational effort is largely reduced.
It is shown that large increases in accuracy can be obtained when the basic dynamics of near-wall coherent structures can be represented using the portion of the modal basis which is free of the subgrid-scale model.
Thus, we propose a new class of preconditioners that exploits the hierarchy of modal basis functions and introduces a flexible order of the off-diagonal Jacobian blocks.
The present work was an attempt to develop a more practical simple "multi-mode theory" based on the linearization of the non-linear algebraic equations, written on the modal basis, in the neighbourhood of each resonance.
In Part I of this series of papers, concerned with geometrically non-linear free and forced vibrations of various beams, a practical simple "multi-mode theory", based on the linearization of the non-linear algebraic equations, written in the modal basis, in the neighbourhood of each resonance has been developed.
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