The frequency window improvement of component modal synthesis techniques

The analytical procedure referred to as the Frequency Window (FW) improvement is applied to the component modal synthesis (CMS) in both time and frequency domains. Essentially this is a way of reducing the amount of coordinates in a CMS structural vibrations problem while still retaining much mathematical detail inherent to a larger problem when solving for modal properties and modal dynamic response.; Beginning with a popular variant of modal synthesis, the specific forms of the frequency window equations are provided, together with guidelines for applying the procedure to a comparably-sized eigenproblem for the purpose of improved modal properties. Closed form expressions are derived for the eigenvalue, eigenvector, and frequency-response function error that would arise from the FW method as compared to that coming from a full-order application of the modal synthesis without FW. Proofs for why the method works, suggestions for programming, and schemes for further improving the FW implementation are also given.; The FW appears to be particularly well-suited when applied to a modified version of a frequency-domain technique used by an aerospace organization for the structural dynamic analysis of spacecraft/launch vehicle combinations. Examples are furnished that will illustrate the beneficial modifications to the frequency-domain technique that complements as well as includes the equations coming from Frequency Windowing. The results indicate that the Frequency Window is a practical, effective manner of obtaining improved modal properties and dynamic response that verges upon those solutions from full-order “exact” benchmarks and yet requires no greater computational effort than that which is used in a fundamental problem (where the amount of freedoms has been greatly reduced).