| 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). |
