Spectral investigation of spatial scales associated with substructures on a fluid-loaded plate

Abstract

A wave-number-based formulation of the surface variational principle is used to investigate the effects of substructures on fluid-loaded systems. The paper examines issues of scale associated with the spatial distribution and representation of substructure attachments. The primary emphasis is suspended discrete spring-mass systems. A further extension considers an elastic beam attached at multiple locations. The main structure is a simply supported plate of infinite width contained in an infinite baffle and exposed to water on one side. Scales are introduced to the formulation by using a spectral Fourier series to represent point attachments. Previous work had considered the case where line masses are fastened to the plate. The concept that evolved entailed comparing the displacement and surface pressure obtained from analyses whose only difference is the number of terms in the spectral series used to represent the attached masses. The difference between such analyses is an indicator of the significance of the scales associated with the additional terms in the series. The work reported here increases the complexity of the system by allowing for the masses to be flexibly attached to the plate. This generalized problem is comparable to the types of systems considered to form fuzzy structures. However, the viewpoint here is deterministic. Results to be presented examine the influence of the scales associated with substructure attachments when the parameters of the suspended substructures have a range of values.