Modal density and modal distribution of bending wave vibration fields in ribbed plates

Abstract

Plates reinforced by ribs or joists are common elements in lightweight building structures, as well as in other engineering structures such as vehicles, ships, and aircraft. These structures, however, are often not well suited for simple structural acoustic prediction models such as statistical energy analysis. One reason is that the modal density is not uniformly distributed due to the spatial periodicity introduced by the ribs. This phenomenon is investigated in the present paper, using a modal model of a ribbed plate. The modal model uses the Fourier sine modes, and the coupling between the plate and ribs is incorporated using Hamilton's principle. This model is then used to investigate the modal density of the considered spatially periodic structure, and a grouping of the modes in different dominating directions is proposed. Suggestions are also given regarding how to proceed towards a simplified prediction model for ribbed plates.

Energy transfer in a beam-framed structure using a modal method and a wave method at mid frequencies

“…The generalised mass matrix of the coupled structure is found, in a similar way to Section 2.2 and also given in [7], to be …”

“…It becomes non-uniform for large number with its main lobe perpendicular to the strip. Dickow et al [7] used a modal model to investigate a spatially periodic ribbed plate. A rectangular plate stiffened by several beams was assumed in the pinned conditions along all four edges.…”

Recent advances in building acoustics: An overview of prediction methods and their applications

“…Davy [120] produced a method for predicting structure-borne sound transmissions across an air cavity via line and rigid point connections theoretically. Dickow et al [121] noted that the classical SEA method was not appropriate in conducting structural acoustic prediction of rib-stiffened plates.…”

Estimating the performance of heavy impact sound insulation using empirical approaches

“…For floor types in which the walking surface covers the entire base via resilient layers, the insulation performance is considerably influenced by the mass of the walking surface and the dynamic stiffness of the resilient material (Gerretsen 1999;Schiavi, Belli, and Russo 2005;e Sousa and Gibbs 2014;Schiavi et al 2007;e Sousa and Gibbs 2011). However, for other floor types, the estimation accuracy is poor for practical applications, even when more factors are considered (e.g., the quasi-longitudinal phase velocity, loss factor, or surface area of the subsystem) (Vér 1971;Stewart and Craik 2000;Hopkins 2014;Dickow, Brunskog, and Ohlrich 2013).…”