No 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.

A companion paper [J. Acoust. Soc. Am. 118, 3010–3020 2005] has examined the phenomena of flexural-longitudinal wave coupling in a practically undamped and semi-infinite periodic waveguide with structural side-branches. The effect of structural damping on wave coupling in such a waveguide is examined in the first part of the present paper, and the damping-dependent decrease in wave coupling is revealed for a structure with multiresonant side-branches. In the second part, the simplifying semi-infinite assumption is relaxed and general expressions for the junction responses of finite and multicoupled periodic systems are derived as a generalization of the governing expressions for finite, mono-coupled periodic systems [Ohlrich, J. Sound Vib. 107, 411–434 (1986)]. The present derivation of the general frequency response of a finite system utilizes the eigenvectors of displacement responses and wave forces that are associated with the characteristic wave-types, which can exist in a multicoupled periodic system [Mead, J. Sound Vib. 40, 19–39 (1975)]. The third part of the paper considers a finite specific test-structure with eight periodic elements and with structural terminations at the extreme ends. Audio-frequency vibration responses of this tri-coupled periodic structure are predicted numerically over a broad range of frequencies and a very good agreement is found with the measurement results obtained from an experiment with a nominally identical, periodic test-structure which is freely suspended.