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Vibration Transmission of a Cylindrical Shell with an Interior Rectangular Plate with the Receptance Method

DOI: 10.1155/2012/581769

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Vibration transmission characteristics of a cylindrical shell with a rectangular plate are discussed in this paper by the substructure receptance method. The system is divided into two substructures: the plate and the shell. After finding the theoretical receptance function of each substructure, the coupling equation of the combined system is solved by considering the continuity conditions at the joint between the plate and the shell. The numerical results are compared with the experimental ones to show the validity of the formulation. After that, effects of the plate's parameters on vibration transmission characteristics are discussed. The parameter study shows that it is important to avoid impedance matching for the plate and the shell in the design of suitable structures with low vibration and noise radiation characteristics. 1. Introduction Plates and shells are widely used as basic components in many engineering structures, such as aircrafts [1] and underwater structures [2]. Until now, their fundamental physical mechanisms and phenomenons, such as free vibration [3], wave propagation [4, 5], and power flow [6], have been discussed intensely. Plates and shells are often utilized by coupling together with welds, bolts, or dampers in practical applications. Dynamic behaviors of these coupled structures become relatively complicated due to vibration energy transmission between the interior plate and the shell. Less literature is available on these topics. However, as vibration transferred from the plate to the shell would result in the shell’s outward noise radiation; it is of great importance for engineers to understand these combined structures’ vibration, especially the effects of parameters on the combinations’ dynamic behaviors, which is helpful for designing suitable structures with low vibration and noise radiation. Forced vibration of one variant of these combined structures, a partitioned cylindrical shell with a longitudinal, interior rectangular plate, has been investigated in this paper to simulate an aircraft fuselage with an interior floor. Vibroacoustic characteristics of a cylindrical shell with an interior rectangular plate have been studied in several papers, which mainly focused on free vibration analysis. The first analytical model was developed by Peterson and Boyd [7] with applications of Rayleigh-Ritz technique. Effects of structural parameters, including rigid joint, hinged joint, thickness and position of the floor on natural frequencies and mode shapes were analyzed. Irie et al. [8] studied free vibration of noncircular

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