Vibroacoustic behavior of an infinitely long cylindrical shell with periodic internal lengthwise ribs

Abstract

The vibroacoustic behavior of an infinitely long cylindrical shell with periodic lengthwise ribs is studied. The shell motion is described by the Donnell equations, and the lengthwise rib is modeled as an elastic beam whose motion is decomposed into longitudinal and flexural vibrations. Analytical expressions are obtained for the shell motion via a circumferential mode expansion based on the periodicity in the circumferential direction and the Fourier transform in the longitudinal direction. Furthermore, the far-field radiated pressure is obtained via the stationary-phase approach. The shell vibration and sound radiation are analyzed using discrete circumferential wavenumbers. Multi-order flexural Bloch waves exist in the circumferential direction when the cylindrical shell is equipped with periodic lengthwise ribs. The supersonic components of the flexural Bloch waves radiate efficiently and lead to acoustic radiation resonances in the far field.

Reduction of Bloch-Floquet bending waves via annular acoustic black holes in periodically supported cylindrical shell structures

“…Exact-closed solutions were proposed therein for some periodically ribbed cylindrical shells with various stiffener geometries, and the frequency passbands and stopbands of the structures were determined. Following the steps in [12], more recent works on the topic have basically addressed the computation of noise radiation by periodic cylindrical shells under different types of excitations (see e.g., [13][14][15][16][17]), yet such issue will be out of the scope of this paper.…”

Noise radiated from a periodically stiffened cylindrical shell excited by a turbulent boundary layer

“…The vibration of an infinitely long cylindrical shell with internal periodic lengthwise ribs was analytically formulated by Tong et al [15]. The lengthwise rib was modeled as an elastic beam with longitudinal and flexural motions.…”