Acoustic scattering from an infinitely long cylindrical shell with periodic internal lengthwise ribs

The acoustic scattering from 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. A circumferential mode expansion is used to obtain numerical results for the scattering sound field. The backscattering characteristics in the far-field can be explained by the resonance and interference phenomena. It is shown that subsonic flexural waves can be generated and radiated by the ribs. Due to the periodical distribution of the ribs, there exist multi-order flexural Bloch waves in the circumferential direction. The multi-order flexural Bloch waves can form standing circumferential waves, which lead to a complex acoustic resonance. The attachments of the ribs to the shell can reflect an acoustic wave directly and the reflected wave will interfere with the specular reflection, which is dominant in the frequency-angle spectra with an increasing number of ribs. Furthermore, the flexural wave and flexural Bloch waves can radiate through the attachments and interfere with the specular reflection. However, the interference fringes in the frequency-angle spectra caused by the flexural wave and flexural Bloch waves are coincident at broadside.