Vibration of cylindrical shells with embedded annular acoustic black holes using the Rayleigh-Ritz method with Gaussian basis functions

The numerical simulation of beams and plates with embedded acoustic black holes (ABHs) is computationally demanding because the very thin thickness attained at ABH central area. Semi-analytical approaches relying on Rayleigh-Ritz method wavelet or Gaussian basis functions have thus revealed as an accurate fast alternative to determine vibration field in parametric studies. To date however, vast majority works ABHs only dealt indentations straight flat plates. It would be also worth exploring feasibility control vibrations curved shells, typically found aerospace naval structures. In this work, we address issue extend expansion (GEM) characterize annular cylindrical shells. First, show how GEM can modified make shape satisfy periodic boundary conditions circumferential direction cylinder. then used shell gets validated by comparison finite element simulations. A thorough analysis performance follows, which stresses differences behavior surfaces. particular, influence that waves propagating operational frequency range ABH. effects viscoelastic layer inclusion longitudinal stiffeners strengthen cylinder rigidity are analyzed means proposed approach. This work broadens previous semi-analytical methods start investigating effect