This research is devoted to the free vibrational analysis of a truncated conical three-layered sandwich shell with a rheological core and functionally graded (FG) porous face sheets. The rheological core can be either electrorheological elastomer (ERF) or magnetorheological fluid (MRF). The mathematical modeling of the layers of the shell is performed based on the first-order shear deformation theory (FSDT) by including the continuity conditions between the core and two face sheets. Three different porosity distribution patterns are investigated including a uniform one and two FG non-uniform ones. The porosity parameters of these distribution patterns are adjusted to result in the same mass (weight) for all patterns. The governing equations and associated boundary conditions are attained through Hamilton’s principle and are solved via a semi-analytical solution to determine the natural frequencies of the shell and corresponding loss factors. This semi-analytical solution includes an exact solution in the circumferential direction followed by an approximate solution in the meridional direction via the differential quadrature method (DQM). The effects of several parameters on the natural frequencies and loss factors are examined such as intensity of the magnetic and electric fields, thickness of the rheological core, distribution pattern and porosity parameter of the FG porous face sheets, and the boundary conditions. Numerical results show that the sandwich shell with ERF core benefits from higher natural frequencies rather than the sandwich shell with MRF core. But, the sandwich shell with MRF core benefits from higher loss factors rather than the sandwich shell with ERF core. پرونده مقاله