Subharmonic and superharmonic resonances of five-layered porous functionally graded sandwich cylindrical shells with two-layered viscoelastic cores

In this research, the subharmonic (SUBH) and superharmonic (SUPH) resonances of five-layered porous functionally graded sandwich (PFGS) cylindrical shells with two-layered viscoelastic cores (VECs) are investigated. The sandwich cylindrical shell is composed of three porous functionally graded (PFG) face layers and two VECs. The VECs are made of Kelvin–Voigt type material. The material properties of the PFG face layers are considered as continuous through the thickness of each face regarding a porosity coefficient and a volume fraction index. Two types of five-layered PFGS cylindrical shells with two-layered VESs, including porosity evenly distributed (Type 1) and porosity unevenly distributed (Type 2) along the thickness direction, are considered in this research. Based on the Donnell shell theory, von-Kármán equation, and Hooke’s law, the stress-strain relations are developed for the five-layered PFGS cylindrical shells. The discretized governing equation via Galerkin’s method is also derived. With the governing equations proposed and the method of multiple scales, the SUBH and SUPH resonances of the shells are investigated systematically. The influences of geometrical, and material parameters on the SUBH and SUPH resonances of the system are studied and presented. New results for SUBH and SUPH resonances of the five-layered PFGS cylindrical shells with two-layered VECs are provided for the first time and can be utilized as a benchmark for researchers and engineers in this area.