Application of Electrorheological Fluid Cores to Improve the Vibration Response of Sandwich Toroidal Shell Elements Covered by Functionally Graded Nanocomposite Faces

This study aims to investigate the dynamic behavior and damping characteristics of sandwich toroidal shell segments featuring an electrorheological fluid (ERF) core and functionally graded graphene platelet reinforced composite (FG-GPLRC) laminated face layers. The primary objective is to explore the potential of this unique material combination in achieving tunable dynamic responses for advanced engineering applications, particularly in active vibration control and energy dissipation. The ERF core is modeled using a Kelvin–Voigt viscoelastic constitutive law to account for its electric field-dependent behavior, enabling the modification of system frequencies and loss factors by varying the applied electric field. The FG-GPLRC face layers incorporate a uniform random distribution of graphene platelets (GPLs), and their homogenized properties are determined using the Halpin–Tsai micromechanical approach. Five different FG models are considered to optimize the system’s performance. The governing dynamic equations are formulated based on the first-order sandwich theory and Donnell kinematic assumptions, utilizing Hamilton’s principle. A semi-analytical solution methodology combining trigonometric expansion (TE) and generalized differential quadrature (GDQ) methods is employed, ensuring high accuracy, rapid convergence, and computational efficiency. Comprehensive validation is conducted by comparing the proposed model with existing simplified analyses in the literature. Through extensive parametric studies, the interplay between material properties and dynamic performance is examined in detail, offering valuable insights for designing and optimizing sandwich toroidal shell segments with tunable dynamic responses.