Dynamic Characterization of Tapered Circular Curved Beams with Honeycomb-Shaped Sections Considering the Impact of Arbitrary Boundary Conditions

This investigation delves into the dynamic behavior of tapered circular curve beams (TCCBs) featuring honeycomb-shaped (HCS) cross-sections. The fundamental motion equations (FMEs) governing TCCB dynamics are established through the application of first-order shear deformation theory (FSDT) and Hamilton’s principle. To solve these FMEs and determine the natural frequencies (NFs), the generalized differential quadrature method (GDQM) is utilized. This simulation examines the effects of multiple factors, such as boundary conditions (BCs), the geometry of honeycomb cells, material characteristics, and thickness distribution patterns, on the NFs of TCCBs. The model incorporates smart composite materials (SCMs) in conjunction with conventional materials to evaluate their effects on dynamic performance. Findings reveal that an increase in honeycomb cell length leads to a reduction in stiffness, thereby decreasing NFs, while a greater honeycomb angle similarly results in lower NFs. Additionally, the incorporation of SCMs with different volumetric content of single-walled carbon nanotubes (SWCNTs) yields higher NFs compared to standard materials, underscoring the superior vibrational characteristics of SCMs. The study also examines the role of boundary springs on NFs, indicating that axial stiffness ([Formula: see text]) does not independently affect NFs but becomes relevant when combined with transverse ([Formula: see text]) and rotational stiffness ([Formula: see text]), resulting in an increase in NFs.