<![CDATA[General background: Torsional oscillations in cylindrical elastic structures filled with viscous fluids are critical in engineering applications such as pipelines, viscoelastic dampers, and rotating machinery. Specific background: Prior studies have focused on uniform-thickness cylinders and compressible fluids, often neglecting realistic variations in layer geometry and their dynamic implications. Knowledge gap: The effect of spatially variable thickness in cylindrical shells on torsional vibration behavior with an enclosed incompressible viscous fluid remains underexplored. Aims: This study aims to mathematically model and analyze torsional oscillations in an elastic cylindrical layer of increasing thickness filled with a viscous incompressible fluid. Results: By employing modified Bessel functions and scalar-vector potentials in cylindrical coordinates, the study reveals that increased wall thickness significantly reduces the system’s natural torsional frequencies. Novelty: The research introduces a coupled solid-fluid framework that integrates radial and axial thickness variations and simplifies high-order equations into engineering-relevant forms using zero and first harmonic approximations. Implications: These findings offer valuable insights into the dynamic behavior of fluid-filled cylindrical systems and support the development of more resilient, vibration-controlled mechanical structures in aerospace, marine, and industrial designs.Highlight : Layer Thickness Effect: Increasing the thickness of the cylindrical shell significantly lowers the natural torsional frequency. Mathematical Modeling: The system is modeled using modified Bessel functions and scalar/vector potentials under cylindrical coordinates. Engineering Relevance: The results help in designing stable and vibration-resistant systems like dampers, pipelines, and aerospace structures. Keywords : Torsional, Oscillations, Cylindrical, Viscous, Fluid]]>
