Influence of Thermal Environment on the Parametric Instability of a Sinusoidally Tapered Rotating Sandwich Beam

Abstract

This study investigates the dynamic stability of rotating sandwich beams featuring a sinusoidal taper profile under combined periodic axial loading and thermal gradients. Using the extended Hamilton's principle, we derive the governing equations that account for shear deformation, rotary inertia, and the unique stiffness distribution created by the sinusoidal thickness variation. The resulting equations are transformed into non-dimensional form and solved using the extended Galerkin method, with parametric instability regions identified through the Saito-Otomi criteria. Our analysis reveals that the amplitude and phase characteristics of the sinusoidal taper significantly influence the stability boundaries, with optimal tapering parameters demonstrating improved vibration suppression compared to traditional uniform, parabolic and linear profiles. The results demonstrate complex interactions between rotational effects, thermal gradient, shear parameter, core-loss factor and taper geometry, showing that moderate sinusoidal tapering combined with high rotational speeds can substantially enhance stability, while thermal gradients tend to reduce the stable operating regions. These findings provide valuable insights for the design of advanced rotating structures in aerospace and energy applications where dynamic stability and weight optimization are critical.