Co-Optimized Geometry and Material for Antiresonance Tuning in Thermally Loaded FG Curved Beams: Achieving Vibration Suppression with High Static Stiffness

Thermal loading alters temperature-dependent properties of functionally graded (FG) structures and, even under uniform temperature, induces non-uniform deformation via graded thermal expansion coefficients, modifying geometry. These coupled alterations jointly govern the structures' static and dynamic responses. This paper investigates the effects of material gradient and structural geometry on the static and dynamic responses of three FG curved beam types under thermal environments, with particular emphasis on the distinct behaviors between constant-curvature and variable-curvature beams. Governing equations for bending and vibration are derived using thin curved beam theory and solved via the Chebyshev spectral method. Results reveal that the height-To-span ratio significantly influences static stiffness, exhibiting an initial increase followed by a decrease. Crucially, thermal loads are found to selectively shift antiresonance frequencies while leaving resonant frequencies almost unchanged. These insights enable targeted vibration suppression through material-structure co-design by tuning antiresonance frequencies in desired frequency bands. We further develop a PSO-based co-optimization framework for material-structure co-design of FG curved beams. Validation through two engineering design cases demonstrates: (1) a circular FG curved beam suppresses > 92% of low-frequency vibration at 26Hz, and (2) a cosine FG curved beam uniquely enables dual-frequency suppression (400/600Hz) with 39.46kN/m stiffness.