Geometry induced strain energy localization and symbolic regression for multiphysics design of kinked composite beams

Kinked geometries are common in lightweight aerospace structures, deployable robotic architectures, and composite assemblies, yet they are typically treated as geometric discontinuities that reduce stiffness or perturb vibration characteristics. Their influence on modal strain-energy distribution and vibration response has received comparatively little attention. This work systematically investigates the free-vibration behaviour of cantilevered kinked beams fabricated from monolithic aluminum and particle-reinforced composites (Al–TiC and Al–SiC) using Timoshenko beam theory. A finite-element formulation incorporating reduced-order viscoelastic damping is developed to examine the influence of kink angle (0°–180°) and normalized kink position on spectral characteristics and strain-energy distribution. The results reveal pronounced non-monotonic frequency evolution, strong mode veering, and substantial redistribution of modal strain energy. As the kink angle increases into the obtuse regime, the kink vertex transitions from a passive geometric junction into an active energy-localization region, producing significant concentration of modal strain energy and higher predicted effective damping. Mesh-convergence studies and validation against the analytical straight-beam solution demonstrate excellent agreement, with a fundamental frequency error of only 0.0077%. To facilitate rapid design-space exploration, symbolic regression is employed to derive compact surrogate equations for the strain-energy localization index and effective damping, achieving close agreement with finite-element predictions within the investigated parameter range. Within the investigated numerical framework, the results indicate that kink geometry can serve as an effective topology-based design parameter for controlling frequency response, modal interaction, strain-energy localization, and damping performance in composite beam systems. These findings provide new insight into the relationship between structural topology and multiphysics behaviour in kinked composite structures.