Triangular lattice metamaterials in curved beam structures: Free vibration analysis with strain gradient beam models

The current study investigates the free vibration behavior of curved beams made of triangular lattice metamaterials. The focus of the study is in simplifying the standard computational analysis by a novel approach of modeling curved lattice structures as homogenized Euler–Bernoulli and Timoshenko beams within the strain gradient theory, to incorporate size effects possessed by lattice structures. The governing equations of the strain gradient beam models are derived through variational methods, and solutions are obtained by using the differential quadrature method. Detailed finite element analyses are adopted for validation. The study examines the effects of thickness, lattice size, center angle and boundary conditions on stiffness and vibration characteristics, demonstrating that the strain gradient beam models provide accurate results unlike the corresponding classical beam models. The findings on the mechanical behavior and modeling approach have practical applications in industries such as aerospace and automotive manufacturing, where lightweight and stiff structures are critical for performance adaptation and optimization. • The stiffness of curved beams is significantly influenced by boundary conditions and center angle. • Incorporates size effects using strain gradient theory for accurate modeling. • Compares classical and strain gradient theories with finite element model for curved beams made of triangular lattices. • Investigation of thickness and lattice cell size effects on beam stiffness with constant relative density. • Effective material properties are defined for lattice homogenization.