Free vibration analysis and multi-objective optimization of lattice sandwich beams

Abstract

The free vibration dynamic modellings of sandwich beams with periodic lattice truss cores are established by combining the Bernoulli–Euler beam theory and Timoshenko beam theory, and the fundamental frequency and unit cell mass of lattice sandwich beams are optimized based on the non-dominated sorting genetic algorithm-II (NSGA-II). Firstly, the vibration control equation of lattice sandwich beams is derived using Hamilton’s principle. Then, it is compared and verified by modal experiment and finite element numerical simulation. On this basis, the influence of different truss cores on the structure’s natural frequency is further analyzed. Finally, taking the sheet thickness, core thickness, and radius of the truss as the optimization design variables and taking the structural fundamental frequency maximization and mass minimization as the optimization objectives, the Pareto front is obtained by NSGA-II, and the optimization results are verified by theoretical and numerically. The research results show that the theoretical method in this article can well predict the natural frequencies of sandwich beams with different truss cores. The optimized sandwich structure has higher fundamental frequency with lighter weight, which effectively improves the anti-vibration ability.