Design of tunable mechanical filters using folded beams with local resonators: band-gap optimisation under force, mass and energy constraints

This work presents a tunable mechanical filter comprising periodic folded beams with local resonators. An exact dynamic stiffness formulation models wave propagation, internal forces, and the finite-structure response. Unlike designs based solely on the stop bands of the infinite structure or transmissibility of the finite structure, the proposed optimisation includes limits on geometric envelope, total mass, resonator forces, and resonator accelerations. A key advantage is that feasibility is enforced directly during optimisation, rather than assessed only after the attenuation performance has been determined. The procedure maximises attenuation around a prescribed target frequency by varying the folding angle, beam-segment length, resonator mass ratio, and tuning frequency. Results show that these parameters jointly control attenuation while satisfying the imposed geometric and mechanical constraints. The approach enables compact, practically feasible filters whose wave attenuation is improved without excessive demand at the resonator attachments.