Design of a local resonator using topology optimization to tailor bandgaps in plate structures

The main aim of this paper is to present a topology optimization method for a local resonator, in order to tailor flexural bandgaps in plate structures. The local resonator is required to be designed systematically in order to tailor the bandgap at the desired frequency range. In previous studies, beam or plate-like resonators were usually used for the design purpose, but the freedom of design is limited particularly when the allowable dimensions are highly limited. Regarding the design issue, this research presents a systematic method using topology optimization to design the local resonator with the maximized bandgap at the target frequency. A plate-like resonator is parameterized to fully exploit the allowable design space of a unit cell. The topology optimization is carried out with the non-gradient based algorithm i.e. simulated annealing (SA). To assist the SA, which requires a large number of function evaluations, two computationally efficient finite element (FE) approaches, namely plate modelling and the reduced Bloch mode expansion, are combined with the topology optimization. In addition, numerical techniques are applied to solve issues arising in the design process (i.e. design disconnection, hinged design, and design redundancy). Numerical examples demonstrate the effectiveness of the presented method for creating bandgaps at frequencies below 500 Hz. The results exhibit increases in vibration isolation up to 20 dB at the designed frequencies.