Maximizing band gaps of single-phase phononic plates: Isogeometric optimal approach and 3D printing experimental validation.

• We present an effective isogeometric shape optimization method to optimize phononic band gaps of periodic plates. • The particle swarm optimization is employed to solve the constrained dynamic maximization problem. • The thickness, i.e., z-component of control point of B-spline surface is defined as optimal design variable. • Several numerical examples for finding optimal phononic band gaps of periodic plates are studied. This work presents an effective isogeometric shape optimization approach for finding and widening the phononic band gaps of single-phase Mindlin plate structures. As the single-phase material phononic plate is easy to be manufactured by additive manufacturing, it has been investigated here by optimized its thickness profile to find and widen the band gaps. The proposed method utilizes a coarse B-spline surface to model the thickness profile of periodic plate and a fine B-spline surface to model the mid-surface of plate structure for simulation. The optimal design variables are the thickness variables, i.e., the z-components of the control points of the coarse B-spline surface. To avoid specifying the initial control point locations manually, the constrained dynamic maximization problem is solved by a particle swarm optimization (PSO) algorithm here. Various numerical examples demonstrate the effectiveness and reliability of the proposed method in finding optimal phononic band gaps of periodic plates. And the numerical results show that there is no band gap for h max = 3 h min , and the band gaps can be found and widen for h max ≥ 5 h min. The obtained band range is 638.9–823.6 Hz with a decreased central frequency of 731.25 Hz for h max = 5 h min and the width and the number of band gaps are increased as the maximum allowable thickness increases. Finally, one optimized design is fabricated through additive manufacturing, and the experimental frequency response is consistent with the results based on isogeometric analysis. [ABSTRACT FROM AUTHOR]