Structural optimization for the design of band-gap structures using discrete structural elements

Band-gap structures can inhibit the propagation of waves in certain frequency ranges, or bands. Phononic band-gap structures that inhibit certain acoustic and elastic waves from propagating have received a great deal of attention recently, and have great potential in engineering applications, as it is hoped that they can be utilized as sound or vibration protection devices, acoustic lasers, acoustic mirrors, frequency filters and waveguides in mechanical structures and MEMS. This paper presents a new structural optimization method for the design of more generic and extendible phononic band-gap structures using discrete structural elements, based on topology optimization techniques. The use of a variety of discrete structural elements has the advantage of enabling the design of higher performance or more sophisticated structures. In addition, in this research, a new objective function is proposed that enables several bands to be simultaneously considered as optimization targets, in contrast to the objective function typically employed in existing design methods for phononic bandgap structures that considers only a single band where attenuation is desired. Using this new objective function, structures incorporating band-gap effects across multiple eigen-frequency bands can be created. The resulting optimal configurations have the potential to dramatically reduce the propagation of waves in specified frequency ranges. Furthermore, several numerical examples confirm the validity and utility of the proposed method.