Abstract
Band-gap structures can prevent the propagation of waves occupying certain frequency ranges, or bands. Phononic band-gap structures that prevent certain acoustic and elastic waves from propagating have received a great deal of attention, and have great potential in engineering applications, as it is hoped that they can be utilized as 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. Furthermore, several numerical examples confirm the validity and utility of the proposed method. Nomenclature A = cross-sectional area of the frame element AD = area of the fixed and extended design domain Amax = maximum cross-sectional area of the frame element C, Ce = global damping matrix and element damping matrix D = fixed and extended design domain D = elasticity matrix
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