An important dispersion-related characteristic of wave propagation through periodic materials is the existence of frequency bands. A medium effectively attenuates all incident waves within stopbands and allows propagation within passbands. The widths and locations of these bands in the frequency domain depend on the layout of contrasting materials and the ratio of their properties. Using a multiobjective genetic algorithm, the topologies of one-dimensional periodic unit cells are designed for target frequency band structures characterizing longitudinal wave motion. The decision variables are the number of layers in the unit cell and the thickness of each layer. Binary and mixed formulations are developed for the treatment of the optimization problems. Designs are generated for the following novel objectives: (1) maximum attenuation of time harmonic waves, (2) maximum isolation of general broadband pulses, and (3) filtering signals at predetermined frequency windows. The saturation of performance with the number of unit-cell layers is shown for the first two cases. In the filtering application, the trade-off between the simultaneous realization of passband and stopband targets is analyzed. It is shown that it is more difficult to design for passbands than it is to design for stopbands. The design approach presented has potential use in the development of vibration and shock isolation structures, sound isolation pads/partitions, and multiple band frequency filters, among other applications.

With growing interest in recovering materials and subassemblies within consumer products at the end of their useful life, there has been an increasing interest in developing decision-making methodologies that determine how to maximize the environmental benefits of end-of-life (EOL) processing while minimizing costs under variable EOL situations. This paper describes a methodology to analyze how product designs and situational variables impact the Pareto set of optimal EOL strategies with the greatest environmental benefit for a given economic cost or profit. Since the determination of this Pareto set via enumeration of all disassembly sequences and EOL fates is prohibitively time-consuming even for relatively simple products, multi-objective genetic algorithms (GA) are utilized to rapidly approximate the Pareto set of optimal EOL trade-offs between cost and environmentally conscious actions. Such rapid calculations of the Pareto set are critical to better understand the influence of situational variables on how disassembly and recycling decisions change under different EOL scenarios (e.g., undervariable regulatory, infrastructure, or market situations). To illustrate the methodology, a case study involving the EOL treatment of a coffee maker is described. Impacts of situational variables on trade-offs between recovered energy and cost in Aachen, Germany, and in Ann Arbor, MI, are elucidated, and a means of presenting the results in the form of a multi-situational EOL strategy graph is described. The impact of the European Union Directive regarding Waste Electric and Electronic Equipment (WEEE) on EOL trade-offs between energy recovery and cost was also considered for both locations.

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The spatial distribution of material phases within a periodic composite can be engineered to produce band gaps in its frequency spectrum. Applications for such composite materials include vibration and sound isolation. Previous research focused on utilizing topology optimization techniques to design two-dimensional (2D) periodic materials with a maximized band gap around a particular frequency or between two particular dispersion branches. While sizable band gaps can be realized, the possibility remains that the frequency bandwidth of the load that is to be isolated might exceed the size of the band gap. In this paper, genetic algorithms are used to design squared bi-material unit cells with a maximized sum of band-gap widths, with or without normalization relative to the central frequency of each band gap, over a prescribed total frequency range of interest. The optimized unit cells therefore exhibit broadband frequency isolation characteristics. The effects of the ratios of contrasting material properties are also studied. The designed cells are subsequently used, with varying levels of material damping, to form a finite vibration isolation structure, which is subjected to broadband loading conditions. Excellent isolation properties of the synthesized material are demonstrated for this structure.

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