Multiobjective evolutionary optimization of periodic layered materials for desired wave dispersion characteristics

Abstract

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.

On Optimum Design and Periodicity of Band-Gap Structures

“…Analogously, for R=1, i.e., j = s = k = n -1, Eqs. (9) and (10) verify that the lower eigenfrequency of the gap corresponds to the simple eigenvalue 2 1 1 n n λ ω − − = . These observations have the important implication that the computational procedure delineated in the sequential sub-section is applicable independently of whether the upper and/or lower eigenfrequencies that define the gap, are members of a multiple eigenfrequency or are just a simple eigenfrequency.…”

“…Due to a wealth of potential applications in vibration protection, noise isolation, waveguiding, etc., the study and development of bandgap rod, mass-spring, beam, grillage, disk and plate structures, in most cases by topology optimization, have attracted increasing attention in recent years, see e.g. [5,[7][8][9][10][11][12][13][14][15][16][17][18]. Elastodynamics of finite or infinite periodic 1D rod or beam structures has been studied in [6,[19][20][21].…”

Dispersive elastodynamics of 1D banded materials and structures: Design

“…The multiscale dispersive design (MDD) methodology utilizes the facts that (i) varying the configuration of the unit cell of a periodic material allows one to control the frequency band structure, i.e., the size and location of stop and pass bands [2][3][4]16,18,20,24], and (ii) with a few cells stacked adjacent to each other, the dispersive dynamic behavior in a structure qualitatively matches that of the constituent periodic material [16][17]. The methodology stipulates that the topology of a periodic composite material, or more than one composite material, is synthesized, and with appropriate scaling these designed materials are used to form a bounded structure with frequency-banded dynamical characteristics that correlate with those of the materials.…”

“…[24]). When l is large, advanced gradient-based or heuristic techniques (such as genetic algorithms) should be utilized for solving Eqs.…”

Wave Based Design Optimisation of Composite Structures Operating in Dynamic Environments

“…With regard to optimising the design characteristics of a layered structure the developed approaches have generally focused on genetic algorithms or particle swarm type techniques [28,29,30]. When it comes to optimising the structural design vis-a-vis the dynamic response performance of a structure, wave based optimisation techniques have been developed [31,32,33,34] by adopting Periodic Structure Theory (PST) assumptions.…”