Dispersive elastodynamics of 1D banded materials and structures: Design

Abstract

Within periodic materials and structures, wave scattering and dispersion occur across constituent material interfaces leading to a banded frequency response. In an earlier paper, the elastodynamics of one-dimensional periodic materials and finite structures comprising these materials were examined with an emphasis on their frequency-dependent characteristics. In this work, a novel design paradigm is presented whereby periodic unit cells are designed for desired frequency band properties, and with appropriate scaling, these cells are used as building blocks for forming fully periodic or partially periodic structures with related dynamical characteristics.Through this multiscale dispersive design methodology, which is hierarchical and integrated, structures can be devised for effective vibration or shock isolation without needing to employ dissipative damping mechanisms. The speed of energy propagation in a designed structure can also be dictated through synthesis of the unit cells. Case studies are presented to demonstrate the effectiveness of the methodology for several applications. Results are given from sensitivity analyses that indicate a high level of robustness to geometric variation.

Thermal characterization of nanoscale phononic crystals using supercell lattice dynamics

“…PnCs are periodic composite materials that consist of more than one phase (usually at least one phase is a solid and the other(s) are solid, fluid or gas). Numerous applications have been developed for PnCs in the macroscopic regime, e.g., elastic or acoustic waveguiding 8 and focusing, 9 vibration minimization, 10 sound collimation, 11 frequency sensing, 12,13 acoustic cloaking, 14 acoustic rectification 15 and opto-mechanical waves coupling in photonic devices. 16 The realization that phononic crystals can now be sized at the nanoscale to influence atomic-scale phonons is opening up a new direction in nanoscale heat transfer and material design.…”

“…As mentioned earlier, this class of PnCs is finding numerous applications across disciplines. [8][9][10][11][12][13][14][15][16] At the nanoscale, however, atomic-scale phenomena cannot be neglected, and hence the necessity to model the PnC unit cell as a non-scalable supercell that incorporates all the atomic information as mentioned above (Fig. 6(b)).…”

On Optimum Design and Periodicity of Band-Gap Structures

“…The phenomenon may occur for elastic, acoustic or electromagnetic waves, see Refs. [1][2][3][4][5][6]. Except for regions close to the boundaries, a band-gap structure usually consists of a periodic distribution of different elastic materials, or repeated identical segments if a single elastic material is prescribed for the structure.…”

“…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].…”

“…[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]. Comparisons between Floquet theory ( [1]) based unit cell analysis of a band structure and the vibration response analysis of the corresponding finite periodic structure, are presented in [22] for one-dimensional diatomic chains of uncoupled spheres and in [14] for 1D rod structures, respectively.…”