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Dynamics of Quasiperiodic Beams

Paul M. Rady Department of Mechanical Engineering, University of Colorado Boulder, Boulder, CO 80309, USA
Author to whom correspondence should be addressed.
Crystals 2020, 10(12), 1144;
Received: 19 October 2020 / Revised: 25 November 2020 / Accepted: 8 December 2020 / Published: 16 December 2020
(This article belongs to the Special Issue Emerging Trends in Phononic Crystals)
Quasiperiodic metastrucures are characterized by edge localized modes of topological nature, which can be of significant technological interest. We here investigate such topological modes for stiffened and sandwich beams, which can be employed as structural members with inherent vibration localization capabilities. Quasiperiodicity is achieved by altering the geometric properties and material properties of the beams. Specifically, in the stiffened beams, the geometric location of stiffeners is modulated to quasiperiodic patterns, while, in the sandwich beams, the core’s material properties are varied in a step-wise manner to generate such patterns. The families of periodic and quasiperiodic beams for both stiffened and sandwich-type are obtained by varying a projection parameter that governs the location of the center of the stiffener or the alternating core, respectively. The dynamics of stiffened quasiperiodic beams is investigated through 3-D finite element simulations, which leads to the observation of the fractal nature of the bulk spectrum and the illustration of topological edge modes that populate bulk spectral bandgaps. The frequency spectrum is further elucidated by employing polarization factors that distinguish multiple contributing modes. The frequency response of the finite stiffened cantilever beams confirms the presence of modes in the non-trivial bandgaps and further demonstrates that those modes are localized at the free edge. A similar analysis is conducted for the analysis of sandwich composite beams, for which computations rely on a dynamic stiffness matrix approach. This work motivates the use of quasiperiodic beams in the design of stiffened and sandwich structures as structural members in applications where vibration isolation is combined with load-carrying functions. View Full-Text
Keywords: quasiperiodic; stiffened beams; sandwich beams; topology; phononic crystal; dynamics quasiperiodic; stiffened beams; sandwich beams; topology; phononic crystal; dynamics
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MDPI and ACS Style

Gupta, M.; Ruzzene, M. Dynamics of Quasiperiodic Beams. Crystals 2020, 10, 1144.

AMA Style

Gupta M, Ruzzene M. Dynamics of Quasiperiodic Beams. Crystals. 2020; 10(12):1144.

Chicago/Turabian Style

Gupta, Mohit, and Massimo Ruzzene. 2020. "Dynamics of Quasiperiodic Beams" Crystals 10, no. 12: 1144.

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