Tunable dispersion and energy harvesting characteristics in nonlinear periodic structures

Bhattacharyya, Aneesh (2026) Tunable dispersion and energy harvesting characteristics in nonlinear periodic structures. PhD thesis, University of Glasgow.

Abstract

This Thesis investigates tunable bandgap behavior and energy harvesting characteristics in nonlinear periodic structures, motivated by the need for passive wave-control strategies that remain effective when disturbances are transient, spatially distributed, and amplitude dependent. Whereas classical periodic structures and conventional resonant harvesters offer limited tunability and typically rely on fixed band structures or sustained external excitation, the work pursued here shows that geometric and magnetic bi-stability, inertereffects, and electromechanical coupling can be used to reshape dispersion, attenuation, and energy-transfer mechanisms in a systematic manner. The thesis therefore develops a unified research arc that connects nonlinear wave propagation with practical energy conversion, moving from bandgap engineering in strongly nonlinear lattices to broadband and spatially localized harvesting from free waves generated solely by initial conditions.
The first part of the Thesis (Chapter 3) focuses on tunable dispersion characteristics in a bi-stable periodic chain with coupled horizontal-vertical dynamics and stable negativeinerter mechanism. A new semi-analytical framework, ALIGN, is developed to bridge weakly and strongly nonlinear regimes through asymptotic analysis, multi-harmonic harmonic balance, robust branch tracking, and amplitude-locked inverse time-domain validation. This framework enables the computation and verification of amplitude-dependent Bloch dispersion in systems with non-polynomial geometric nonlinearities, while also identifying well-defined mass-ratio thresholds, branch-merging behavior, and systematic routes for bandgap manipulation. In this sense, the work demonstrates that combining bistability with appropriately chosen inertial coupling produces a richer and more tunable wave environment than classical linear periodic chains or simpler nonlinear lattices and simultaneously enables the exploitation of inexpensive analytical/semi-analytical models to capture this environment adequately without relying solely on computationally heavy numerical simulations.
The second part of the Thesis (Chapter 4, Chapter 5) exploits these wave phenomena for energy harvesting in periodic piezoelectric and piezomagnetoelastic chains under free or unforced propagation. First, a linear piezoelectric baseline is established in which Bloch-reduced electromechanical dynamics is combined with the concept of settling time to define and optimize the maximum steady-state harvested power under unforced transient motion. This idea is then extended to inertially coupled nonlinear piezomagnetoelastic chains, where magnetic bi-stability is shown to transform a sharply tuned linear optimum into a broad quasi-saturated band of near-optimal intrawell performance, while interwell dynamics is shown to give rise to spatially localized harvesting through slowly modulated ϕ4-type transition fronts rather than exact conservative solitons. The final work (Chapter 6) then introduces mass-diatomicity in the nonlinear piezomagnetoelastic chain, where richer branch and bandgap behavior in the large-amplitude nonlinear regime intrinsically gives rise to almost 102 times higher harvesting performance favoring shorter wavelength components of the transient free wave.
Taken together, the results establish a physically realizable and analytically informed design framework for multifunctional nonlinear metamaterials that can simultaneously tailor bandgaps, guide and attenuate waves, and harvest useful energy from transient disturbances relevant to self-powered sensing and vibration-control applications.

• Item Type: Thesis (PhD)
• Qualification Level: Doctoral
• Additional Information: Supported by a Ph.D. scholarship from the James Watt School of Engineering, University of Glasgow.
• Subjects: T Technology > TA Engineering (General). Civil engineering (General)
• Colleges/Schools: College of Science and Engineering > School of Engineering
• Funder's Name: James Watt School of Engineering, University of Glasgow
• Supervisor's Name: Adhikari, Professor Sondipon
• Date of Award: 2026
• Depositing User: Theses Team
• Unique ID: glathesis:2026-86321
• Copyright: Copyright of this thesis is held by the author.
• Date Deposited: 09 Nov 2026 14:23
• Last Modified: 09 Nov 2026 14:27
• Thesis DOI: 10.5525/gla.thesis.86321
• URI: https://theses.gla.ac.uk/id/eprint/86321

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