Passive energy management in acoustical and dynamical systems

Tempelman, Joshua Robert

Permalink

https://hdl.handle.net/2142/124235 Copy

Description

Title

Passive energy management in acoustical and dynamical systems

Author(s)

Tempelman, Joshua Robert

Issue Date

2024-04-15

Director of Research (if dissertation) or Advisor (if thesis)

• Matlack, Kathryn H
• Vakakis, Alexander F

Doctoral Committee Chair(s)

Matlack, Kathryn H

Committee Member(s)

• Flynn, Eric B
• Tawfick, Sameh H

Department of Study

Mechanical Sci & Engineering

Discipline

Mechanical Engineering

Degree Granting Institution

University of Illinois at Urbana-Champaign

Degree Name

Ph.D.

Degree Level

Dissertation

Keyword(s)

• Targeted Energy Transfer
• Topological Phononics
• Wave Scattering
• Inverse Modeling
• Physics-Informed Machine Learning

Abstract

Managing acoustical and dynamical energy is critical for the safety and sustainability of many engineered systems. Historically, this has been achieved by employing either active or passive control frameworks. Whereas active frameworks require the use of sensors and controllers, passive frameworks utilize intrinsic material or structural properties to manage energy. For this reason, passive energy management is preferred in many applications as it does not require a power source or specialized electronics. To this end, the design of passive energy management mechanisms is typically informed by either an acoustics- or dynamics-based analysis, depending on the application. However, while these two frameworks are intrinsically linked, they are seldom studied in a unified framework. This dissertation aims to bridge this gap by developing passive energy management frameworks at the intersections of wave propagation, periodic materials, and nonlinear dynamics, with focuses on energy confinement, frequency energy scattering, and spatial energy scattering. We first analyze the energy localization enabled by topological band theories from the perspective of linear and nonlinear normal mode theory. We consider a Su-Schrieffer-Heeger (SSH) model with nonlinear couplings and show that the nonlinear normal modes (NNMs) of the truncated (finite) lattice may predict the existence and stability of strongly nonlinear topological interface states. Moreover, we relate the NNM-based predictions to topological band theory by numerically studying the phases of the nonlinear lattice; these predictions are then verified by a computational study. We proceed to analyze the 2D propagation of localized valley-Hall edge waves in a graphene interface lattice. By employing the modal basis of the truncated lattice, we show that the localized 2D propagation may be represented by a relatively low dimensional subset of modes that are isolated from the bulk spectrum, localized at the interface, and possess the necessary phase differences to achieve propagation when superimposed. These results are related to the topological character of the corresponding infinite lattice, and various applications of the modal description are presented. Next, we study the spectral energy scattering induced by non-resonant nonlinearity. By considering a cantilever beam with localized vibro-impact (VI) nonlinearity, we show that rapid low-to-high inter-modal targeted energy transfer (IMTET) is achievable in both experimental and computational frameworks. We then extend the IMTET phenomena to acoustics by considering localized VI unit cells in an otherwise linear phononic lattice. By performing parametric studies and developing a suitable post-processing routine, we show that the VIs may redistribute the energy of transient propagating waves along the lattice’s underlying linear band structure. Moreover, we demonstrate that the propagating energy may be transferred from low-to-high optical bands of the dispersion relation, i.e., inter-band targeted energy transfer (IBTET). Lastly, a reduced order model of a VI unit cell is used to provide physically-informed arguments that relate the observed wave scattering to the NNMs of the reduced order model. Lastly, we consider the resonant spatial energy scattering of elastic waves interacting with localized clusters of oscillators that are attached to a free boundary of an underlying continuum. To introduce frequency-energy tunability of the scattering clusters, we consider nonlinear oscillators and proceed to extend the method of multiple scattering to accommodate the nonlinear forces. To solve the nonlinear problem, a customized harmonic balance procedure, termed self-consistent harmonic balance, is developed to provide the necessary residual expression for resolving periodic solutions. Next, continuation and stability procedures are formulated to recover the nonlinear frequency responses of wave scattering clusters, and to track their corresponding stability proprieties. We then consider the problem of inverse multiple scattering modeling by developing a physics-informed neural network that maps an observed scattering wavefield to a predicted cluster of oscillators. Physics-based loss functions are derived and deployed in the training, and a customized multi-staged hyperparameter optimization scheme is developed to optimize model performance. We demonstrate the effectiveness of the proposed model to design the necessary clusters of scatterers for recreating observed scattering wavefields and emulating synthetic (engineered) wavefields.

Graduation Semester

2024-05

Type of Resource

Thesis

Copyright and License Information

Copyright 2024 by Joshua Robert Tempelman. All rights reserved.

Owning Collections