{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/117569"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/117569","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Controlling radial waves through effective periodicity","abstract":"Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2024-12-01","abstract_html":"Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2024-12-01","abstract_has_math":false,"creators":["Arretche, Ignacio"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mechanical Engineering","degree_department":null,"school":null,"contributors":["Matlack, Kathryn H","Vakakis, Alexander F","Elbanna, Ahmed","Tawfick, Sameh H"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2022,"date_issued":"2022-12","date_published":"2022-12","updated_at":"2026-07-22T22:24:56Z","subjects":["Metamaterials","Phononic Crystals","Radial Waves","Wave Propagation","Rotor Dynamics"],"languages":["en","eng"],"rights":["Copyright 2022 Ignacio Arretche"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/2142/117569","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Matlack, Kathryn H","Vakakis, Alexander F","Elbanna, Ahmed","Tawfick, Sameh H"]},{"key":"dc:creator","label":"Author","values":["Arretche, Ignacio"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2022-12","2022-11-29"]},{"key":"dc:type","label":"Dc Type","values":["text","Thesis"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mechanical Engineering"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Metamaterials","Phononic Crystals","Radial Waves","Wave Propagation","Rotor Dynamics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en","eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2022 Ignacio Arretche"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://hdl.handle.net/2142/117569"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2024-12-01","The student, Ignacio Arretche, accepted the attached license on 2022-11-23 at 10:45.","The student, Ignacio Arretche, submitted this Dissertation for approval on 2022-11-23 at 15:01.","This Dissertation was approved for publication on 2022-11-29 at 14:57.","DSpace SAF Submission Ingestion Package generated from Vireo submission #18627 on 2023-04-12 at 11:35:16","Phononic crystals (PCs) and acoustic metamaterials (AMs) show unprecedented wave propagation phenomena such as band gas, negative refraction, and topologically protected states. Most PCs and AMs are built and designed under plane wave assumptions because a plane wave propagating through a periodic medium is described by equations of motion that have periodic coefficients. This enables the use of the Bloch theorem and the study of the infinite system can be reduced to that of a single unit cell. However, this is not the case for radial waves. In this case, a material that is invariant to radial translations does not result in periodic equations of motion, and the Bloch theorem cannot be applied. Therefore, to obtain the already-developed properties of PCs and AMs in radial waves we must find alternative approaches. It is the overarching objective of this research to develop a mathematical and physical framework that allows for the design of PCs and AMs that support the well-known novel wave propagation control in radial elastic waves. The thesis introduces the concept of effective phononic crystals (EPCs), which combine periodicity and radially varying isotropic material properties to force the equations of motion of radial torsional waves to have invariance to radial translations. EPCs can be analyzed through the Bloch theorem and thus support canonical properties of PCs, such as band gaps and topological interface modes in radial elastic waves. The thesis goes on to extend the concept of EPC to include local resonances in what we call locally resonant effective phononic crystals (LREPCs). LREPCs consist of a radially varying matrix with attached torsional resonators. LREPCs support canonical properties of AMs such as locally resonant band gaps and negative effective properties for radial waves. One of the challenges of EPCs and LREPCs is their physical realization because of the need for specific radially varying material properties. The work physically realizes an LREPC using a radially varying impedance, i.e. out-of-plane thickness, and rings of soft/light and stiff/heavy materials for the spring and resonators, respectively. Interestingly, there is an intrinsic effective periodicity in the resonator physical realization, i.e. to keep all resonators the same in terms of their torsional stiffness and inertia, they must be all geometrically different. The samples are fabricated using a combination of additive manufacturing and machining and tested in a custom-made setup that allows for the excitation and accurate measurement of radial torsional waves. This way, the thesis experimentally validates the theoretical framework it presents. Motivated by the potential application of these EPCs and LREPCs in rotating machinery, the thesis studies the effects of rotation on elastic wave propagation in AMs. Previous work in this area focuses on studying the Coriolis or gyroscopic effects while neglecting the effects of centrifugal forces. In this work, the study of plane waves propagating through a rotating shaft with lumped resonances shows that the effects of centrifugal forces can have a strong influence on wave propagation. The stress stiffening effects from centrifugal forces can be leveraged to self-align band gaps to attenuate synchronous vibrations over a broad range of frequencies. Finally, the new concepts of rotating AMs introduced in this work are expanded to radial waves using the concept of effective periodicity. This is an example of the potential impact of effective periodicity when dealing with radial wave control."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Controlling radial waves through effective periodicity"]}]}],"canonical_facts":{"dc:contributor":["Matlack, Kathryn H","Vakakis, Alexander F","Elbanna, Ahmed","Tawfick, Sameh H"],"dc:creator":["Arretche, Ignacio"],"dc:date":["2022-12","2022-11-29"],"dc:description":["Submission published under a 24 month embargo labeled 'Closed Access', the embargo will last until 2024-12-01","The student, Ignacio Arretche, accepted the attached license on 2022-11-23 at 10:45.","The student, Ignacio Arretche, submitted this Dissertation for approval on 2022-11-23 at 15:01.","This Dissertation was approved for publication on 2022-11-29 at 14:57.","DSpace SAF Submission Ingestion Package generated from Vireo submission #18627 on 2023-04-12 at 11:35:16","Phononic crystals (PCs) and acoustic metamaterials (AMs) show unprecedented wave propagation phenomena such as band gas, negative refraction, and topologically protected states. Most PCs and AMs are built and designed under plane wave assumptions because a plane wave propagating through a periodic medium is described by equations of motion that have periodic coefficients. This enables the use of the Bloch theorem and the study of the infinite system can be reduced to that of a single unit cell. However, this is not the case for radial waves. In this case, a material that is invariant to radial translations does not result in periodic equations of motion, and the Bloch theorem cannot be applied. Therefore, to obtain the already-developed properties of PCs and AMs in radial waves we must find alternative approaches. It is the overarching objective of this research to develop a mathematical and physical framework that allows for the design of PCs and AMs that support the well-known novel wave propagation control in radial elastic waves. The thesis introduces the concept of effective phononic crystals (EPCs), which combine periodicity and radially varying isotropic material properties to force the equations of motion of radial torsional waves to have invariance to radial translations. EPCs can be analyzed through the Bloch theorem and thus support canonical properties of PCs, such as band gaps and topological interface modes in radial elastic waves. The thesis goes on to extend the concept of EPC to include local resonances in what we call locally resonant effective phononic crystals (LREPCs). LREPCs consist of a radially varying matrix with attached torsional resonators. LREPCs support canonical properties of AMs such as locally resonant band gaps and negative effective properties for radial waves. One of the challenges of EPCs and LREPCs is their physical realization because of the need for specific radially varying material properties. The work physically realizes an LREPC using a radially varying impedance, i.e. out-of-plane thickness, and rings of soft/light and stiff/heavy materials for the spring and resonators, respectively. Interestingly, there is an intrinsic effective periodicity in the resonator physical realization, i.e. to keep all resonators the same in terms of their torsional stiffness and inertia, they must be all geometrically different. The samples are fabricated using a combination of additive manufacturing and machining and tested in a custom-made setup that allows for the excitation and accurate measurement of radial torsional waves. This way, the thesis experimentally validates the theoretical framework it presents. Motivated by the potential application of these EPCs and LREPCs in rotating machinery, the thesis studies the effects of rotation on elastic wave propagation in AMs. Previous work in this area focuses on studying the Coriolis or gyroscopic effects while neglecting the effects of centrifugal forces. In this work, the study of plane waves propagating through a rotating shaft with lumped resonances shows that the effects of centrifugal forces can have a strong influence on wave propagation. The stress stiffening effects from centrifugal forces can be leveraged to self-align band gaps to attenuate synchronous vibrations over a broad range of frequencies. Finally, the new concepts of rotating AMs introduced in this work are expanded to radial waves using the concept of effective periodicity. This is an example of the potential impact of effective periodicity when dealing with radial wave control."],"dc:format":["application/pdf"],"dc:identifier":["https://hdl.handle.net/2142/117569"],"dc:language":["en","eng"],"dc:rights":["Copyright 2022 Ignacio Arretche"],"dc:subject":["Metamaterials","Phononic Crystals","Radial Waves","Wave Propagation","Rotor Dynamics"],"dc:title":["Controlling radial waves through effective periodicity"],"dc:type":["text","Thesis"],"thesis:degree_discipline":["Mechanical Engineering"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Ph.D."],"thesis:institution_name":["University of Illinois at Urbana-Champaign"]},"updated_at":"2026-07-22T22:24:56Z"}