dc.contributor.author | Men, Han | |
dc.contributor.author | Freund, Robert Michael | |
dc.contributor.author | Nguyen, Ngoc Cuong | |
dc.contributor.author | Saa-Seoane, Joel | |
dc.contributor.author | Peraire, Jaime | |
dc.date.accessioned | 2017-05-19T18:09:17Z | |
dc.date.available | 2017-05-19T18:09:17Z | |
dc.date.issued | 2013-11 | |
dc.date.submitted | 2013-11 | |
dc.identifier.isbn | 978-0-7918-5643-7 | |
dc.identifier.uri | http://hdl.handle.net/1721.1/109223 | |
dc.description.abstract | Designing phononic crystals by creating frequency bandgaps is of particular interest in the engineering of elastic and acoustic microstructured materials. Mathematically, the problem of optimizing the frequency bandgaps is often nonconvex, as it requires the maximization of the higher indexed eigenfrequency and the minimization of the lower indexed eigenfrequency. A novel algorithm [1] has been previously developed to reformulate the original nonlinear, nonconvex optimization problem to an iteration-specific semidefinite program (SDP). This algorithm separates two consecutive eigenvalues — effectively maximizing bandgap (or bandwidth) — by separating the gap between two orthogonal subspaces, which are comprised columnwise of “important” eigenvectors associated with the eigenvalues being bounded. By doing so, we avoid the need of computation of eigenvalue gradient by computing the gradient of affine matrices with respect to the decision variables. In this work, we propose an even more efficient algorithm based on linear programming (LP). The new formulation is obtained via approximation of the semidefinite cones by judiciously chosen linear bases, coupled with “delayed constraint generation”. We apply the two convex conic formulations, namely, the semidefinite program and the linear program, to solve the bandgap optimization problems. By comparing the two methods, we demonstrate the efficacy and efficiency of the LP-based algorithm in solving the category of eigenvalue bandgap optimization problems. | en_US |
dc.description.sponsorship | United States. Air Force Office of Scientific Research (FA9550-11- 1-0141) | en_US |
dc.language.iso | en_US | |
dc.publisher | American Society of Mechanical Engineers (ASME) | en_US |
dc.relation.isversionof | http://dx.doi.org/10.1115/IMECE2013-64694 | en_US |
dc.rights | Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use. | en_US |
dc.source | American Society of Mechanical Engineers (ASME) | en_US |
dc.title | Designing Phononic Crystals With Convex Optimization | en_US |
dc.type | Article | en_US |
dc.identifier.citation | Men, Han; Freund, Robert M.; Nguyen, Ngoc C.; Saa-Seoane, Joel and Peraire, Jaime. “Designing Phononic Crystals With Convex Optimization.” ASME 2013 International Mechanical Engineering Congress and Exposition, Volume 14: Vibration, Acoustics and Wave Propagation November 15-21 2013, ASME International, November 2013 © 2013 American Society of Mechanical Engineers (ASME) | en_US |
dc.contributor.department | Massachusetts Institute of Technology. Department of Aeronautics and Astronautics | en_US |
dc.contributor.department | Sloan School of Management | en_US |
dc.contributor.mitauthor | Men, Han | |
dc.contributor.mitauthor | Freund, Robert Michael | |
dc.contributor.mitauthor | Nguyen, Ngoc Cuong | |
dc.contributor.mitauthor | Saa-Seoane, Joel | |
dc.contributor.mitauthor | Peraire, Jaime | |
dc.relation.journal | ASME 2013 International Mechanical Engineering Congress and Exposition, Volume 14: Vibration, Acoustics and Wave Propagation | en_US |
dc.eprint.version | Final published version | en_US |
dc.type.uri | http://purl.org/eprint/type/ConferencePaper | en_US |
eprint.status | http://purl.org/eprint/status/NonPeerReviewed | en_US |
dspace.orderedauthors | Men, Han; Freund, Robert M.; Nguyen, Ngoc C.; Saa-Seoane, Joel; Peraire, Jaime | en_US |
dspace.embargo.terms | N | en_US |
dc.identifier.orcid | https://orcid.org/0000-0002-1733-5363 | |
dc.identifier.orcid | https://orcid.org/0000-0002-8556-685X | |
mit.license | PUBLISHER_POLICY | en_US |