Good morning, everyone! It is my pleasure to present our recent work on nonlinear energy harvesting. The work was done by Dr Ze-Qi Lu, a Postdoc fellow, and me. We come from Shanghai University. First of all, I’ll show you the outline of the talk. The talk is divided into 5 parts. It begins with an introduction to explain the background and the motivation of the investigation. Then the physical model and the mathematical model are presented and the frequency response equation is derived from the method of harmonic balance. It follows some numerical results to demonstrate the forming and the disappearance of bubble shaped frequency response curves. Then some numerical simulations are done to examine the harvesting performance under Gaussian random excitation. Finally, some concluding remarks end the talk. Now turn to the Introduction. As we well know, energy harvesting is a significant issue. Especially, vibratory energy harvesting is to transform the kinetic energy of waste vibration into electricity. Linear models have been widely used to design, to analyze, and to simulate energy harvesters. However, there is an essential limitation of linear energy harvesting. As a resonator, a linear energy harvester works only in a narrow frequency range near the resonance. Actually, its reason can be found in any textbooks on vibration. To overcome the limitation, several approaches have been proposed. For example, multi-modal energy harvesters have been designed so that the working frequency range contains several resonant frequencies. Anyway, our talk is not on the topic. Another promising approach is to introduce nonlinearity intentionally. Our work belongs to this aspect. Among many features of nonlinear oscillation, the jumping is a striking one. As we all know, an amplitude-frequency response curve of a linear oscillator is with a symmetric peak. The introduction of nonlinearity may destroy the symmetry. Hardening nonlinearity bends the peak to the increasing frequency direction, while softening nonlinearity the decreasing frequency direction. As you may observe, the bending of the frequency response curve makes the amplitude sufficiently large in a wider frequency range. Therefore, the jumping provides with a possibility of developing broadband vibration-based energy harvesters. The detailed discussions can be found in a recent review paper published in Applied Mechanics Reviews. If jumping can enhance energy harvesting, it is a natural idea that double-jumping, jumping in both sides, does the job better. Internal resonance leads to double-jumping. Our group constructed conceptually an electromagnetic energy harvester with internal resonance. The method of multiple scales was developed to reveal the double-jumping in the power frequency response curves. The analytical outcome was supported by the numerical integrations. Numerical results also showed that the internal resonance designproduces more power than other designs under the Gaussian white noise. The results were published in ASME Journal of Applied Mechanics. By the way, our analytical and numerical prediction on enlarged band width has been experimentally supported. For example, an experiment was reported in recent Applied PhysicsLetters. Our group’s experimental work would probably published in ASME Journalof Vibration and Acoustics. In double-jumping, bending is back-to-back. That is, the right branch of the response curve bends to the right, while the leftone to the left. Now, the problem is what happens if the bending is face-to-face. That is the right branch of the response curve bends to the left, and the lift right. In this case, there may be a bubble shaped response curve. It is the motivation of the work. In other words, the objective of the work is to explore the possibility of using bubble shaped response curves to enhance vibration-based energy harvesting. To do so, a system should be conceptually designed with the bubble shaped response curve. Fortunately, previous works on vibration isolations shed some lights on the issue. An electromagnetic energy harvester is proposed as a linear-nonlinear coupled system. In addition, numerical simulations are done to examine the harvester performance under Gaussian white noise.
I am pleased to inform you that your revised manuscript, referenced below, has been accepted for publication in Applied Physics Letters, and materials are being prepared for sending to AIP Production Services. At this time, the manuscript has not as yet been scheduled for a particular issue and/or given an AIP code number. Please allow at least 7-10 days before checking the AMSIS website for any further production information. "Shear dependent nonlinear vibration in a high quality factor single crystal silicon micromechanical resonator" L12-06188R When your page proofs are ready for your review, you will receive an e-mail from AIP Production Services which will inform you of the AIP Production Number assigned to your submission. After receiving that email, direct all questions pertaining to papers in the production process to: Editorial Supervisor, Applied Physics Letters, American Institute of Physics, Suite 1NO1, 2 Huntington Quadrangle, Melville, NY 11747-4502 USA; E-mail: apl@aip.org; Phone: 516-576-2416; Fax: 516-576-2633. Be sure to include the AIP Production Number on all correspondence. During the production process, authors may access information about their accepted manuscript by visiting the AMSIS website To support the cost of wide dissemination of research results through publication of journal pages and production of a database of articles, the author's institution is requested to pay a page charge of $115 per page (with a one-page minimum) and an article charge of $20 per article. A link to the Rightslink service, for payment of applicable publication charges and ordering reprints, will be provided when proofs are ready for review. Thank you for your contribution to the Journal. If you have any questions, feel free to contact us at apl@anl.gov. Sincerely yours, Associate Editor APPLIED PHYSICS LETTERS Published by the American Institute of Physics Argonne National Laboratory Building 203, Room R-127 Argonne, IL 60439-4843, USA --------------------------------------------------------------------- Manuscript #L12-06188R: Reviewer Comments: Reviewer #1 Evaluations: RECOMMENDATION: Publish in APL as is Paper Interesting: Yes Original Paper: Yes Sufficient Physics: Yes Well Organized: Yes Clear and Error Free: Yes Conclusions Supported: Yes Appropriate Title: Yes Good Abstract: Yes Satisfactory English: Yes Adequate References: Yes Clear Figures: Yes OVERALL RATING: Excellent --------------------------------------------------------------------------------------------------- Themanuscript, referenced below, has been reviewed for Applied Physics Letters. "Shear dependent nonlinear vibration in a high quality factor single crystal silicon micromechanical resonator" L12-06188 The reviewer is of the opinion that it should be revised. His/Her comments are included below and/or attached. Please indicate how the manuscript has been revised in a separate Response Letter file so that the editors can see whether you have complied with the reviewer's comments. Please use ADD FILE to upload the Response Letter file and use REPLACE for any files that have been revised or changed. This could save a second request to the reviewer and the resultant delay in publication. Revised manuscripts must be submitted through the online submission system. They are not accepted by email. If you have any questions, feel free to contact us at apl@anl.gov. Sincerely yours, Associate Editor APPLIED PHYSICS LETTERS Published by the American Institute of Physics Argonne National Laboratory Building 203, Room R-127 Argonne, IL 60439-4843, USA --------------------------------------------------------------------- Manuscript #L12-06188: Reviewer Comments: Reviewer #1 Evaluations: RECOMMENDATION: Publish in APL with optional revision Paper Interesting: Yes Original Paper: Yes Sufficient Physics: Yes Well Organized: Yes Clear and Error Free: Yes Conclusions Supported: Yes Appropriate Title: Yes Good Abstract: Yes Satisfactory English: Yes Adequate References: Yes Clear Figures: Yes OVERALL RATING: Excellent Reviewer #1 (Comments to the Author): In this manuscript, Zhu et al. investigate the shear dependent nonlinear vibration in a high quality factor single crystal silicon micromechanical resonator. The authors do show a novel idea to provide an atomic-scale explanation to the experimentally-observed device-level nonlinear behavior. And the simulation results are validated by the experiments. The atomic level first-principles calculation results agree with the known elastic property of silicon. A device-level behavior model is also explicitly built to relate the nonlinear vibration to the nonlinear strain-stress relation. The calculated nonlinear response matches the experimental results. However, the authors should explain more details about their model and result discussions. *********************************** In summary, I suggest acceptance of this manuscript after minor revision.
标签: vibration
