{"title":"具有强 Duffing 非线性的微型机械谐振器中的一对二内部共振","authors":"Jun Yu, Ata Donmez, Hansaja Herath, Hanna Cho","doi":"10.1088/1361-6439/ad0de8","DOIUrl":null,"url":null,"abstract":"This paper investigates the implementation of 1:2 internal resonance (InRes) in a clamped–clamped stepped beam resonator with a strong Duffing effect, focusing on its potential for frequency stabilization in micro-electro-mechanical systems (MEMS) resonators. InRes can arise in a nonlinear system of which mode frequencies are close to an integer ratio, facilitating the internal exchange of energy from an externally driven mode to an undriven mode. The presence of 1:2 InRes and Duffing hardening nonlinearity can result in frequency saturation phenomena, leading to a flat amplitude-frequency response range, which forms the basis for frequency stabilization. The stepped beam resonator design, combined with thermal frequency tuning, enables precise alteration of the frequency ratio between the second and third flexural modes required to achieve the desired 1:2 ratio for InRes. Experimental characterization and theoretical analysis revealed that frequency mismatch plays a significant role, with larger mismatch conditions leading to stronger energy exchange and a wider range of drive force for frequency saturation. The study highlights the frequency saturation mechanism utilizing 1:2 InRes and emphasizes the advantage of Duffing nonlinearity and larger intermodal frequency mismatch for broader frequency stabilization, providing valuable insights for the design and optimization of MEMS resonators.","PeriodicalId":16346,"journal":{"name":"Journal of Micromechanics and Microengineering","volume":"1 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"One-to-two internal resonance in a micro-mechanical resonator with strong Duffing nonlinearity\",\"authors\":\"Jun Yu, Ata Donmez, Hansaja Herath, Hanna Cho\",\"doi\":\"10.1088/1361-6439/ad0de8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper investigates the implementation of 1:2 internal resonance (InRes) in a clamped–clamped stepped beam resonator with a strong Duffing effect, focusing on its potential for frequency stabilization in micro-electro-mechanical systems (MEMS) resonators. InRes can arise in a nonlinear system of which mode frequencies are close to an integer ratio, facilitating the internal exchange of energy from an externally driven mode to an undriven mode. The presence of 1:2 InRes and Duffing hardening nonlinearity can result in frequency saturation phenomena, leading to a flat amplitude-frequency response range, which forms the basis for frequency stabilization. The stepped beam resonator design, combined with thermal frequency tuning, enables precise alteration of the frequency ratio between the second and third flexural modes required to achieve the desired 1:2 ratio for InRes. Experimental characterization and theoretical analysis revealed that frequency mismatch plays a significant role, with larger mismatch conditions leading to stronger energy exchange and a wider range of drive force for frequency saturation. The study highlights the frequency saturation mechanism utilizing 1:2 InRes and emphasizes the advantage of Duffing nonlinearity and larger intermodal frequency mismatch for broader frequency stabilization, providing valuable insights for the design and optimization of MEMS resonators.\",\"PeriodicalId\":16346,\"journal\":{\"name\":\"Journal of Micromechanics and Microengineering\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":2.4000,\"publicationDate\":\"2023-12-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Micromechanics and Microengineering\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://doi.org/10.1088/1361-6439/ad0de8\",\"RegionNum\":4,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, ELECTRICAL & ELECTRONIC\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Micromechanics and Microengineering","FirstCategoryId":"5","ListUrlMain":"https://doi.org/10.1088/1361-6439/ad0de8","RegionNum":4,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, ELECTRICAL & ELECTRONIC","Score":null,"Total":0}
One-to-two internal resonance in a micro-mechanical resonator with strong Duffing nonlinearity
This paper investigates the implementation of 1:2 internal resonance (InRes) in a clamped–clamped stepped beam resonator with a strong Duffing effect, focusing on its potential for frequency stabilization in micro-electro-mechanical systems (MEMS) resonators. InRes can arise in a nonlinear system of which mode frequencies are close to an integer ratio, facilitating the internal exchange of energy from an externally driven mode to an undriven mode. The presence of 1:2 InRes and Duffing hardening nonlinearity can result in frequency saturation phenomena, leading to a flat amplitude-frequency response range, which forms the basis for frequency stabilization. The stepped beam resonator design, combined with thermal frequency tuning, enables precise alteration of the frequency ratio between the second and third flexural modes required to achieve the desired 1:2 ratio for InRes. Experimental characterization and theoretical analysis revealed that frequency mismatch plays a significant role, with larger mismatch conditions leading to stronger energy exchange and a wider range of drive force for frequency saturation. The study highlights the frequency saturation mechanism utilizing 1:2 InRes and emphasizes the advantage of Duffing nonlinearity and larger intermodal frequency mismatch for broader frequency stabilization, providing valuable insights for the design and optimization of MEMS resonators.
期刊介绍:
Journal of Micromechanics and Microengineering (JMM) primarily covers experimental work, however relevant modelling papers are considered where supported by experimental data.
The journal is focussed on all aspects of:
-nano- and micro- mechanical systems
-nano- and micro- electomechanical systems
-nano- and micro- electrical and mechatronic systems
-nano- and micro- engineering
-nano- and micro- scale science
Please note that we do not publish materials papers with no obvious application or link to nano- or micro-engineering.
Below are some examples of the topics that are included within the scope of the journal:
-MEMS and NEMS:
Including sensors, optical MEMS/NEMS, RF MEMS/NEMS, etc.
-Fabrication techniques and manufacturing:
Including micromachining, etching, lithography, deposition, patterning, self-assembly, 3d printing, inkjet printing.
-Packaging and Integration technologies.
-Materials, testing, and reliability.
-Micro- and nano-fluidics:
Including optofluidics, acoustofluidics, droplets, microreactors, organ-on-a-chip.
-Lab-on-a-chip and micro- and nano-total analysis systems.
-Biomedical systems and devices:
Including bio MEMS, biosensors, assays, organ-on-a-chip, drug delivery, cells, biointerfaces.
-Energy and power:
Including power MEMS/NEMS, energy harvesters, actuators, microbatteries.
-Electronics:
Including flexible electronics, wearable electronics, interface electronics.
-Optical systems.
-Robotics.