{"title":"分数达芬系统的阻尼效率及其求解精度评估","authors":"","doi":"10.1016/j.jsv.2024.118690","DOIUrl":null,"url":null,"abstract":"<div><p>Dynamical systems with high damping efficiency in a wide frequency band can be useful on a small scale – for harvesting energy from ambient vibrations, and on a large scale – for damping harmful vibrations of mechanical structures. In this paper we present an assessment of the quality of solutions and damping efficiency of systems with fractional order derivatives. To simulate the fractional system the fourth-order Runge–Kutta method and Grünwald–Letnikov methods are used. We propose a coefficient for assessing the quality of solutions to fractional systems by reference to the quality of the calculated energy balance. As an exemplary system we study the Duffing model with embedded additional fractional-order derivative terms. Based on this coefficient, intervals of key numerical simulation parameters are determined to ensure the appropriate quality for the calculations of energy flows and energy balance. The determined values of these parameters are then used in tests of the damping efficiency of the studied system. Our results show that by modifying the fractional terms it is possible to configure a system that exhibits a “broadband effect”, i.e. a system that is characterized by high-amplitude vibrations and, consequently, high energy efficiency in a wide range of excitation frequencies.</p></div>","PeriodicalId":17233,"journal":{"name":"Journal of Sound and Vibration","volume":null,"pages":null},"PeriodicalIF":4.3000,"publicationDate":"2024-08-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.sciencedirect.com/science/article/pii/S0022460X24004528/pdfft?md5=e72561c48018a74be1b2cdf239228334&pid=1-s2.0-S0022460X24004528-main.pdf","citationCount":"0","resultStr":"{\"title\":\"Damping efficiency of the fractional Duffing system and an assessment of its solution accuracy\",\"authors\":\"\",\"doi\":\"10.1016/j.jsv.2024.118690\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Dynamical systems with high damping efficiency in a wide frequency band can be useful on a small scale – for harvesting energy from ambient vibrations, and on a large scale – for damping harmful vibrations of mechanical structures. In this paper we present an assessment of the quality of solutions and damping efficiency of systems with fractional order derivatives. To simulate the fractional system the fourth-order Runge–Kutta method and Grünwald–Letnikov methods are used. We propose a coefficient for assessing the quality of solutions to fractional systems by reference to the quality of the calculated energy balance. As an exemplary system we study the Duffing model with embedded additional fractional-order derivative terms. Based on this coefficient, intervals of key numerical simulation parameters are determined to ensure the appropriate quality for the calculations of energy flows and energy balance. The determined values of these parameters are then used in tests of the damping efficiency of the studied system. Our results show that by modifying the fractional terms it is possible to configure a system that exhibits a “broadband effect”, i.e. a system that is characterized by high-amplitude vibrations and, consequently, high energy efficiency in a wide range of excitation frequencies.</p></div>\",\"PeriodicalId\":17233,\"journal\":{\"name\":\"Journal of Sound and Vibration\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":4.3000,\"publicationDate\":\"2024-08-23\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.sciencedirect.com/science/article/pii/S0022460X24004528/pdfft?md5=e72561c48018a74be1b2cdf239228334&pid=1-s2.0-S0022460X24004528-main.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Sound and Vibration\",\"FirstCategoryId\":\"5\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S0022460X24004528\",\"RegionNum\":2,\"RegionCategory\":\"工程技术\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"ACOUSTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Sound and Vibration","FirstCategoryId":"5","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022460X24004528","RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"ACOUSTICS","Score":null,"Total":0}
Damping efficiency of the fractional Duffing system and an assessment of its solution accuracy
Dynamical systems with high damping efficiency in a wide frequency band can be useful on a small scale – for harvesting energy from ambient vibrations, and on a large scale – for damping harmful vibrations of mechanical structures. In this paper we present an assessment of the quality of solutions and damping efficiency of systems with fractional order derivatives. To simulate the fractional system the fourth-order Runge–Kutta method and Grünwald–Letnikov methods are used. We propose a coefficient for assessing the quality of solutions to fractional systems by reference to the quality of the calculated energy balance. As an exemplary system we study the Duffing model with embedded additional fractional-order derivative terms. Based on this coefficient, intervals of key numerical simulation parameters are determined to ensure the appropriate quality for the calculations of energy flows and energy balance. The determined values of these parameters are then used in tests of the damping efficiency of the studied system. Our results show that by modifying the fractional terms it is possible to configure a system that exhibits a “broadband effect”, i.e. a system that is characterized by high-amplitude vibrations and, consequently, high energy efficiency in a wide range of excitation frequencies.
期刊介绍:
The Journal of Sound and Vibration (JSV) is an independent journal devoted to the prompt publication of original papers, both theoretical and experimental, that provide new information on any aspect of sound or vibration. There is an emphasis on fundamental work that has potential for practical application.
JSV was founded and operates on the premise that the subject of sound and vibration requires a journal that publishes papers of a high technical standard across the various subdisciplines, thus facilitating awareness of techniques and discoveries in one area that may be applicable in others.