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An Approach to Nonlinear Oscillations Through Randomization
An Approach to Nonlinear Oscillations Through Randomization
상세정보
- 자료유형
- 학위논문 서양
- 최종처리일시
- 20250211150935
- ISBN
- 9798384451594
- DDC
- 621
- 저자명
- Byun, Jaeseung.
- 서명/저자
- An Approach to Nonlinear Oscillations Through Randomization
- 발행사항
- [Sl] : University of California, Berkeley, 2024
- 발행사항
- Ann Arbor : ProQuest Dissertations & Theses, 2024
- 형태사항
- 119 p
- 주기사항
- Source: Dissertations Abstracts International, Volume: 86-03, Section: B.
- 주기사항
- Advisor: Ma, Fai.
- 학위논문주기
- Thesis (Ph.D.)--University of California, Berkeley, 2024.
- 초록/해제
- 요약In this thesis, a novel investigation of deterministic nonlinear systems is presented. When autonomous dynamical systems are randomized by white-noise excitation, their behaviors are governed by diffusion equations. The core idea behind the method of randomization involves replacing a nonlinear ordinary differential equation of motion by a linear partial differential equation of diffusion.Exact analytical solutions are feasible for only a limited number of nonlinear systems. However, some nonlinear systems, which are difficult to analyze using deterministic methods, possess stationary diffusion equations with exact solutions. These diffusion responses provide deeper insights into the qualitative behaviors of nonlinear systems, such as stability at multiple equilibria, limit cycles, and bifurcations. To demonstrate the potential and feasibility of randomization, numerous nonlinear oscillators are considered. When both the deterministic systems and the associated randomized systems can be analyzed, there is complete agreement in their qualitative properties. Furthermore, some example systems inaccessible through deterministic approaches can be readily examined using randomization, suggesting that randomization could be an alternative tool for investigating nonlinear oscillations.
- 일반주제명
- Mechanical engineering
- 일반주제명
- Applied physics
- 일반주제명
- Applied mathematics
- 일반주제명
- Systems science
- 키워드
- Random vibration
- 키워드
- Randomization
- 기타저자
- University of California, Berkeley Mechanical Engineering
- 기본자료저록
- Dissertations Abstracts International. 86-03B.
- 전자적 위치 및 접속
- 로그인 후 원문을 볼 수 있습니다.
MARC
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■007cr#unu||||||||
■020 ▼a9798384451594
■035 ▼a(MiAaPQ)AAI30990796
■040 ▼aMiAaPQ▼cMiAaPQ
■0820 ▼a621
■1001 ▼aByun, Jaeseung.
■24513▼aAn Approach to Nonlinear Oscillations Through Randomization
■260 ▼a[Sl]▼bUniversity of California, Berkeley▼c2024
■260 1▼aAnn Arbor▼bProQuest Dissertations & Theses▼c2024
■300 ▼a119 p
■500 ▼aSource: Dissertations Abstracts International, Volume: 86-03, Section: B.
■500 ▼aAdvisor: Ma, Fai.
■5021 ▼aThesis (Ph.D.)--University of California, Berkeley, 2024.
■520 ▼aIn this thesis, a novel investigation of deterministic nonlinear systems is presented. When autonomous dynamical systems are randomized by white-noise excitation, their behaviors are governed by diffusion equations. The core idea behind the method of randomization involves replacing a nonlinear ordinary differential equation of motion by a linear partial differential equation of diffusion.Exact analytical solutions are feasible for only a limited number of nonlinear systems. However, some nonlinear systems, which are difficult to analyze using deterministic methods, possess stationary diffusion equations with exact solutions. These diffusion responses provide deeper insights into the qualitative behaviors of nonlinear systems, such as stability at multiple equilibria, limit cycles, and bifurcations. To demonstrate the potential and feasibility of randomization, numerous nonlinear oscillators are considered. When both the deterministic systems and the associated randomized systems can be analyzed, there is complete agreement in their qualitative properties. Furthermore, some example systems inaccessible through deterministic approaches can be readily examined using randomization, suggesting that randomization could be an alternative tool for investigating nonlinear oscillations.
■590 ▼aSchool code: 0028.
■650 4▼aMechanical engineering
■650 4▼aApplied physics
■650 4▼aApplied mathematics
■650 4▼aSystems science
■653 ▼aFokker-Planck equation
■653 ▼aForward diffusion equation
■653 ▼aNonlinear dynamical system
■653 ▼aRandom vibration
■653 ▼aRandomization
■653 ▼aStochastic process
■690 ▼a0548
■690 ▼a0215
■690 ▼a0364
■690 ▼a0790
■71020▼aUniversity of California, Berkeley▼bMechanical Engineering.
■7730 ▼tDissertations Abstracts International▼g86-03B.
■790 ▼a0028
■791 ▼aPh.D.
■792 ▼a2024
■793 ▼aEnglish
■85640▼uhttp://www.riss.kr/pdu/ddodLink.do?id=T17160214▼nKERIS▼z이 자료의 원문은 한국교육학술정보원에서 제공합니다.
