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課程名稱 |
非線性振動學
Nonlinear Oscillations |
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開課學期 |
106-2 |
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授課對象 |
工學院 機械工程學研究所 |
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授課教師 |
陳振山 |
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課號 |
ME7147 |
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課程識別碼 |
522 M4140 |
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班次 |
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學分 |
3.0 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期四6,7,8(13:20~16:20) |
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上課地點 |
工綜213 |
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備註 |
總人數上限：40人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1062ME7147_nonlinosc |
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課程簡介影片 |
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核心能力關聯 |
核心能力與課程規劃關聯圖 |
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課程大綱
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課程概述 |
This course covers the nonlinear aspect of vibrating systems. The students should be familiar with the linear vibration theory in order to take this course. In linear vibration, the frequencies are independent of the amplitude of the vibration. In nonlinear system, the frequencies depends on amplitude. In linear system, one input produces one output. In nonlinear system the solution may not be unique. |
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課程目標 |
The goal of this course is to prepare the graduate students for the advanced study in the field of nonlinear oscillation. Following the introduction of basic theory and techniques, we will introduce the students to the cutting-edge research topic of this field, in which this lecturer is currently working on. |
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課程要求 |
The students should have taken linear vibration course.
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預期每週課後學習時數 |
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Office Hours |
每週二 09:00~11:00 |
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指定閱讀 |
Nayfeh, A.H., and Mook, D.T., Nonlinear Oscillations, Wiley, New York, 1979. |
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參考書目 |
待補 |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Weekly homework |
40% |
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2. |
Projects |
60% |
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週次 |
日期 |
單元主題 |
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第1週 |
3/01 |
Free vibrations; forced vibrstiond; Classification of problems |
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第2週 |
3/08 |
Introduction, qualitative analysis |
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第3週 |
3/15 |
Quantitative analysis, straightforward expansion, Lindstedt-Poincare method
method, multiple scale method
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第4週 |
3/22 |
multiple scale method |
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第5週 |
3/29 |
More on multiple scale analysis, secular behavior, nonuniformity |
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第6週 |
4/05 |
Duffing’s equation, harmonic balance method, simple pendulum, motion of a particle on a rotating parabola |
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第7週 |
4/12 |
Damping mechanisms, qualitative analysis, properties of singular points, Lienard method |
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第8週 |
4/19 |
Approximate solutions, multiple scale method, averaging method |
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第9週 |
4/26 |
Nonstationary vibrations, relaxation oscillations |
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第10週 |
5/03 |
Duffing equation: primary resonances, superharmonic resonances, subharmonic resonances |
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第11週 |
5/10 |
Duffing equation: combination resonances for two-term excitations, super-and subharmonic resonances simultaneously, three-term excitation
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第12週 |
5/17 |
Nonstationary oscillations due to time-dependent excitations, nonideal systems with excitation depending on response
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第13週 |
5/24 |
Examples, Floquet theory, single and multi-DOF systems |
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第14週 |
5/31 |
Approximate methods to find stability boundary for Mathieu’s equation: (1) Hill’s infinite determinant, (2) method of strained parameters, (3) multiple scale method. Hill’s equation, effects of viscous damping, nonstationary excitation
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第15週 |
6/07 |
Linear systems having distinct frequencies, a column under periodic follower axial load, effects of viscous damping, gyroscopic systems, nonlinear effects
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第16週 |
6/14 |
Free oscillation: internal resonance, systems with quadratic nonlinearity, systems with cubic nonlinearity, gyroscopic systems
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第17週 |
6/21 |
Forced response: internal resonance, systems with quadratic nonlinearity, systems with cubic nonlinearity, gyroscopic systems |
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