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課程名稱 |
波動力學
Stress Waves in Solids |
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開課學期 |
104-2 |
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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 |
馬劍清 |
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課號 |
ME7123 |
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課程識別碼 |
522 M3060 |
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班次 |
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學分 |
3 |
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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 |
星期二7,8,9(14:20~17:20) |
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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/1042ME7123_ |
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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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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
編製中 |
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課程目標 |
教導學生明瞭固體動態問題之基本知識及應力波傳所呈現之物理現象；傳授學生分析彈性材料受動態外力加載後變形與應力的方法與技巧，期使學生能將所學的知識應用於解釋與解決與固體承受動態負載相關的課題。 |
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課程要求 |
待補 |
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預期每週課後學習時數 |
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Office Hours |
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指定閱讀 |
“Wave Propagation in Elastic Solids”, J. D. Achenbach, North-Holland
Publication Company, 1973. |
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參考書目 |
(1) “Wave Motion in Elastic Solids”, K. F. Graff, Ohio State University Press, 1975.
(2) “The Theory of Elastic Waves and Waveguides”, J. Miklowitz, North-Holland Publication Company, 1978.
輔助教材：自編講義
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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. |
期中考 |
40% |
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2. |
期末考 |
40% |
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3. |
作業 |
20% |
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週次 |
日期 |
單元主題 |
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第1週 |
2/23 |
Chap. 0. Introduction
1. Solid Mechanics general information, related courses
2.Wave Propagation in Elastic Solids general concept and application
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第2週 |
3/01 |
Chap. 1. Index Notation and Basic Formulation of Linear Elasticity
1. Index Notation
summation convention, calculus of Cartesian tensors
2. Basic Formulation of Linear Elasticity
stress tensor and traction vector, deformation and strain tensor, stress and strain relation, restrictions on elastic moduli
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第3週 |
3/08 |
Chap. 1. Index Notation and Basic Formulation of Linear Elasticity
2. Basic Formulation of Linear Elasticity
stress tensor and traction vector, deformation and strain tensor, stress and strain relation, restrictions on elastic moduli
3. Equations of Motion and Boundary Conditions
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第4週 |
3/15 |
Chap. 2. One Dimensional Problems
1. Basic Governing Equations
longitudinal strain, longitudinal stress, shear stress, the D’Alembert solution
2.One Dimensional Boundary Value Problem for a Semi-infinite Medium
general solution method, Laplace transform method
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第5週 |
3/22 |
Chap. 2. One Dimensional Problems
3. Reflection and Transmission
traction free boundary, interface boundary, the split Hopkinson pressure bar
4. Solutions for Infinite Bodies
the initial value problem, domain of dependence, forced motion of an infinite body, the Green’s function solution
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第6週 |
3/29 |
Chap. 2. One Dimensional Problems
5. Harmonic Waves
traveling waves, standing waves, modes of vibration
6. Dynamic Motion of a String
the normal mode solution, Sturm-Liouville theory, boundary conditions for a string, the orthogonality of the normal modes, forced motions of a string
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第7週 |
4/05 |
Chap. 2. One Dimensional Problems
7. Dynamic Motion of a Finite Rod
free vibration of a finite rod, forced vibration of a finite rod, impulse loading of a finite rod.
8. The String on an Elastic Foundation
phase velocity, frequency spectrum and dispersion curve, group velocity
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第8週 |
4/12 |
Chap. 2. One Dimensional Problems
9. Flexural Waves in Bernoulli-Euler Beams
propagation of harmonic waves, free vibrations of finite beams, orthogonality of normal modes, forced motions of beams, transient response of a simply supported beam
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第9週 |
4/19 |
期中考試 |
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第10週 |
4/26 |
Chap. 3. Elastodynamic Formulation and Theory
1. Displacement Equations of Motion
Helmholtz decomposition of a vector, displacement potentials, dilatation and rotation waves, the relations of stress components and displacement potentials, the ideal fluid
2. Two-Dimensional Formulation
anti-plane shear motion, in-plane motion, two-dimensional displacement potentials
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第11週 |
5/03 |
Chap. 3. Elastodynamic Formulation and Theory
3. Elastodynamic Theory
kinetic energy and strain energy,uniqueness of solution, dynamic reciprocal identity
4. Wave Motion due to Body Forces
the solution for point sources, the solution for distributed sources, elastodynamic solution due to body forces, steady-state time harmonic response, the singular solution of elastodynamic
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第12週 |
5/10 |
Chap. 3. Elastodynamic Formulation and Theory
4. Wave Motion due to Body Forces
the solution for point sources, the solution for distributed sources, elastodynamic solution due to body forces, steady-state time harmonic response, the singular solution of elastodynamic
5. Two-Dimensional Problems
two-dimensional radiation problems, anti-plane line load, in-plane line load, boundary value problems
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第13週 |
5/17 |
Chap. 4. Elastic Waves in an Unbounded Medium
1. Plane Waves
in anisotropic elastic solid, acoustic tensor and characteristic equation, in transversely isotropic solid, in isotropic solid
2. Example
uniform pressure on a spherical cavity
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第14週 |
5/24 |
Chap. 4. Elastic Waves in an Unbounded Medium
2. Example
uniform pressure on a spherical cavity
Chap. 5. Plane Harmonic Waves in Elastic Half-Space
1. Incident, Reflection and Refraction of Plane Waves
reflection of incident longitudinal wave, reflection and refraction of incident SH shear wave
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第15週 |
5/31 |
Chap. 5. Plane Harmonic Waves in Elastic Half-Space
1. Incident, Reflection and Refraction of Plane Waves
reflection of incident longitudinal wave, reflection and refraction of incident SH shear wave
2. Surface Waves
slowness diagram, Rayleigh surface wave, roots of function in the complex plane
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第16週 |
6/07 |
Chap. 6. Harmonic Waves in Waveguides
1. SH Waves in an Elastic Layer
SH shear wave, frequency equation and frequency spectrum, energy transport by SH wave in a layer, Love waves in a layered half-space
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第17週 |
6/14 |
Chap. 6. Harmonic Waves in Waveguides
2. Plain Strain Waves in an Elastic Layer
Rayleigh-Lamb frequency spectrum, longitudinal mode, Flexural mode
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