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課程資訊

課程名稱	波動力學 Stress Waves in Solids
開課學期	103-2
授課對象	工學院機械工程學研究所
授課教師	馬劍清
課號	ME7123
課程識別碼	522 M3060
班次
學分	3
全/半年	半年
必/選修	選修
上課時間	星期二6,7,8(13:20~16:20)
上課地點	工綜213
備註	總人數上限：40人
Ceiba 課程網頁	http://ceiba.ntu.edu.tw/1032ME7123_
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課程概述	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。
課程目標	波動力學是研習固體力學相關課程中有關動態問題的基礎課程，內容闡述了應力波在彈性固體中的波傳現象與數學解析，由於在動態問題中所有的物理量（包括應力、應變與位移）皆為時間相關，且在短時間內有劇烈的變化，所以動態問題的解析較以靜態問題為主的彈性力學為繁難，但也具有較多的有趣的物理現象與實際在工程及工業界的應用實例，如超音波非破壞檢測，固體受撞擊時的動態反應，地震波對於結構體的影響，地質的探勘，船艦的聲納系統，聲波的傳播與噪音防制等，這些實際的工程應用皆是以波動力學為基礎再作深入的研究發展而成的範例。由於應力及應變並不是以往所熟知的純量以及向量場，而是更高階的物理量，所以本課程中首先以彈性力學為基礎說明這些物理量，並推導所需之基本方程式。本課程亦介紹以簡潔的符號系統來表示以及推導複雜的數學方程式，此符號系統將應用在本課程中以簡化一些繁複的數學推導以及方程式的表示式，修習的同學應熟悉此符號系統以利課程之學習。接著以較簡單的一維相關問題（如繩索、桿、樑）為例詳細說明波傳的基本特性及數學解析方法，再以連續體的理論模型為基礎建立三維波傳問題的控制方程式以及解析方法和動態問題基本特性探討。最後以平面簡諧波為例，詳細說明了其在無窮域及半平面的波傳和兩平面間的波導現象，並推導其中重要公式。雖然本課程是固體力學相關研究領域動態問題的入門課程，但是本課程的內容及深度卻非一般大學部課程所可比擬，尤其有較多的數學推導以說明波傳的現象，故修習本課程的同學應具備良好的工程數學基礎以及彈性力學基本知識。希望同學們修習完這門課後能奠定良好的固體力學有關動態問題的知識基礎，以便將來能以正確的觀念來處理固體力學方面相關的問題，並在實際工程問題中得以應用。
課程要求	先修課程: 線性彈性力學、工程數學適修年級: 碩博士班研究生
預期每週課後學習時數
Office Hours	備註：成績評量方式： 1. 期中考 (40%)，期末考 (40%)。 2. 作業(20%)。
指定閱讀	教科書：“Wave Propagation in Elastic Solids”, J. D. Achenbach, North-Holland Publication Company, 1973. 輔助教材：自編講義
參考書目	參考書： (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.
評量方式 (僅供參考)

課程進度

週次	日期	單元主題
第1週	2/24	Chap. 0. Introduction 1. Solid Mechanics general information, related courses 2. Wave Propagation in Elastic Solids general concept and application
第2週	3/03	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
第3週	3/10	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
第4週	3/17	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
第5週	3/24	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
第6週	3/31	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
第7週	4/07	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
第8週	4/14	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
第9週	4/21	期中考試
第10週	4/28	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
第11週	5/05	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
第12週	5/12	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
第13週	5/19	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
第14週	5/26	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
第15週	6/02	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
第16週	6/09	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
第17週	6/16	2. Plain Strain Waves in an Elastic Layer Rayleigh-Lamb frequency spectrum, longitudinal mode, Flexural mode
第18週		期末考試(依照學校規定時間)