11310 高等振動學

# Electives # Graduate Program # Solid & Nano Mechanics
17 Lectures / 56 Sections / 23h 7m 4s
Lecture 1：Course Introduction
Section 1
18:16
Lecture 2：Vibrations of 1-DOF Dynamic Systems
Section 1
48:07
Section 2
40:05
Lecture 3：Newtonian Dynamics: Rotational Mechanical System
Section 1
03:34
Section 2
23:10
Section 3
00:00
Section 4
05:47
Section 5
24:13
Lecture 4：Newtonian Dynamics: Dynamic Load Analysis
Section 1
43:32
Section 2
27:56
Section 3
15:21
Section 4
07:22
Section 5
32:17
Lecture 5：Analytical Dynamics
Section 1
39:53
Lecture 6：Vibrations of Discrete Multi-DOF Systems
Section 1
01:00:10
Lecture 7：Forced Vibrations of Discrete Multi-DOF Systems
Section 1
41:00
Section 2
41:37
Section 3
39:47
Lecture 8：Fourier Transform
Section 1
01:18:39
Section 2
31:43
Lecture 9：Vibration Measurements
Section 1
15:44
Section 2
11:11
Section 3
02:53
Section 4
04:56
Section 5
38:11
Lecture 10：Equation of Motions for Continuous System (Part I to IV)
Lecture 11：Part I: Infinitesimal Element Approach
Section 1
07:58
Section 2
18:48
Section 3
15:30
Section 4
01:24:24
Section 5
56:29
Lecture 12：Part II: Variational Approach (Hamilton's Principle)
Section 1
18:47
Section 2
41:32
Section 3
22:15
Lecture 13：Part III: Variational Approach for Vibration Problem
Section 1
10:59
Section 2
37:31
Section 3
06:12
Section 4
13:06
Section 5
32:25
Section 6
06:03
Section 7
12:25
Lecture 14：Part IV: The Lagrange's Equation
Section 1
17:02
Section 2
22:05
Section 3
17:27
Section 4
16:00
Section 5
07:55
Lecture 15：Functional Analysis
Section 1
19:45
Section 2
13:07
Section 3
22:36
Lecture 16：Properties of Eigenvalue Problems
Section 1
15:09
Section 2
17:46
Section 3
11:05
Lecture 17：Eigenvalue Problems for Continuous Systems
Section 1
22:22
Section 2
02:30
Section 3
43:09
Section 4
32:13
Section 5
27:05
Introduction
Duration｜ 23h 7m 4s
Total Lectures｜ 17 Lectures 56 Sections

Brief course descriptions

The subject area for this course is mechanical vibration, at a level appropriate for master and doctoral graduate students. Classical techniques in mechanical vibration are developed for the modeling and analysis of discrete and continuous linear dynamic systems. Continuous systems are described within the broader context of operator theory to emphasize the physical and mathematical analogies with discrete systems.

Course keywords

Vibrations, Hamilton’s principle, Variational method, Eigenvalue Problem, Galerkin's metho, Modal analysis, Rayleigh quotient

Prerequisites

PME 332000 “Mechanical Vibrations,” or its equivalent.

Textbook

L. Meirovitch, Analytical Methods in Vibrations, Macmillan.

Lecture notes/materials provided by Professor Chang.

Course Outline and Reading Schedule

Discrete Systems:

1. Review of Single Degree of Freedom Systems (Meirovitch, Chapter 1)

2. Equations of Motion for Multi-Degree of Freedom Systems (Chapter 2, 3)

3. Free Vibration (Chapter 4)

4. Modal Analysis (Chapter 7.1-7.6 and 9.1-9.5)

Continuous Systems:

5. Equations of Motion for Continuous Systems (Course notes and Chapters 5, and 10.1-10.5)

6. Eigenvalue Problems of Continuous Systems (Course notes and Chapter 5)

7. Modal Analysis (Course notes and Chapter 7.7-7.17)

8. Special topics

Lectures
Lecture 1：Course Introduction
Section 1 - Overall View
18:16
Lecture 2：Vibrations of 1-DOF Dynamic Systems
Section 1 - Equations, Free Vibrations, and Analytical Solutions
48:07
Section 2 - 1st-Order System and 2nd-Order System
40:05
Lecture 3：Newtonian Dynamics: Rotational Mechanical System
Section 1 - Variables
03:34
Section 2 - Element Laws
23:10
Section 3 - Dynamic Model of Translational Mechanical System
Section 4 - Interconnection Laws and Dynamic Model of Translational Mechanical System
05:47
Section 5 - Review, Example and Summary of Stiffness Matrix
24:13
Lecture 4：Newtonian Dynamics: Dynamic Load Analysis
Section 1 - Variables
43:32
Section 2 - Element Laws
27:56
Section 3 - Interconnection Laws
15:21
Section 4 - Dynamic Model of Translational Mechanical System
07:22
Section 5 - In-class Exercise/Solution
32:17
Lecture 5：Analytical Dynamics
Section 1 - Lagrangian Method, Newtonian/Lagrangian Approaches on Dynamic Systems
39:53
Lecture 6：Vibrations of Discrete Multi-DOF Systems
Section 1 - Motivations, Multi-DOF System Description, Eigenvalue Problem, System with Relative Displacement
01:00:10
Lecture 7：Forced Vibrations of Discrete Multi-DOF Systems
Section 1 - Vibration Analysis, Vibration Modes, Normalizaion
41:00
Section 2 - Forced Response, Step Response, Impulse Response
41:37
Section 3 - Response to Arbitrary Excitation f(t), Harmonic Excitation, System Damping
39:47
Lecture 8：Fourier Transform
Section 1 - A Quick Note on Fourier Transform, More Illustration about Impulse
01:18:39
Section 2 - Signals (Frequencies) and Fourier Transform
31:43
Lecture 9：Vibration Measurements
Section 1 - Stimulation (Exitation)
15:44
Section 2 - Sensor: Accelerometers
11:11
Section 3 - Sensor: Eddy Current Probe, Velocity Pickups
02:53
Section 4 - Sensor: LDV
04:56
Section 5 - Measurement and Analyzation
38:11
Lecture 10：Equation of Motions for Continuous System (Part I to IV)
Lecture 11：Part I: Infinitesimal Element Approach
Section 1 - Overall View
07:58
Section 2 - Transition from discrete system
18:48
Section 3 - Infinitesimal element approach - 2nd order stiffness systems
15:30
Section 4 - The 2nd order stiffness systems (review and finish)
01:24:24
Section 5 - Infinitesimal element approach - 4th order stiffness systems
56:29
Lecture 12：Part II: Variational Approach (Hamilton's Principle)
Section 1 - Introduction of Viriational Approach, Hamilton's Principle
18:47
Section 2 - Stationary of a function
41:32
Section 3 - Fundamental Lemma of Calculus of Variation
22:15
Lecture 13：Part III: Variational Approach for Vibration Problem
Section 1 - Extended Hamilton's Principle
10:59
Section 2 - Applying to Modeling of Continuous Systems
37:31
Section 3 - Sub Summary
06:12
Section 4 - Recap
13:06
Section 5 - Transverse Beam Vibrations
32:25
Section 6 - Transverse Beam Vibrations (continued)
06:03
Section 7 - Vibrations of Membrance
12:25
Lecture 14：Part IV: The Lagrange's Equation
Section 1 - Purpose, Model Problem
17:02
Section 2 - Transforming to Generalized Coordinate, d'Alembert's Principle
22:05
Section 3 - Intermediate Mathematical Identities, Fundamental/Standard Form of Lagrange's Equation
17:27
Section 4 - System with Multiple Degrees of Freedom, Type of Natural Systems, Euqation of Motion
16:00
Section 5 - Recap
07:55
Lecture 15：Functional Analysis
Section 1 - Spaces
19:45
Section 2 - Linear Operators
13:07
Section 3 - Properties of Linear Operators
22:36
Lecture 16：Properties of Eigenvalue Problems
Section 1 - Fundamentals of Real, Symmetric, Positive Definite Eigenvalue Problems
15:09
Section 2 - Properties of Eigenvalues and Eigenvectors: Distinctness and Orthogonality
17:46
Section 3 - Special Cases in Eigenvalue Problems: Repeated Values and Non-Symmetric Systems
11:05
Lecture 17：Eigenvalue Problems for Continuous Systems
Section 1 - Eigensolutions and Eigenfunctions of the Free-Free Euler-Bernoulli Beam
22:22
Section 2 - Sub Summary (Functional Analysis, Eigenvalue Problems)
02:30
Section 3 - Eigensolutions and Eigenfunctions of the Euler-Bernoulli Beam
43:09
Section 4 - Eigenvalue Problems for Plates and Membranes
32:13
Section 5 - Solutions of the Eigenvalue Problem
27:05
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Prof. Chang (James) Jen-Yuan
Prof. Chang (James) Jen-Yuan

Dept.  Power Mechanical Engineering

Research Field

Mechatronics, Robotics, Mechanical vibrations, Dynamic systems and control, Smart machinery and manufacturing

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