Vibration Engineering 2

Course title

A0015000

Course description

All bodies possessing mass and elasticity are capable of vibrations. Most engineering machines and structures experience vibrations to some degree and their design generally requires consideration of their oscillatory motions. Students will analyze free and forced vibrations of multi-degree-of-freedom system and will develop mathematical techniques to model mechanical systems.

Purpose of class

The objective for this course is for students to learn analytical and numerical treatment of vibration phenomena. Topics include modes of vibrations, dynamic vibration absorber, modal analysis, Lagrange’s equation and matrix techniques suitable for computer simulations.

Goals and objectives

To formulate the equations of motion of two-degree-of-freedom systems
To identify the mass, stiffness and damping matrices from equations of motion
To obtain the mode shapes and natural frequencies of the system
To formulate the equations of motion of multi-degree of freedom system using Lagrange’s equation
To predict the steady-state response of a multi-degree of freedom system subject to harmonic excitation

Relationship between 'Goals and Objectives' and 'Course Outcomes'

	Midterm exam 1	Midterm exam 2	Final exam	Total.
1.	10%	0%	10%	20%
2.	10%	0%	10%	20%
3.	0%	10%	10%	20%
4.	0%	10%	10%	20%
5.	0%	10%	10%	20%
Total.	20%	30%	50%	-

Evaluation method and criteria

The grade weights are
Mid-term exam 1:　20%
Mid-term exam 2:　20%
Final exam: 60%

Scored larger than 60 points will be passed.

Language

Japanese

Class schedule

	Class schedule	HW assignments (Including preparation and review of the class.)	Amount of Time Required
1.	Balancing ・Types of unbalance: static and dynamic ・Static and dynamic unbalance	Make sure students have read chapter 4 (pp.94-99).	190minutes
2.	Derivation of Equations of motion of two degree of freedom system ・System with translational displacements ・System with translational and rotational displacements ・System with rotational displacements	Make sure students have read chapter 5 (pp.101-104).	90minutes
2.		Solve the problems written in the handout.	100minutes
3.	Free vibration of two degree of freedom system (1) ・Free vibration analysis of two degree of freedom system (1) ・Natural frequencies	Make sure students have read chapter 5 (pp.105-108).	90minutes
3.		Solve the problems written in the handout.	100minutes
4.	Free vibration of two degree of freedom system (2) ・Free vibration analysis of two degree of freedom system (2) ・Ratio of the amplitudes ・Modes of vibration	Make sure students have read chapter 5(pp.109-112).	90minutes
4.		Solve the problems written in the handout.	100minutes
5.	Forced vibration of two degree of freedom system ・Response of two degree of freedom system ・Dynamic vibration absorber (Tuned vibration absorber)	Make sure students have read chapter 5(pp.112-119).	90minutes
5.		Solve the problems written in the handout.	100minutes
6.	Midterm Exam 1	Review for Midterm Exam 1.	190minutes
7.	Lagrange’s equation ・Derivation of the equation of motion using Lagrange’s equation.	Make sure students have read chapter 5(pp.120-122).	90minutes
7.		Solve the problems written in the handout.	100minutes
8.	Modal analysis ・Orthogonality ・procedure for modal analysis	Make sure students have read chapter 6.	100minutes
8.	Modal analysis ・Orthogonality ・procedure for modal analysis	Solve the problems written in the handout.	90minutes
9.	Mechanism of the vibratory equipment ・Vibratory conveyance	Make sure students have read chapter 8.	100minutes
9.	Mechanism of the vibratory equipment ・Vibratory conveyance	Solve the problems written in the handout.	90minutes
10.	Midterm Exam 2	Review for Midterm Exam 2.	190minutes
11.	Vibration of strings and Transverse vibration of beams ・Equation of motion and boundary conditions ・Natural frequencies and mode shapes	Make sure students have read chapter 6(pp.146-161).	90minutes
11.		Solve the problems written in the handout.	100minutes
12.	Transverse vibration of beams (2) ・Natural frequencies and mode shapes ・Rayleigh’s energy method	Make sure students have read chapter 6(pp.162-164).	90minutes
12.		Solve the problems written in the handout.	100minutes
13.	Nonlinear vibration ・Free vibration ・Forced vibration ・Parametric excitation	Make sure students have read chapter 8(pp.175-194).	90minutes
13.		Solve the problems written in the handout.	100minutes
14.	Final Exam	Review what students learn in this course.	190minutes
Total.	-	-	2660minutes

Feedback on exams, assignments, etc.

ways of feedback	specific contents about "Other"
The Others	授業内および授業外で適宜フィードバックを行う．

Textbooks and reference materials

・教科書：岩田，佐伯，小松崎「機械振動学」(数理工学社)
・参考書：岩田，佐伯，小松崎「基礎演習　機械振動学」(数理工学社)
　　　　　その他，機械力学，振動工学に関する図書．

Prerequisites

Students are required to review "Fundamentals of Mechanical Vibrations".

Office hours and How to contact professors for questions

Thursday 10:00〜12:00

Regionally-oriented

Non-regionally-oriented course

Development of social and professional independence

Course that cultivates an ability for utilizing knowledge

Active-learning course

About half of the classes are interactive

Course by professor with work experience

Work experience	Work experience and relevance to the course content if applicable
Applicable	Work experience on Vibration Engineering is introduced.

Education related SDGs:the Sustainable Development Goals

4.QUALITY EDUCATION
9.INDUSTRY, INNOVATION AND INFRASTRUCTURE
12.RESPONSIBLE CONSUMPTION & PRODUCTION

Last modified : Sat Mar 08 04:21:07 JST 2025