2024 Faculty Courses School of Engineering Undergraduate major in Mechanical Engineering
Vibration Analysis
- Academic unit or major
- Undergraduate major in Mechanical Engineering
- Instructor(s)
- Hiroki Takahara / Yutaka Nakano
- Class Format
- Lecture (Face-to-face)
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 1-4 Thu
- Class
- -
- Course Code
- MEC.D311
- Number of credits
- 200
- Course offered
- 2024
- Offered quarter
- 1Q
- Syllabus updated
- Mar 14, 2025
- Language
- Japanese
Syllabus
Course overview and goals
【Course description】
The course teaches vibration analysis of multi degree of freedom system, continuum such as a string, beam and membrane. It also teaches how to analyze nonlinear vibration systems.
【Aims】
The real vibration system is usually multi-degree-of freedom system, but it's necessary to choose an appropriate model to analyze vibration behavior for vibration reduction. The aim of this course is to learn about vibration behavior in a typical model of multi-degree-of freedom system and to understand analysis method and its characteristics of nonlinear vibration.
Course description and aims
By the end of this course, students will be able to:
1. Obtain the natural frequencies and the natural vibration modes of multi degree of freedom vibration systems and the fundamental continuous vibration systems (Ex. Strings, Beams).
2. By using modal analysis, obtain the time histories of free vibration and the frequency responses of continuous vibration systems.
3. Explain the characteristics of nonlinear vibrations.
4. By the analytical methods, obtain the backbone curves and frequency responses of nonlinear vibration systems.
5. Explain the characteristics of self-excited vibrations and parametric vibrations.
Keywords
multi-degree-of-freedom system, distributed parameter system, non-linear vibration, parametric vibration, self excitation system
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
- This class aims at learning 6 and 7 of learning objective.
Class flow
At the beginning of each class, solutions to exercise problems that were assigned during the previous class are reviewed. Towards the end of class, students are given exercise problems related to the lecture given that day to solve. To prepare for class, students should read the course schedule section and check what topics will be covered. Required learning should be completed outside of the classroom for preparation and review purposes.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Overview of vibration problems of mechanical systems | Understand how vibration occurs and how vibration becomes a problem. |
| Class 2 | Kinetic equation of multi-degree-of-freedom system, natural frequencies and eigenmodes | Build kinetic equation and calculate natural frequencies and their eigenmodes. |
| Class 3 | Forced and base excitation response of multi-degree-of-freedom system | Draw simple overview of forced and base excitation response and explain it. |
| Class 4 | Distributed parameter systems: Vibration behavior, natural frequencies and eigenmodes of string | Calculate natural frequencies and eigenmodes of a string. |
| Class 5 | Distributed parameter systems: Mode expansion of string and axial vibration of rod | Understand mode expansion with string and axial vibration of rod. |
| Class 6 | Distributed parameter systems: Vibration of beam | Understand vibration behavior of bending beam. |
| Class 7 | Distributed parameter systems: Vibration of rectangular memblane | Understand vibration behavior of rectangular memblane. |
| Class 8 | Distributed parameter systems: Vibration of circlular memblane | Understand vibration behavior of circular memblane. |
| Class 9 | Non-linear vibration's characteristics | Understand non-linear vibration behaviors. |
| Class 10 | Understand non-linear vibration behaviors. | Understand perturbation method. |
| Class 11 | Non-linear vibration analysis: Average method | Understand approximate solution with average method. |
| Class 12 | Non-linear vibration analysis: Stability of steady solution and methodo of harmonic balance | Understand method of harmonic balance and stability of non-linear vibration. |
| Class 13 | Non-linear vibration analysis: Self excited vibration | Understand self excited vibration. |
| Class 14 | Non-linear vibration analysis: Parametric vibration, Review of the whole course. | Understand parametric vibration. Review of the whole course. |
Study advice (preparation and review)
To enhance effective learning, students are encouraged to spend approximately 100 minutes preparing for class and another 100 minutes reviewing class content afterwards (including assignments) for each class.
They should do so by referring to textbooks and other course material.
Textbook(s)
Not specified.
Reference books, course materials, etc.
Upload course materials to T2SCHOLA.
Evaluation methods and criteria
To be evaluated based on the final exam(70％) and the assignments(30％) given during the lecture. When the final exam is not available, to be evaluated based on the assignments given during the lecture.
Related courses
- MEC.D201 ： Mechanical Vibrations
Prerequisites
Students should have completed Mechanical Vibrations(MEC.D201) or have equivalent knowledge.
In FY2024, students who enrolled after April 1, 2023 (23B) will not be able to register for this course.