2021 Faculty Courses School of Environment and Society Department of Civil and Environmental Engineering Graduate major in Civil Engineering
Analysis of Vibrations and Elastic Waves
- Academic unit or major
- Graduate major in Civil Engineering
- Instructor(s)
- Sohichi Hirose
- Class Format
- Lecture
- Media-enhanced courses
- -
- Day of week/Period
(Classrooms) - 5-6 Tue / 5-6 Fri
- Class
- -
- Course Code
- CVE.A403
- Number of credits
- 200
- Course offered
- 2021
- Offered quarter
- 2Q
- Syllabus updated
- Jul 10, 2025
- Language
- English
Syllabus
Course overview and goals
This course gives fundamental theories and analytical methods for mechanical disturbances in solids like vibrations and elastic waves. In addition, various engineering applications related to wave theories will be presented.
Theories of vibrations and elastic waves are useful in various engineering fields, including structural dynamics, seismic engineering, ultrasonic nondestructive testing and so forth. This course aims to teach students basic mathematical theories of vibrations and waves in solids, and to suggest a unified approach to other wave phenomena, including acoustic waves and electromagnetic waves.
Course description and aims
By the end of this course, students will be able to:
1. Explain mathematically basic wave phenomena, including propagation, reflection, transmission, dispersion and scattering of waves.
2. Solve simple problems of one dimensional waves analytically.
3. Demonstrate wave phenomena of two or three dimensional waves using computational calculations.
4. Explain applications of vibrations and elastic waves in various engineering fields.
Keywords
wave propagation, reflection and transmission, dispersion, scattering, fundamental solution, integral expression, structural dynamics, earthquake engineering, ultrasonic nondestructive testing
Competencies
- Specialist skills
- Intercultural skills
- Communication skills
- Critical thinking skills
- Practical and/or problem-solving skills
Class flow
This course will be mainly provided in lecture style and are divided in three parts. The first part is related to the theories of one dimensional waves. The second part is for two or three dimensional waves. The last part is concerned with applications of wave theories in engineering fields. After lectures of the first part, midterm exam will be given to check the understanding of students.
Course schedule/Objectives
| Course schedule | Objectives | |
|---|---|---|
| Class 1 | Fundamental equations for one dimensional vibrations and waves | Explain the concept of fundamental equations for one dimensional vibrations and waves. |
| Class 2 | Reflection and transmission of one dimensional waves | Explain reflection and transmission of one dimensional waves, and solve some related problems analytically. |
| Class 3 | Dispersion of one dimensional waves | Explain dispersion of one dimensional waves, and solve some related problems analytically. |
| Class 4 | Free vibration in one dimensional problems | Explain one dimensional free vibration, and solve some related problems analytically. |
| Class 5 | Fundamental solutions and integral formulation for one dimensional problems | Explain fundamental solutions and integral formulation for one dimensional problems. |
| Class 6 | Integral expression and analysis of one dimensional waves | Explain integral expression and analysis of one dimensional waves, and solve some related problems analytically. |
| Class 7 | Review of theories of one dimensional problems | Review of theories of one dimensional problems and solve some related problems. |
| Class 8 | Fundamental equations for multidimensional vibrations and waves | Explain the concept of fundamental equations for multidimensional vibrations and waves. |
| Class 9 | Reflection and transmission of multidimensional waves | Explain reflection and transmission of multidimensional waves, and solve some related problems numerically. |
| Class 10 | Dispersion of multidimensional waves | Explain dispersion of multidimensional waves, and solve some related problems numerically. |
| Class 11 | Scattering of multidimensional waves | Explain scattering of multidimensional waves, and solve some related problems numerically. |
| Class 12 | Fundamental solutions and integral formulation for multidimensional problems | Explain fundamental solutions and integral formulation for multidimensional problems. |
| Class 13 | Integral expression and analysis of multidimensional waves | Explain integral expression and analysis of multidimensional waves, and solve some related problems numerically. |
| Class 14 | Application of vibration and elastic waves in seismic engineering | Explain application of vibration and elastic waves in engineering. |
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)
None required.
Reference books, course materials, etc.
Lecture materials will be uploaded on OCW-i.
Karl F. Graff, Wave Motion in Elastic Solids, Oxford: Clarendon Press, 1975. (Paperback 1991, ISBN: 080-0759667451)
J. D. Achenbach，Wave Propagation in Elastic Solids, Amsterdam : North-Holland, 1973. (Paperback 1984, ISBN: 978-0-7204-0325-1)
Evaluation methods and criteria
Assignment(50%) and midterm examination(50%)
Related courses
- CVE.A210 ： Structural Dynamics in Civil Engineering
Prerequisites
Students must have successfully completed Structural Dynamics in Civil Engineering （CVE.A210) or have equivalent knowledge. To solve assignment problems, programming skills may be required.