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.
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.
wave propagation, reflection and transmission, dispersion, scattering, fundamental solution, integral expression, structural dynamics, earthquake engineering, ultrasonic nondestructive testing
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
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 | Required learning | |
---|---|---|
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 | Fundamental solutions and integral formulation for multidimensional problems | Explain fundamental solutions and integral formulation for multidimensional problems. |
Class 12 | Integral expression and analysis of multidimensional waves | Explain integral expression and analysis of multidimensional waves, and solve some related problems numerically. |
Class 13 | Application of vibration and elastic waves in structural dynamics | Explain application of vibration and elastic waves in structural dynamics. |
Class 14 | Application of vibration and elastic waves in seismic engineering | Explain application of vibration and elastic waves in seismic engineering. |
Class 15 | Application of vibration and elastic waves in ultrasonic nondestructive testing | Explain application of vibration and elastic waves in ultrasonic nondestructive testing. |
None required.
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)
Assignment(50%) and midterm examination(50%)
Students must have successfully completed Structural Dynamics in Civil Engineering （CVE.A210) or have equivalent knowledge.