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.
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.
- 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
| 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 |
| 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 |
| 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 |
| 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 |
| 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 |
| Solve the problems written in the handout. | 100minutes | ||
| 8. | Modal analysis ・Orthogonality ・procedure for modal analysis |
Make sure students have read chapter 6. | 100minutes |
| Solve the problems written in the handout. | 90minutes | ||
| 9. | Mechanism of the vibratory equipment ・Vibratory conveyance |
Make sure students have read chapter 8. | 100minutes |
| Solve the problems written in the handout. | 90minutes | ||
| 10. | Midterm Exam 2 | Review for Midterm Exam 2. | 190minutes |
| 11. | Vibration of strings ・Equation of motion and boundary conditions ・Natural frequencies and mode shapes |
Make sure students have read chapter 6(pp.146-151). | 90minutes |
| Solve the problems written in the handout. | 100minutes | ||
| 12. | Transverse vibration of beams (1) ・Equation of motion and boundary conditions |
Make sure students have read chapter 6(pp.159-161). | 90minutes |
| Solve the problems written in the handout. | 100minutes | ||
| 13. | 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 |
| Solve the problems written in the handout. | 100minutes | ||
| 14. | Final Exam | Review what students learn in this course. | 190minutes |
| Total. | - | - | 2660minutes |
| 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% | - |
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.
Mid-term exam 1: 20%
Mid-term exam 2: 20%
Final exam: 60%
Scored larger than 60 points will be passed.
・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．
・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．
- Course that cultivates an ability for utilizing knowledge
| Work experience | Work experience and relevance to the course content if applicatable |
|---|---|
| Applicatable | Work experience on Vibration Engineering is introduced. |
Last modified : Sat Oct 26 04:07:38 JST 2019