The course teaches on the following contents as the basis of measures against vibration problems.
1. Equation of motion
2. Vibration characteristics (natural frequency, frequency response) of a single degree of freedom sysmtem
3. Vibration analysis methods of two degrees of freedom systems
By the end of this course, students will be able to:
1) Understand natural frequency of single degree of freedom systems, frequency response, resonance, transmissibility(vibration isolation), comlex vector, etc., and solve actual vibration problems．
2) Understand coupled natural frequencies and natural modes of two degrees of freedom systems, and explain the consept of modal analysis.
3) Understand principles of dynamic absorber and how to derive their optimum parameters with the fixed points theory.
Free vibration and forced vibration for single degree of freedom systems，Response characteristics of single degree of freedom systems subjected to harmonic excitation，Coupled natural frequencies and natural modes of two degree of freedom systems，Dynamic absorber
✔ Specialist skills | Intercultural skills | Communication skills | Critical thinking skills | Practical and/or problem-solving skills |
At the beginning of each class, overview and highlights of the previous class are reviewed. To allow students to get a good understanding of the course contents and practice application, exercise problems related to the contents of this course are provided.
Course schedule | Required learning | |
---|---|---|
Class 1 | Introduction to vibration phenomena | Give some examples of vibration problems. |
Class 2 | Two degrees freedom systems - Equation of motions and free vibrations. | Derive equation of motion, free vibaration solution and natural angular frequency for undamped single degree freedom systems. |
Class 3 | Damped single degree freedom systems - Equation of motions and free vibrations. | Derive equation of motion and its solution for damped single degree freedom systems. Explain critical damping and damped natural angular frequency. |
Class 4 | Response of single degree of freedom systems to harmonic excitation force | Derive response of single degree of freedom systems to harmonic excitation force. Explain resonance phenomena for single degree of freedom systems. |
Class 5 | Derivation of frequency response function using complex harmonic function | Derive frequency response function of single degree of freedom systems using complex harmonic function. |
Class 6 | Properties of frequency response curve and vibration isolation | Derive transmissibility of single degree of freedom systems subjected to harmonic excitation. Explain principles of vibration isolation. |
Class 7 | Response of single degree of freedom systems to displacement excitation | Derive frequency response of single degree of freedom systems to displacement excitation. |
Class 8 | Response of single degree of freedom systems to arbitary excitation force | Derive response of single degree of freedom systems to arbitary excitation force. |
Class 9 | Two degrees freedom systems - Equation of motions and free vibrations. | Derive coupled natural frequencies from equations of motion of two degrees of freedom systems. |
Class 10 | Modal analysis: Natural modes of two degrees of freedom system | Derive natural modes of two degrees of freedom systems. |
Class 11 | Orthogonality of natural modes and modal expansion | Prove the orthoganality of natural modes. |
Class 12 | Time response of two degrees of freedom systems | Express equations of motion of two degrees of freedom systems using modal coordinate. Derive time responses of two degrees of freedom systems. |
Class 13 | Frequency response of two degrees of freedom systems | Derive time responses and frequency response of two degrees of freedom systems. |
Class 14 | Dynamic Absorber | Explain principles of dynamic absorber, and derive their optimum parameters with the fixed points theory. |
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.
For example;
Mechanical Vibrations, J. P. Den Hartog
Schaum's Outline of Mechanical Vibrations (Schaum's Outlines), S Kelly
The Japan Society of Mechanical Engineers，『JSME Text Series (6) Mechanical Vibration』，ISBN-13: 978-4888981286 (Japanese).
Course materials are provided during class.
・ Small examination (every week: every two lectures) 100%
Not required.