【Course description】
The course teaches the vibration characteristics of single degree freedom systems(natural frequency, frequency response, resonance, etc.) and the vibration analysis methods of two degrees of freedom systems which are the fundamentals of mechanical vibrations.
【Aims】
Students learn the fundamental vibration analysis methods for single degree of freedom systems and two degrees of freedom systems and can classify various machhine vibrations which are important in engneering and sensitivity. They will be able to solve unknown vibration problems.
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 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
Intercultural skills | Communication skills | Specialist skills | Critical thinking skills | Practical and/or problem-solving skills |
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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 usual once every 5 lessons.
Course schedule | Required learning | |
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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 | Exercise problems | Solve exercise problems related to the contents of this course from class 2 to class 4. |
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 | Derivation of frequency response function using complex harmonic function | Derive frequency response function of single degree of freedom systems using complex harmonic function. |
Class 8 | Response of single degree of freedom systems to displacement excitation | Derive frequency response of single degree of freedom systems to displacement excitation. |
Class 9 | Response of single degree of freedom systems to arbitary excitation force | Derive response of single degree of freedom systems to arbitary excitation force. |
Class 10 | Exercise problems | Solve exercise problems related to the contents of this course from class 6 to class 9. |
Class 11 | 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 12 | Natural modes of two degrees of freedom systems and Orthogonality of natural modes | Derive natural modes of two degrees of freedom systems. Prove the orthoganality of natural modes. |
Class 13 | Modal analysis | Express equations of motion of two degrees of freedom systems using modal coordinate. |
Class 14 | Time response and frequency response of two degrees of freedom systems | Derive time responses and frequency response of two degrees of freedom systems. |
Class 15 | Dynamic Absorber | Explain principles of dynamic absorber, and derive their optimum parameters with the fixed points theory. |
None required.
The Japan Society of Mechanical Engineers，『JSME Text Series (6) Mechanical Vibration』，ISBN-13: 978-4888981286 (Japanese).
Course materials are provided during class.
Learning achievement is evaluated by exercise problems and a final exam.
Not required.