2017 Theory of Oscillations

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Academic unit or major
Undergraduate major in Systems and Control Engineering
Kimura Koji 
Course component(s)
Day/Period(Room No.)
Tue5-6(W932)  Fri5-6(W932)  
Course number
Academic year
Offered quarter
Syllabus updated
Lecture notes updated
Language used
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Course description and aims

Vibration phenomena are observed in nature and in daily life. They are related to the performance, efficiency and safety of machines and structures. Learning the theory of vibrations is useful and necessary to understand the characteristics of various kinds of vibration phenomena, solve the vibration problems in engineering and also design the use of vibrations. This course covers from single to multi degree of freedom systems and continuous systems. The course focuses on considering the underlying principles and the characteristics of vibrations of each system.

Student learning outcomes

By the end of this course, the students will be able to:
1) Understand the basic concepts of vibrations
2) Learn the systematic approach to vibrations.
3) Explain the characteristics of various kinds of vibration phenomena.


Vibration Phenomena, Free Vibration, Forced Vibration, Transient Vibration, Parametric Vibration, Single Degree of Freedom Systems,
Multi Degree of Freedom Systems, Continuous Systems, Advanced Vibrations

Competencies that will be developed

Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills

Class flow

At the beginning of each class, the points of the previous class are reviewed. Towards the end of class, the subjects planned on that day will be explained and discussed.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Introduction to Vibration  -Vibration, Harmonic motion Various kinds of vibration phenomena
Class 2 Single Degree of Freedom Systems: Undamped Free Vibrations  -Various oscillatory systems, Natural frequency Characteristics of free vibrations
Class 3 Single Degree of Freedom Systems: Damped Free Vibrations  -Resistance force and damping, Damping ratio, Logarithmic decrement Characteristics of damped free vibrations
Class 4 Single Degree of Freedom Systems: Forced Vibration ・Vibration response to harmonic excitatios, Resonance, Transmissibility Characteristics of vibration response to harmonic excitations
Class 5 Single Degree of Freedom Systems: Forced Vibration (Base Displacement Excitations)  -Vibrometer and seismogragh Characteristics of vibration response to base displacement excitations, Principle of vibrometer
Class 6 Single Degree of Freedom Systems: Vibration of Rotating Shaft  -Critical speed, Whirling motion Various kinds of rotating machines
Class 7 Single Degree of Freedom Systems: Transient Vibration  -Impulse response, Step response, Response to pulse excitations Characteristics of transient vibration
Class 8 Two Degree of Freedom Systems: Free Vibrations  -Coupled vibration, Coupled natural frequencies, Principal vibrations Characteristics of coupled vibration
Class 9 Two Degree of Freedom Systems: Forced Vibration  -Mass-spring system, Damped system, Dynamic vibration absorber Characteristics of forced vibration, Principle of dynamic vibration absorber
Class 10 Multi Degree of Freedom Systems: Free Vibrations  -Natural vibration mode Natural vibration mode
Class 11 Multi Degree of Freedom Systems: Forced Vibration  -Modal analysis Modal analysis
Class 12 Vibration of Continuous Systems  -From system with MDOF to continuous, Various continuous systems Expression of vibration of continuous systems
Class 13 Vibration of Continuous Systems  -Vibration of string, Bending vibration of beam Characteristics of vibration of continuous systems
Class 14 Parametric Vibrations  -Parametrically excited systems, Simple example Characteristics of parametric vibrations
Class 15 Advanced Vibrations  -Flow induced vibrations, aseismic design, nonlinear oscillation, random vibration and so on Vibrations in various research fields


None Required

Reference books, course materials, etc.

None Required

Assessment criteria and methods

1) Students will be assessed on their understanding of the basic theory and its application associated with vibrations.
2) Students’ course scores are based on final exam and exercise reports.

Related courses

  • SCE.M201 : Fundamental Kinematics and Kinetics for Mechanical Systems
  • SCE.M202 : Fundamentals of Analytical Dynamics (Systems and Control)

Prerequisites (i.e., required knowledge, skills, courses, etc.)

No prerequisites

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