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2024　Mechanical Vibrations

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Academic unit or major
Undergraduate major in Mechanical Engineering
Instructor(s)
Shino Motoki 
Class Format
Lecture / Exercise     
Media-enhanced courses
Day/Period(Room No.)
-
Group
-
Course number
MEC.D201
Credits
2
Academic year
2024
Offered quarter
3Q
Syllabus updated
2024/3/14
Lecture notes updated
-
Language used
Japanese
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Course description and aims

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 one-degree-of-freedom systems
3. Vibration analysis methods of two-degree-of-freedom systems

Student learning outcomes

By the end of this course, students will be able to:
1) Understand the natural frequency of one-degree-of-freedom vibration systems, frequency response, resonance, transmissibility (vibration isolation), etc., and understand and apply them to actual vibration problems．
2) Understand coupled natural frequencies and natural modes of two-degree-of-freedom vibration systems and explain the concept of modal analysis.
3) Understand principles of dynamic absorber and how to derive their optimum parameters with the fixed points theory.

Keywords

Free vibration and forced vibration for one-degree-of-freedom systems, Response characteristics of one-degree-of-freedom vibration systems subjected to harmonic excitation, Coupled natural frequencies and natural modes of two-degree-of-freedom systems, Dynamic absorber

Competencies that will be developed

✔ Specialist skills Intercultural skills Communication skills Critical thinking skills Practical and/or problem-solving skills
✔ This subject corresponds to the acquisition of basic technical skills in the learning objectives of 1.

Class flow

At the beginning of 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

  Course schedule Required learning
Class 1 Introduction to vibration phenomena Give some examples of vibration problems.
Class 2 One-degree-of-freedom systems - Equation of motions and free vibrations. Derive equation of motion, free vibration solution and natural angular frequency for undamped one-degree-of-freedom systems.
Class 3 Damped one-degree-of-freedom systems - Equation of motions and free vibrations. Derive equation of motion and its solution for damped one-degree-of-freedom systems. Explain critical damping and damped natural angular frequency.
Class 4 Response of one-degree-of-freedom systems to harmonic excitation force Derive response of one-degree-of-freedom systems to harmonic excitation force. Explain resonance phenomena for one-degree-of-freedom systems.
Class 5 Derivation of frequency response 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 one-degree-of-freedom systems subjected to harmonic excitation. Explain principles of vibration isolation.
Class 7 Response of one-degree-of-freedom systems to displacement excitation Derive frequency response of one-degree-of-freedom systems to displacement excitation.
Class 8 Midterm Examination Midterm Examination
Class 9 Response of one-degree-of-freedom systems to arbitrary excitation force Derive response of one-degree-of-freedom systems to arbitrary excitation force.
Class 10 Equations of motion and free vibration of two-degree-of-freedom systems Derive coupled natural frequencies from equations of motion of two-degree-of freedom systems.
Class 11 Modal analysis: Natural modes of two-degree-of-freedom systems Derive natural modes of two-degree-of-freedom systems.
Class 12 Time response of two-degree-of-freedom systems Express equations of motion of two degree-of-freedom system using modal coordinate.　Derive time responses of two-degree-of-freedom systems.
Class 13 Frequency response of two-degree-of-freedom systems Derive time responses and frequency response of two-degree-of-freedom systems.
Class 14 Dynamic Absorber Explain principles of dynamic absorber, and derive their optimum parameters with the fixed points theory.

Out-of-Class Study Time (Preparation and Review)

To enhance the effectiveness of learning, students are encouraged to refer to the textbook and handouts, review the contents of the class, and complete exercises in approximately 90 minutes after each lecture.

Textbook(s)

For example;
Mechanical Vibrations, J. P. Den Hartog
Schaum's Outline of Mechanical Vibrations (Schaum's Outlines), S Kelly

Reference books, course materials, etc.

The Japan Society of Mechanical Engineers，『JSME Text Series (6)　Mechanical Vibration』，ISBN-13: 978-4888981286　(Japanese).
Course materials are provided during class.

Assessment criteria and methods

・Report (every two lectures) 40%
・Midterm Examination 30% and Final Examination 30%（It may be replaced with assignment, if attendance is restricted.）

Related courses

  • MEC.A201 ： Engineering Mechanics
  • MEC.B211 ： Ordinary Differential Equations
  • MEC.B212 ： Complex Function Theory
  • MEC.P211 ： Basic Experiments for Mechanical Engineering

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

Not required.

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