2017 Vibration Analysis B

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Academic unit or major
Undergraduate major in Mechanical Engineering
Okuma Masaaki  Yamaura Hiroshi  Takahara Hiroki  Matsumura Shigeki  Nakano Yutaka 
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Course description and aims

【Course description】
The course teaches vibration analysis of multi degree of freedom system, continuum such as a string, beam and membrane. It also teaches how to analyze nonlinear vibration systems.

The real vibration system is usually multi-degree-of freedom system, but it's necessary to choose an appropriate model to analyze vibration behavior for vibration reduction. The aim of this course is to learn about vibration behavior in a typical model of multi-degree-of freedom system and to understand analysis method and its characteristics of nonlinear vibration.

Student learning outcomes

Aim of this course is to understand various analysis method of mechanical vibration for multi-degree-of-freedom systems and non-linear vibration systems and know how to apply for real vibration problems.


multi-degree-of-freedom system, distributed parameter system, non-linear vibration, parametric vibration, self excitation system

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, solutions to exercise problems that were assigned during the previous class are reviewed. Towards the end of class, students are given exercise problems related to the lecture given that day to solve. To prepare for class, students should read the course schedule section and check what topics will be covered. Required learning should be completed outside of the classroom for preparation and review purposes.

Course schedule/Required learning

  Course schedule Required learning
Class 1 Overview of vibration problems of mechanical systems Understand how vibration occurs and how vibration becomes a problem.
Class 2 Kinetic equation of multi-degree-of-freedom system, natural frequencies and eigenmodes Build kinetic equation and calculate natural frequencies and their eigenmodes.
Class 3 Forced and base excitation response of multi-degree-of-freedom system Draw simple overview of forced and base excitation response and explain it.
Class 4 Distributed parameter systems: Vibration behavior, natural frequencies and eigenmodes of string Calculate natural frequencies and eigenmodes of a string.
Class 5 Distributed parameter systems: Mode expansion of string and axial vibration of rod Understand mode expansion with string and axial vibration of rod.
Class 6 Distributed parameter systems: Vibration of beam Understand vibration behavior of bending beam.
Class 7 Distributed parameter systems: Vibration of rectangular memblane Understand vibration behavior of rectangular memblane.
Class 8 Distributed parameter systems: Vibration of circlular memblane Understand vibration behavior of circular memblane.
Class 9 Distributed parameter systems: Vibration of plate Distributed parameter systems: Vibration of plate
Class 10 Non-linear vibration's characteristics Understand non-linear vibration behaviors.
Class 11 Understand non-linear vibration behaviors. Understand perturbation method.
Class 12 Non-linear vibration analysis: Average method Understand approximate solution with average method.
Class 13 Non-linear vibration analysis: Stability of steady solution and methodo of harmonic balance Understand method of harmonic balance and stability of non-linear vibration.
Class 14 Non-linear vibration analysis: Parametric vibration and self excited vibration Understand parametric vibration and self excited vibration.
Class 15 Overview of vibration measurement, diagnosis and analysis Understand how to measure, diagnose and analyze real mechanical system's vibration behavior.


Not specified.

Reference books, course materials, etc.

Course materials are provided during class.

Assessment criteria and methods

Learning achievement is evaluated by exercise problems and a final exam.

Related courses

  • MEC.D201 : Mechanical Vibrations

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

Students should have completed Mechanical Vibrations(MEC.D201) or have equivalent knowledge.

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