COURSE UNIT TITLE

: NON-LINEAR VIBRATION

DEGREE PROGRAMMES

Description of Individual Course Units

Course Unit Code Course Unit Title Type Of Course D U L ECTS
MEE 5026 NON-LINEAR VIBRATION ELECTIVE 3 0 0 8

Offered By

Graduate School of Natural and Applied Sciences

Level of Course Unit

Second Cycle Programmes (Master's Degree)

Course Coordinator

PROFESSOR MUSTAFA SABUNCU

Offered to

Machine Theory and Dynamics
Machine Theory and Dynamics

Course Objective

The objective of this course is to teach the analysis of nonlinear continuous systems rather than discrete system models. Starting with single degree of freedom systems with nonlinear stiffness and damping and variable inertia problems, various analytical, graphical and numerical techniques, including stability analysis are discussed. A concise treatment of variational principles and their application to vibration problems is given in the course.

Learning Outcomes of the Course Unit

1   To realize Nonlinear systems.
2   To formulate To formulate mathematical models of nonlinear systems.
3   To solve the equations of motions of free oscillations of nonlinear systems.
4   To solve the equations of motions of forced oscillations of nonlinear systems.
5   To make the dynamic stability analysis of nonlinear vibrational systems.

Mode of Delivery

Face -to- Face

Prerequisites and Co-requisites

None

Recomended Optional Programme Components

None

Course Contents

Week Subject Description
1 Nonlinear vibration of simple systems: Perturbation method, Periodic solution of damped system
2 Modifed Euler method, Runge Kutta method, Phase plane method
3 Routh-Hurwitz criteria, Direct stability method, Floquet's theory of stability
4 Mathieu's equation
5 Forced oscillations of nonlinear systems: Harmonic oscillations of Duffing's equation
6 Stability of Duffng's equation, Transient behavior of forced oscillations, Transient behaviour in phase plane
7 1st Mid-term.
8 Higher harmonic oscillations, Subharmonic oscillations, Perturbation method for forced oscillations. Phase plane delta method
9 Variational principles, Calculus of a single variable, First variation, The delta operator
10 Case of several dependent variables, Functional with higher order derivatives, Boundary conditions, Functional with two depended variables
11 Functional containing integrals, Principle of virtual work, Hamilton's principle
12 2nd Mid-term.
13 Complementary virtual work, Reissner's principle, Lagrange method
14 Ritz method, Galerkin method

Recomended or Required Reading

J.S.RAO, Advance Theory of Vibration (Nonlinear Vibration and One Dimensional Structures), Mc Willey Eastern Publication. 1992.

Planned Learning Activities and Teaching Methods

Presentation + Application + Homework

Assessment Methods

SORTING NUMBER SHORT CODE LONG CODE FORMULA
1 MTE 1 MIDTERM EXAM 1
2 MTE 2 MIDTERM EXAM 2
3 ASG ASSIGNMENT
4 FIN FINAL EXAM
5 FCG FINAL COURSE GRADE MTE 1 * 0.20 + MTE 2 * 0.20 + ASG * 0.10 + FIN * 0.50
6 RST RESIT
7 FCGR FINAL COURSE GRADE (RESIT) MTE 1 * 0.20 + MTE 2 * 0.20 + ASG * 0.10 + RST * 0.50


Further Notes About Assessment Methods

None

Assessment Criteria

Homeworks are assigned to the students after the weekly lessons. Students strengthen their learning by solving homeworks. The successes of the students are evaluated by mid-term exams, homework and the final exam.

Language of Instruction

English

Course Policies and Rules

To be announced.

Contact Details for the Lecturer(s)

1-Dokuz Eylül University, Faculty of Engineering, Department of Mechanical Engineering, e-mail:: mustafa.sabuncu@deu.edu.tr , phone: 0 232 3019208.

2-Dokuz Eylül University, Graduate School of Natural and Applied Sciences, e-mail:: mustafa.sabuncu@deu.edu.tr , phone: 0 232 3017999.

Office Hours

Will be announced by the instructor according to the weekly schedule.

Work Placement(s)

None

Workload Calculation

Activities Number Time (hours) Total Work Load (hours)
Lectures 12 3 36
Preparation before/after weekly lectures 12 7 84
Preparation for Mid-term Exam 2 20 40
Preparation for Final Exam 1 18 18
Preparing Individual Assignments 1 11 11
Preparing Presentations 1 6 6
Final 1 2 2
Midterm 2 2 4
TOTAL WORKLOAD (hours) 201

Contribution of Learning Outcomes to Programme Outcomes

PO/LOPO.1PO.2PO.3PO.4PO.5PO.6PO.7PO.8PO.9PO.10PO.11PO.12PO.13PO.14PO.15
LO.1324224322233233
LO.2325224322233233
LO.3325334323333333
LO.4435334333334333
LO.5434344333334333

CONTACT INFORMATION
Dokuz Eylül Üniversitesi Cumhuriyet Bulvarı No: 144 35210 Alsancak / İZMİR
Phone: +90(232) 412 12 12 - Fax: +90 (232) 464 81 35

Copyright 2015 DEÜ. BİD

HOME / ABOUT US / DEGREE PROGRAMMES / GENERAL INFORMATION FOR STUDENTS / INTERNATIONAL RELATIONS