ME579 NONLINEAR VIBRATIONS
| Course Code: | 5690579 |
| METU Credit (Theoretical-Laboratory hours/week): | 3 (3.00 - 0.00) |
| ECTS Credit: | 8.0 |
| Department: | Mechanical Engineering |
| Language of Instruction: | English |
| Level of Study: | Graduate |
| Course Coordinator: | Prof.Dr. ENDER CİĞEROĞLU |
| Offered Semester: | Fall and Spring Semesters. |
Course Objectives
The main objective of the course is to develop skills to model and analyze systems with nonlinearities. At the end of this course, students will be able to identify nonlinear systems and nonlinearities. They will be able to solve set of nonlinear algebraic equations. Students will be able to obtain forced response of nonlinear systems in frequency domain using Describing Function Method and Harmonic Balance Method. They will be able to perform forced response analysis of nonlinear systems considering higher harmonics in the solution. Students will be able to obtain steady-state periodic response of nonlinear systems with many degrees of freedom. They will be able to model dry friction and obtain periodic response of systems with dry friction damping.
Course Content
Introduction to nonlinear systems, phase plane analysis, bifurcations. Averaging and perturbation methods. Forced response in frequency domain. Solution of systems of nonlinear algebraic equations, Newtons method, path following methods for nonlinear equations. Describing functions, Describing Function Method (DFM). Harmonic Balance Method (HBM), multi harmonic HBM. Nonlinear forced response of structures having many degrees of freedom, receptance methods, model summation methods. Modeling dry fiction, one and two dimensional dry fiction models, mixed frequency and time domain methods. Vibrations of systems with dry fiction.
Course Learning Outcomes
Students, who pass the course satisfactorily will be able to:
- identify nonlinear system and types of nonlinearities
- solve systems of nonlinear algebraic equations
- apply Describing Function Method to solve nonlinear systems in frequency domain
- apply Harmonic Balance Method to solve nonlinear systems in frequency domain
- obtain solution of nonlinear systems by using single or multiple harmonics
- use Adaptive Harmonic Balance Methods to efficiently solve problems utilizing multi-harmonics
- solve large ordered nonlinear systems by using state of the art solution methods
- understand nonlinear normal modes and response dependent nonlinear normal modes
- determine stick, slip and separation transitions in dry friction modeling
Program Outcomes Matrix
| Contribution | |||||
| # | Program Outcomes | No | Yes | ||
| 1 | Acquires the fundamental scientific knowledge required to analyze and solve advanced-level problems in the field of mechanical engineering. | ✔ | |||
| 2 | Gains the competence to utilize advanced engineering mathematics methods in the formulation, analysis, and solution of engineering problems. | ✔ | |||
| 3 | Conducts literature reviews using printed and online sources, analyzes the collected literature, and identifies the current state-of-the-art in the relevant scientific field. | ✔ | |||
| 4 | Demonstrates the ability to prepare and deliver a seminar on a technical subject. | ✔ | |||
| 5 | Develops the ability to conduct independent research on a specific topic and solve advanced engineering problems. | ✔ | |||
| 6 | Contributes to the national and/or international body of knowledge through original research. | ✔ | |||
| 7 | Gains the competence to effectively communicate the process and results of research conducted on a specific subject through scientifically structured written reports and oral presentations. | ✔ | |||
| 8 | Acquires the ability to publish research findings as articles in national and/or international scientific journals and/or present them as papers at conferences. | ✔ | |||
| 9 | Acts in accordance with universal principles of research and publication ethics. | ✔ | |||