ME526 VIBRATION OF CONT.SYS.WITH COMPUT.METH
| Course Code: | 5690526 |
| 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
By the end of this course, students will be able to:
- Understand the principles of analytical dynamics and their application to continuous structural systems.
- Apply Hamilton’s principle to derive partial differential equations of motion.
- Formulate and solve boundary-value and eigenvalue problems for vibration analysis.
- Determine the natural vibration modes of strings, rods, beams, and membranes using analytical methods.
- Apply computational methods such as Rayleigh’s method, Rayleigh–Ritz, assumed modes, and weighted residual techniques.
- Compare exact and approximate solution methods for the response of undamped continuous systems.
- Integrate theoretical and computational approaches to model and simulate structural and mechanical systems.
Course Content
Generalized coordinates and Hamilton's principle. Boundary value problem. The eigenvalue problem and generalized orthogonality. Vibration of strings, bars and membranes. Variational methods in vibration of plates. Approximate methods. Classical and variational methods in conjunction with finite difference technique. Modal analysis and response of undamped continuous systems. (R/F)
Course Learning Outcomes
Students who successfully complete the course will be able to:
- Apply elasticity, strain energy concepts, and Hamilton’s principle to derive governing partial differential equations of motion and boundary conditions for continuous systems.
- Formulate eigenvalue problems and determine natural modes of vibration using analytical methods.
- Determine natural modes of vibration for strings, rods, beams, and membranes using computational techniques.
- Compute the free and forced responses of undamped continuous systems through exact modal analysis and approximate solution methods.
- Interpret and apply the results of both exact and approximate methods to practical engineering applications.
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. | ✔ | |||