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Mechanical Vibrations (Spring 2013) |
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| Course code : | ME-MEV-U1 | ||
| ECTS Credits : | 5 | Status : | Optional |
| Revised : | 22/04 2013 | Written : | 24/08 2009 |
| Placement : | 6. semester | Hours per week : | 4 |
| Length : | 1 semester | Teaching Language : | English |
| Objective : | To provide the students with a firm foundation for solving vibration problems related to structures and machines, using analytical and numerical methods. To give the students a basic background for advanced studies in dynamics and vibrations. A student who has met the objectives of the course will be able to: • Identify sources for inertia, stiffness, energy-dissipation and external loads in some standard mechanical systems. • Use Newton"s second law, free body diagrams and the energy method to derive the equations of motion (scalar or matrix-vector form) for simple models of mechanical systems with a finite or infinite number of degrees of freedom • Determine the natural frequencies for mechanical systems with a finite or infinite number of degrees of freedom. • Use analytical and numerical methods to solve standard equations of motion for mechanical system models. • Understand and explain eigenfunctions, eigenvectors and eigenvalues. • Identify resonance problems for mechanical systems whose dynamics (i.e. inertia and energy dissipation) can not be neglected. • Account for the limitations in the models and methods used, and predict the possible consequences of making simplified assumptions, especially linearization and limitation of the number of degrees of freedom. • Write technical reports, with correct description of theoretical and experimental procedures, in a clear way, using technical terms, giving physical interpretations and evaluations of results. • Use the computer software DAMA and MATLAB for solving vibration problems. • To give the students a basic background for advanced studies in dynamics and vibrations. • Read engineering literature on mechanical vibrations. |
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| Principal Content : | Equations of motion with initial conditions. Vibrations of linear single-degree-of-freedom systems: Free and forced vibrations for translation and rotation. Viscous damped systems and vibration isolators. Pendulums and mass moment of inertia. Vibrations of linear two-degree-of-freedom systems: Free and forced vibrations. Vibration absorbers. Viscous damping. Vibrations of continuous systems: Equations of motion for strings, bars and beams. Boundary and initial conditions. Eigenfunctions, eigenvectors and eigenvalues. Whirling shafts and Dunkerley’s formula. Finite Element Methods: Mass and Stiffness matrices and equations of motion for bar and beam expressed in Matrix form. Introduction to non-linear vibration. The software “DAMA” will be used to generate computer simulations and animations in order to enhance the students’ understanding of the motion and vibration of mechanical systems. |
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| Teaching method : | The teaching is both project-oriented and problem-based, using realistic systems. There will be lectures. 4 assignments and a project based upon experiments with Frequency Analyzer must both be handed in. MATLAB simulation will be use in the project. | ||
| Required prequisites : | ME-MAT1-U5 and ME-MEK2-U5 | ||
| Recommended prerequisites : | ME-MEK1-U5 | ||
| Relations : | Courses in numerical methods, control systems and advanced dynamics. | ||
| Type of examination : | Look under remarks | ||
| External examiner : | Internal | ||
| Marking : | 7 step scale | ||
| Remarks : | 30 minute oral examination based upon the assignments, setting up equations of motion and demonstrating how to solve practical vibration problems. 50 % of the grade will be based on the 4 assignments and the Project. This is a relevant course in the study of control systems and advanced dynamics and especially when doing bachelor project concerning vibration and noise. |
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| Teaching material : | Dynamics and Vibration: An Introduction, ISBN-13: 978-0-470-72300-5, by Magd Abdel Wahab, Wiley 2008. - Lecture notes on CampusNet. |
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