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Mechanical Vibrations (Fall 2010) |
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| Course code : | ME-MEV-U1 | ||
| ECTS Credits : | 5 | Status : | Optional |
| Revised : | 10/12 2009 | 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. • 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 computer softwares, currently DAMA, MATLAB and SolidWorks, for the solution and the graphical illustration of vibration problems. |
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| Principal Content : | 1) Vibrations of linear single-degree-of-freedom systems: Free and forced vibrations; viscous damped systems; vibration isolators. 2) Vibrations of linear two-degree-of-freedom systems: Equations of motion; free and forced vibrations; vibration absorbers; viscous damping. 3) Vibrations of continuous systems: Flexural, axial and torsional vibrations of strings, cables, bars and beams; whirling shafts; Dunkerley’s formula. 4) Finite Element Methods: Mass & stiffness matrices and equations of motion for bar and beam elements. The LabView 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 introductory and summing up lectures. Project work in small groups includes tutorial exercises, physical experiments and demonstrations, computer simulations, use of internet search engines and case studies. Each group should submit a report, which contains the project work and solutions of the assigned problems. | ||
| Required prequisites : | Applied Mathematics 1 and Applied Mechanics 2. | ||
| Recommended prerequisites : | Applied Mechanics 1. | ||
| Relations : | Courses in numerical analysis, linear algebra, control systems and advanced dynamics. | ||
| Type of examination : | Look under remarks | ||
| External examiner : | External | ||
| Marking : | 7 step scale | ||
| Remarks : | Oral examination based on a number of course assignments. The final evaluation of each student will be based on an assessment of the presentation of assignments and the group report. This course is primarily for students enrolled in the study program “Engineering Design & Industrial Innovation” offered by the Department of Mechanical Engineering. |
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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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| Responsible teacher : | Imad Abou-Hayt
, iabo@dtu.dk |
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