Code: | PRODEM013 | Acronym: | DE |
Keywords | |
---|---|
Classification | Keyword |
OFICIAL | Mechanical Engineering |
Active? | Yes |
Responsible unit: | Applied Mechanics Section |
Course/CS Responsible: | Doctoral Program in Mechanical Engineering |
Acronym | No. of Students | Study Plan | Curricular Years | Credits UCN | Credits ECTS | Contact hours | Total Time |
---|---|---|---|---|---|---|---|
PRODEM | 1 | Syllabus since 2009/10 | 1 | - | 6 | 28 | 162 |
Objectives: - analytical and experimental modelling of mechanical systems to analyse dynamic behaviour; - analytical/numerical techniques of dynamic models resolution to determine dynamic properties and the response of mechanical systems; - vibration control
It is expected that at the end of the semester, the student:
• knows the main basic concepts of structural dynamics (stiffness, inertia, damping, natural frequencies, mode shapes,....);
• is able to understand the dynamic behaviour of structures;
• is able to define physical models and establish mathematical models for structural dynamic analysis;
• is able to solve the models established;
• is able to criticise the results;
• is able to design a structures so that its dynamical properties are the ones desired for a particular application.
1. Introduction
Motivation and brief review of vibration of one degree of freedom systems.
2. Equations of motion of discrete systems
Direct application of Newton’s second law. Influence coefficients. Principle of virtual work. Kinetic and potential energy. Hamilton’s principle. Lagrange equations.
3. Free vibrations of n-degree of freedom systems (brief review)
Natural modes of vibration. Orthogonality and normalization of modes of vibration. Free or natural response. Expansion theorem. Rayleigh’s quotient.
4. Forced vibrations of n-degree of freedom systems (brief review)
Response to harmonic load. Modal overlapping. Truncated modal superposition.
5. Continuous Systems – Structural Elements
Transverse vibration of cables, longitudinal vibration of bars and torsion vibration. Beam flexion vibration (Bernoulli- Euler). Transverse vibration of membranes. Transverse vibration of plates.
6. Approximation methods
Rayleigh-Ritz method; Galerkin method and finite element method
7. Numerical methods to determine natural frequencies and vibration
Iteraction method of vectors and Jacobi method.
8. Numerical Integration of equations of motion
Centred finite differences method. Linear acceleration method. Wilson-theta method. Newmark method.
9. Additional topics in continuous systems: Timoshenko’s model for beams. Beams under axial load. Beams on elastic foundations. Beams under live loads.
10. Introduction to experimental modal analysis
Frequency response functions (FRFs), modal expansion of FRFs, modal parameters identification, FRFs measurement, estimators.
Exposition of the topics, exercises and essay.
Designation | Weight (%) |
---|---|
Exame | 100,00 |
Total: | 100,00 |
Designation | Time (hours) |
---|---|
Elaboração de relatório/dissertação/tese | 8,00 |
Estudo autónomo | 100,00 |
Frequência das aulas | 56,00 |
Trabalho laboratorial | 8,00 |
Total: | 172,00 |
Students cannot miss more classes than allowed by the rules.
Final Grade (FG): Final Grade is based on the grade of the exam
EXAM (EX): Written exam graded from 0 to 20. It is composed by a CLOSED BOOK THEORETICAL part (8 marks) and an open book PRACTICAL part (12 marks). The exam is 3 hours long.
Not applicable
Not applicable
EXAM (EX): Written exam graded from 0 to 20. It is composed by a CLOSED BOOK THEORETICAL part (8 marks) and an open book PRACTICAL part (12 marks). The exam is 3 hours long.
It will take place at the appropriate season of exams, according to General Evaluation Rules of FEUP.
EXAM (EX): Written exam graded from 0 to 20. It is composed by a CLOSED BOOK THEORETICAL part (8 marks) and an open book PRACTICAL part (12 marks). The exam is 3 hours long.
It will take place at the appropriate season of exams, according to General Evaluation Rules of FEUP.
Students should be familiarised with computer software “Matlab®”.