Structural Dynamics

Code:

PRODEM013

Acronym:

DE

Keywords
Classification	Keyword
OFICIAL	Mechanical Engineering

Instance: 2010/2011 - 2S

Active?	Yes
Responsible unit:	Applied Mechanics Section
Course/CS Responsible:	Doctoral Program in Mechanical Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
PRODEM	1	Syllabus since 2009/10	1	-	6,5	60	175,5

Teaching language

Portuguese

Objectives

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.

Program

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.

Mandatory literature

José Dias Rodrigues; Apontamentos de Vibrações de Sistemas Mecânicos, 2007
José Dias Rodrigues; Apontamentos de Dinâmica das Estruturas, 2007

Complementary Bibliography

Clough, Ray W.; Dynamics of structures. ISBN: 0-07-011392-0
Bathe, Klaus-Jurgen; Finite element procedures in engineering analysis. ISBN: 0-13-317305-4

Teaching methods and learning activities

Exposition of the topics, exercises and essay.

Software

Matlab 6 R12.1

keywords

Technological sciences > Engineering > Mechanical engineering > Vibration engineering

Evaluation Type

Evaluation with final exam

Eligibility for exams

Students cannot miss more classes than allowed by the rules.

Calculation formula of final grade

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.

Examinations or Special Assignments

Not applicable

Special assessment (TE, DA, ...)

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.

Classification improvement

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.

Observations

Students should be familiarised with computer software “Matlab®”.