Structural Dynamics

Recommended Prerequisites

Linear Algebra, Mathematical Analysis, Numerical Analysis, Continuum Mechanics, Strength of Materials and Structural Analysis (at the level of a master's degree).

Teaching Methods

The traditional blackboard lecture style is used for (1) the motivation and detailed exposition of the fundamental ideas, concepts and methods and (2) the application and illustration of the theory, by working through selected examples in detail. The student is then expected to solve, under the supervision of the instructor, a collection of systematically arranged problems; the aim is (1) to suggest to him useful lines of disciplined thought in dealing with more complex problems and (2) to promote his autonomy.

Learning Outcomes

After this curricular unit, students will be able to:

A) Calculate the dynamic properties and response of discrete, or semi-discretized, linear systems (including the selection of appropriate algorithms) and critically assess the results.

B) Establish mathematical and numerical models for continuous linear systems (solids and structures), with a thorough understanding of the assumptions underlying these models and their limitations.

C) Understand the rudiments of stochastic dynamics and the characterization of seismic actions in current standards and codes of practice.

Work Placement(s)

No

Syllabus

Deterministic dynamics

1. Discrete linear systems

1.1 Single-degree-of-freedom systems

1.1.1 Free vibration

1.1.2 Forced vibration

1.1.3 Numerical integration of the equation of motion

1.2 Multi-degree-of-freedom systems

1.2.1 Undamped free vibration and the generalized algebraic eigenproblem

1.2.2 Modal damping and mode superposition

1.2.3 Direct numerical integration of the equation of motion

2. Continuous linear systems

2.1 Elastodynamics

2.1.1 The fundamental field equations. Initial and boundary conditions

2.1.2 Variational principles

2.1.3 Wave propagation

2.1.4 Free vibration

2.2 Dynamics of structures

2.2.1 Beams (Rayleigh and Timoshenko models)

2.2.2 Plates (Kirchhoff and Mindlin models)

2.3 Damping models

2.4 Finite element semi-discretization

Stochastic dynamics

3. Elements of the theory of stationary stochastic processes

4. Excitation-response relations for discrete linear systems

5. Statistics of narrow band processes.

Assessment Methods

Assessment
Resolution Problems: 50.0%
Exam: 50.0%

Bibliography

Argyris J.H., Mlejnek H.P. (1991), Dynamics of Structures, North-Holland

Bathe K.J. (2014), Finite Element Procedures (2nd ed.), author’s edition

Chopra A.K. (2020), Dynamics of Structures – Theory and Applications to Earthquake Engineering (5th ed.), Pearson

Cunha A. (1990), Dinâmica Estrutural Estocástica – Aplicações à Engenharia Sísmica, Tese, Universidade do Porto

Géradin M., Rixen D.J. (2015), Mechanical Vibrations – Theory and Application to Structural Dynamics (3rd ed.), Wiley

Gmür T. (1997), Dynamique des Structures – Analyse Modale Numérique, Presses Polytechniques et Universitaires Romandes

Gurtin M.E. (1984). The linear theory of elasticity. Mechanics of Solids II, C. Truesdell (ed.), Springer, 1-295

Hughes T.J.R. (1987), The Finite Element Method – Linear Static and Dynamic Finite Element Analysis, Prentice-Hall

Newland D.E. (1993), An Introduction to Random Vibrations, Spectral and Wavelet Analysis (3rd ed.), Longman

Wood W.L. (1990), Practical Time-Stepping Schemes, OUP