Structural Dynamics

Recommended Prerequisites

Linear Algebra, Mathematical Analysis, Continuum Mechanics, Strength of Materials and Structural Analysis.

Teaching Methods

The traditional blackboard lecture style, with synchronous online transmission and the help of commercial analysis software, 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

At the end of this curricular unit, students will be able to:
A) Calculate the dynamic properties and response of discrete, or semi-discretized, linear systems 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.

Work Placement(s)

No

Syllabus

1. Discrete linear systems
1.1 Single-degree-of-freedom systems
1.1.1 Free motion
1.1.2 Forced motion
1.1.3 Numerical integration of the equation of motion
1.2 Multi-degree-of-freedom systems
1.2.1 Undamped free motion and the generalized algebraic eigenproblem
1.2.2 Modal damping
1.2.3 Mode superposition
2. Continuous linear systems
2.1 Elastodynamics
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
3. Computer-aided illustration of dynamical analyses.

Assessment Methods

Assessment
Resolution Problems: 50.0%
Exam: 50.0%

Bibliography

Chopra A.K. (2020), Dynamics of Structures – Theory and Applications to Earthquake Engineering (5th ed.), Pearson
Géradin M., Rixen D.J. (2015), Mechanical Vibrations – Theory and Application to Structural Dynamics (3rd ed.), Wiley
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.