Structural Dynamics

Code:

PRODEM013

Acronym:

DE

Keywords
Classification	Keyword
OFICIAL	Mechanical Engineering

Instance: 2008/2009 - 1S

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

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

2. Equations of Motion of Discrete Systems:
Direct application of Newton’s laws, Influence coefficients, Principle of the Virtual Work, Hamilton’s principle, Lagrange equations.

3. Free vibrations of n-degree of freedom systems: Quick review.

4. Forced vibrations of n-degree of freedom systems: Quick review.

5.Continuous systems – structural elements: Cables, bars, shafts and beams (Bernoulli-Euler).
Membranes and plates (Kirchhoff).

6. Approximation methods: Rayleigh-Ritz and Galerkin. Finite element method.

7. Numerical methods to solve eigenvalue problems: global and partial algorithms, application to determine natural frequencies and mode shapes.

8. Direct numerical integration of the equations of motion in the time domain: Finite differences, Newmark, Wilson.

9. Additional topics in continuous systems: Timoshenko’s model for beams, beams subjected to axial loads, beams on elastic foundation, beams subjected to moving loads.

10. 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

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	0,00
	Total:	-	0,00

Eligibility for exams

Attend the classes.