Machine Dynamics

Code:

M.EM006

Acronym:

DM

Keywords
Classification	Keyword
OFICIAL	Applied Mechanics

Instance: 2021/2022 - 1S

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

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
M.EM	37	Syllabus	1	-	4,5	39	121,5

Teaching language

English

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

Learning outcomes and competences

Learning Outcomes: By the end of the semester, students should:

• be able to use analytical and experimental modelling in mechanical systems to analyse its dynamic behaviour;
• be able to apply solution methods and resolution techniques to determine dynamic properties and the time and frequency response of mechanical systems;
• be able to measure dynamic response and identify dynamic properties;
• understand the dynamic behaviour of mechanical systems;
• be acquainted with vibration control solutions and how to dimensioning them;
• be capable of interpreting and criticizing results;
• be capable of dimensioning mechanical systems under prescribed operational conditions.

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

Students should have attended the UC Mechanical Vibrations

Program

Formulation of the equations of motion

• Hamilton's principle, Lagrange's equation.

Discrete systems with multiple degrees of freedom

• Equations of motion, natural frequencies and mode shapes, forced response, modal analysis, direct integration methods;
• Frequency response model.

Approximate methods in dynamic analysis of structures and machines

• Rayleigh-Ritz Method;
• assumed Modes Method;
• Finite element method: shaft, bar and beam elements;
• Reduction of the number of the degrees of freedom: condensation techniques.

Experimental modal analysis

• Spatial, modal and frequency response models, modal expansion, modal identification, synthetization of frequency response functions;
• Vibration measurement: transducers, spectral analysis, FFT analysers, frequency response functions.

Dynamics of rotating machinery

• “Laval” model: equation of motion, precession motion, critical velocities, forced response, auto-centering effect;
• Rotor balancing.

Dynamics of reciprocating machines

• Equivalent system for torsional vibrations;
• Forced vibrations;
• Balancing of reciprocating machines.

Mechanical condition monitoring

• Characteristic frequencies: bearings, gears.

Mandatory literature

Singiresu S. Rao; Mechanical Vibrations. ISBN: 0-13-048987-5
Jose Dias Rodrigues; Apontamentos de Vibrações de Sistemas Mecânicos, jdr, 2020 (Available at the website of the UC.)
José Dias Rodrigues; Apontamentos de Dinâmica de Máquinas, 2016

Complementary Bibliography

Meirovitch, Leonard; Elements of vibration analysis. ISBN: 0-07-041342-8
Kelly, S. Graham; Fundamentals of mechanical vibrations. ISBN: 0-07-911533-0

Teaching methods and learning activities

•Theoretical-practical classes – exposition and discussion of problems

Software

Octave
Matlab 6 R12.1

keywords

Technological sciences > Engineering > Mechanical engineering > Vibration engineering

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	80,00
Trabalho escrito	20,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	78,00
Frequência das aulas	39,00
Trabalho laboratorial	4,50
Total:	121,50

Eligibility for exams

Students must be enrolled and attend to a minimum number of classes- according to General Evaluation Rules of FEUP

Calculation formula of final grade

Final Mark (FM): Distributed classification (DC) will worth 20% of the final mark, while the final exam (FE) will worth 80% of the final mark: FM=0.2xDC+0.8xFE

Examinations or Special Assignments

Distributed classification (DC) will be based on the following assignments:
•Homework (HW): exercises given during classes to be done as homework. Students should give them back to the Professor in order to be corrected (they will be graded with a mark from 0 to 20). 4 assignments will be asked;
•Laboratory Assignments (LA): Reports of laboratory assignments should be given to the Professor in order to be corrected (they will be graded with a mark from 0 to 20). 1 laboratory assignments will be asked;
•Distributed classification (DC) will be as follows: DC= (HW1+HW2…+LA1+LA2…)/n;
• Final exam (FE): a written exam that will be graded from 0 to 20 and it will be divided into two: theoretical part (8) where students cannot consult notes and a practical part (12) where students are allowed to consult notes. The exam will last 3 hours.

Special assessment (TE, DA, ...)

According to General Evaluation Rules of FEUP

Classification improvement

A written exam- According to General Evaluation Rules of FEUP

Observations

Temporary connection for class participation:
https://videoconf-colibri.zoom.us/j/83427335014



Students should be acquainted with “Matlab/Octave “software.