Machine Dynamics

Code:

M.EM006

Acronym:

DM

Keywords
Classification	Keyword
OFICIAL	Applied Mechanics

Instance: 2021/2022 - 2S

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	25	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.

Continuous systems

• Torsion vibration of shafts
• Bending vibration of beams
• General solution and boundary conditions: natural frequencies and mode shapes of vibration
• Forced response: modal analysis

Approximate methods in dynamic analysis of structures and machines

• Rayleigh and 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

Complementary Bibliography

José Dias Rodrigues; Apontamentos de Vibrações de Sistemas Mecânicos, 2022 (Available at the website of the UC)
José Dias Rodrigues; Apontamentos de Dinâmica de Máquinas, 2016 (Available at the website of the UC)
Kelly, S. Graham; Fundamentals of mechanical vibrations. ISBN: 0-07-911533-0
Meirovitch, Leonard; Elements of vibration analysis. ISBN: 0-07-041342-8

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

Evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	100,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	83,00
Frequência das aulas	39,00
Total:	122,00

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):
The final mark (FM) is equal to the final exam (FE) grade: FM=FE

Examinations or Special Assignments

• 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 curricular unity notes or a textbook. 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

Students should be acquainted with Matlab/Octave software.