Mechanics III

Code:

EM0098

Acronym:

MECIII

Keywords
Classification	Keyword
OFICIAL	Applied Mechanics

Instance: 2014/2015 - 2S

Active?	Yes
Web Page:	http://sigarra.up.pt/feup/pt/ucurr_geral.ficha_uc_view?pv_ocorrencia_id=275663
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
MIEM	443	Syllabus since 2006/2007	3	-	6	58,5	162

Teaching language

Portuguese

Objectives

Objectives:

• to understand the mechanical vibration phenomena;

• to analyse and to describe the oscillatory motion of mechanical systems and associated forces;

• to determine vibration effects on the performance and safety of mechanical systems.

Learning outcomes and competences

By the end of the semester, students should:

• be acquainted with the basic principles and terminology related with the theory of mechanical vibrations;

• be acquainted with the behaviour of canonical systems;

• be capable of establishing physical/mathematical discrete and continuous one-dimensional models to analyse the vibration of mechanical systems;

• be capable of adapting suitable solution methods to determine dynamic characteristics and mechanical systems response under dynamic excitations;

• be capable of applying some techniques of vibration control.

Working method

Presencial

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

•Students should be acquainted with vector calculus and ordinary differential equations;

•Students should have attended and completed the courses on Mechanics I (equilibrium of rigid bodies, centroids and moments of inertia), Mechanics II (kinematics and dynamics of rigid bodies, work and energy), Solid Mechanics (tension-compression, torsion, bending and boundary conditions).

•Students should be acquainted with Matlab® software.

Program

Fundaments of vibration: Generalities, basic concepts, vibration classification, vibration analysis procedure, elements of vibratory systems, harmonic analysis.

Systems with one degree of freedom: differential equation of motion, free vibration, natural frequency, logarithmic decrement, forced vibration, response to harmonic excitation, resonance frequency, transmissibility, vibration transducers, frequency response function, response to periodic excitation, response to transient excitation, shock spectrum, direct integration.

Systems with n degrees of freedom: generalized coordinates, potential and kinetic energy, Lagrange’s equations, equations of motionin matricial notation, free undamped vibration, natural frequencies and modeshapes of vibration, orthogonality properties of modal vectors, expansion theorem, response to initial deisplacement and velocity conditions, Rayleigh’s quotient, response to harmonic excitation, response to generic excitation, natural coordinates, modal analysis, direct integration methods.

Vibration control: vibration isolation, vibration absorber.

Continuous systems: transverse vibration of strings, wave equation, longitudinal vibration of bars, torsional vibration of shafts, bending vibration of beams, natural frequencies and modeshapes, forced response, modal analysis, approximate methods, Rayleigh’s energy method.

Noise: fundamental concepts of noise, sound propagation through the air and structures, pression, intensity and sound power, control of industrial noise.

Mandatory literature

José Dias Rodrigues; Apontamentos de Vibrações de Sistemas Mecânicos, FEUP, 2015 (Available on the website of the UC)

Complementary Bibliography

Rao, Singiresu S.; Mechanical Vibrations. ISBN: 0-13-048987-5
Kelly, S. Graham; Fundamentals of mechanical vibrations. ISBN: 0-07-911533-0
Meirovitch, Leonard; Elements of vibration analysis. ISBN: 0-07-041342-8
William T. Thomson; Vibration theory and aplications. ISBN: 0-04-531003-3

Teaching methods and learning activities

•Theoretical classes (1 per week- 1.5 hour) – presentation and discussion of themes.

•Theoretical-practical classes (2 per week- 1.5 hour each) - exercises

Software

Matlab

keywords

Technological sciences > Engineering > Mechanical engineering > Vibration engineering

Evaluation Type

Evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	100,00
Participação presencial	0,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	99,00
Frequência das aulas	63,00
Total:	162,00

Eligibility for exams

According to General Evaluation Rules of FEUP, students must attend to 75% of the classes.

Calculation formula of final grade

1. Students will be assessed by Final Exam (Normal and Recurso);

2. Each of the two tests (Normal and Recurso) is a written assignment that is graded from 0 to 20. They comprise a THEORETICAL part (graded to 8) CLOSED BOOK and a PRACTICAL part (graded to 12), where students can use notes called “Apontamentos de Vibrações de Sistemas Mecânicos” (Notes on Vibrations of Mechanical Systems). Each of the tests will last 3 hours;

3. The Final Mark is the higher from Final Exam (Normal and Recurso);

4. Only students who achieve a mark of 10 out of 20 have completed the course.

Examinations or Special Assignments

Not applicable.

Special assessment (TE, DA, ...)

An exam: A written assignment that is graded from 0 to 20. It comprises a THEORETICAL part (graded to 8) CLOSED BOOK and a PRACTICAL part (graded to 12), where students can use notes called “Apontamentos de Vibrações de Sistemas Mecânicos” (Notes on Vibrations of Mechanical Systems). It covers all the themes of the course. Each of the tests will last 3 hours. The exam will take place in a day according to General Evaluation Rules of FEUP

Classification improvement

An exam: A written assignment that is graded from 0 to 20. It comprises a THEORETICAL part (graded to 8) CLOSED BOOK and a PRACTICAL part (graded to 12), where students can use notes called “Apontamentos de Vibrações de Sistemas Mecânicos” (Notes on Vibrations of Mechanical Systems). It covers all the themes of the course. Each of the tests will last 3 hours. The exam will take place in a day according to General Evaluation Rules of FEUP

Observations

•Students should be acquainted with vector calculus and ordinary differential equations;

•Students should have attended and completed the courses on Mechanics I (equilibrium of rigid bodies, centroids and moments of inertia), Mechanics II (kinematics and dynamics of rigid bodies, work and energy), Solid Mechanics (tension-compression, torsion, bending and boundary conditions).

•Students should be acquainted with Matlab® software.