Mechanical Vibrations and Noise

Code:

EM0043

Acronym:

VR

Keywords
Classification	Keyword
OFICIAL	Applied Mechanics

Instance: 2010/2011 - 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
MIEM	253	Syllabus since 2006/2007	4	-	6	56	160

Teaching language

Portuguese

Objectives

Objectives:
- to understand the mechanical vibration phenomena;
- to analyse and to describe the semi rotary motion of mechanical systems and associated forces;
- to determine vibration effects on the performance and safety of mechanical systems

Learning Outcomes:
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 solicitations;
- be capable of applying some techniques of vibration control

Program

Fundaments of vibration: Generalities, basic concepts, vibration classification, vibration analysis procedures, elements of vibration systems, harmonic analysis;

Systems with a degree of freedom: differential equation of motion, free vibration, natural frequency, forced vibration, response to harmonic excitation, resonance frequency, transmissivity, 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 equation, equation of motion from matrix, free undamped vibration, frequencies and natural forms of vibration, modal vector orthogonality, expansion theorem, initial excitation response, Rayleigh’s quotient, response to harmonic excitation, response to generic excitation, natural coordinates, modal analysis, direct integration, space model, modal model, response model

Vibration control: vibration isolation, vibration absorber

Continuous systems: transverse vibration of a wire, wave equation, longitudinal vibration of bars, shaft torsional vibration, beam flexion vibration, natural frequencies and shapes, forced response, modal analysis, approximate methods, Rayleigh’s methods

Noise: fundamental concepts of noise, sound propagation through the air and structures, to determine the intensity and sound potency, control of industrial noise, legislation

Mandatory literature

José Dias Rodrigues ; Apontamentos de Vibrações de Sistemas Mecânicos , 2011

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 (2 per week- 1 hour each) – presentation and discussion of themes
Theoretical-practical classes (1 per week- 2 hours) - exercises

Software

Matlab

keywords

Technological sciences > Engineering > Mechanical engineering > Vibration engineering

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Description	Type	Time (hours)	Weight (%)	End date
Attendance (estimated)	Participação presencial	56,00
	Exame	6,00
	Teste	49,00
	Total:	-	0,00

Amount of time allocated to each course unit

Description	Type	Time (hours)	End date
	Estudo autónomo	42
	Estudo autónomo	14
	Total:	56,00

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 in two different ways: Continuous Assessment and Final Exam
2. Continuous Assessment will be based on two tests: a mid-term test in April and the other in June
3. The content of the tests are exclusive
4. In each of the tests, students must achieve a minimum grade of 7 out of 20
5. Both tests worth the same (50%) of the Continuous Assessment Mark
6. The final mark of Continuous Assessment is the average grade of the tests. However, it can be a 9 out of 20 if the average grade of both tests is 10 or higher, but in one of the tests students could not reach a 7.
7. Students who:
- did not achieve an average grade of 10 out of 20 in the tests
- have skipped both tests
can attend to the Recurso exam in July.
8. Each of the three tests is a written assignment that is graded from 0 to 20. They comprise a THEORETICAL part (8) CLOSED BOOK and a PRACTICAL part (12), where students can use notes called “Apontamentos de Vibrações e Sistemas Mecânicos” (Notes on Vibrations and Mechanical Systems). Each of the tests will last 3 hours.
9. The Final Mark is the same as the Continuous Assessment Mark (see number 6) or Recurso Exam.
10. Only students who achieve a 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 (8) CLOSED BOOK and a PRACTICAL part (12), where students can use notes called “Apontamentos de Vibrações e Sistemas Mecânicos” (Notes on Vibrations and 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 (8) CLOSED BOOK and a PRACTICAL part (12), where students can use notes called “Apontamentos de Vibrações e Sistemas Mecânicos” (Notes on Vibrations and 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 Matlab® software.
Students should have attended and completed the courses on Mechanics II, Solid Mechanics and Structural Mechanics I.