Dynamics of Machines and Structures

Code:

EM0069

Acronym:

DM

Keywords
Classification	Keyword
OFICIAL	Applied Mechanics

Instance: 2011/2012 - 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
MIEM	19	Syllabus since 2006/2007	5	-	6	56	160

Teaching language

Portuguese

Objectives

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:
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.

Program

Formulation of equations of motion: generalized coordinates, Hamilton’s principle, Lagrange’s equation

Discrete systems with multiple degrees of freedom: equations of motion, semi defined systems, frequencies and natural forms, forced response, modal analysis, direct integration, stability analysis

Approximate methods in dynamic analysis: Rayleigh-Ritz method, function approximation. Finite element Method, shaft elements, bar and beam element

Rotor dynamics: equation of motion, precession motion, critical velocities, forced response, auto centring effect, stability analysis

Vibration control: control of natural frequencies, damping, isolation, absorber, balancing

Vibration measuring and applications: vibration transducers, measurement instruments, vibration exciter, spectral analysis, digital signal processing, discrete Fourier transform, FFT analysers, dynamic test of machines and structures, monitoring machine condition

Mandatory literature

J. Dias Rodrigues; Apontamentos de Vibrações de Sistemas Mecânicos, 2011
J. Dias Rodrigues; Apontamentos de Dinâmica de Máquinas, 2011

Complementary Bibliography

Rao, Singiresu S.; Mechanical Vibrations. ISBN: 0-13-048987-5
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 classes – exposition and discussion of problems
Practical classes- problem solving, assignment discussion and laboratory assignments

Software

Matlab 6 R12.1

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
Evaluation	Exame	6,00
Problems solving	Teste	38,00
Laboratory work	Trabalho laboratorial	12,00
	Total:	-	0,00

Amount of time allocated to each course unit

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

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): Distributed classification (DC) will worth 40% of the final mark, while the final exam (FE) will worth 60% of the final mark: FM=0.4xDC+0.6xFE

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). 2 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

Students should be acquainted with “Matlab® “software.