Vibration of Mechanical Systems

Code:

EM514

Acronym:

VSM

Instance: 2003/2004 - 1S

Active?	Yes
Responsible unit:	Applied Mechanics Section
Institution Responsible:	Faculty of Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
LEM	32	Plano de Estudos EM Oficial a partir de 2000	5	3,5	7	-
		Plano para Bachareis EM a partir 2000	2	3,5	7	-

Teaching language

Portuguese

Objectives

The purpose of this course is to present the basic concepts of the theory of vibration and the methods for analyzing the vibratory motion developed in a mechanical or structural system when it is subjected to a dynamic loading.

Program

Fundamentals of vibration: Basic concepts of vibration, Harmonic motion, Harmonic analysis.
Single Degree of Freedom Systems: Free Vibration with viscous damping, Response of a damped system under harmonic force, Response of a damped system under the harmonic motion of the base, Response of a damped system under rotating unbalance, Frequency response function, Response under a general periodic force, Response under a nonperiodic force, Convolution integral, Response spectrum.
Two Degree of Freedom Systems: Equations of motion for forced vibration, Free vibration analysis of an undamped system, Coordinate coupling and principal coordinates, Forced vibration analysis, Semi-definite systems, Undamped vibration absorber.
Multidegree of Freedom Systems: Equations of motion, Influence coefficients, Lagrange’s equations, Eigenvalue problem, Expansion theorem, Free vibration of undamped systems, Forced vibration of viscously damped systems.
Determination of natural frequencies and mode shapes: Rayleigh’s method, Vector iteration method, Jacobi’s method.
Numerical Integration Methods in Vibration Analysis: Central difference method for single and multidegree of freedom systems.
Continuous Systems: Transverse vibration of a string or cable, Longitudinal vibration of a bar or rod, Torsional vibration of a shaft or rod, Lateral vibration of beams, Rayleigh’s energy method, Rayleigh-Ritz method, Assumed-modes method.

Main Bibliography

• José Dias Rodrigues, Apontamentos de Vibrações de Sistemas Mecânicos, FEUP-DEMEGI, 2003/04

Complementary Bibliography

• Graham Kelly S., Fundamentals of Mechanical Vibrations, McGraw-Hill International Editions, 1993
• Meirovitch L., Elements of Vibration Analysis, McGraw-Hill International Editions, 1986
• Rao S.S., Mechanical Vibrations, Addison-Wesley Publishing Company, 1986
• Timoshenko S.P., Young D.H., Weaver W., Vibration Problems in Engineering, John Wiley & Sons, 1974
• Den Hartog J.P., Mechanical Vibration ,McGraw-Hill, 1956
• Thomson William T., Teoria da Vibração, Editora Interciência,1973.

Teaching methods and learning activities

Theoretical lessons.
Practical lessons.

Software

Matlab®

Evaluation Type

Distributed evaluation with final exam

Eligibility for exams

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Calculation formula of final grade

The final classification is equal to 20% of the continuous evaluation classification plus 80% of the final exam classification.

Examinations or Special Assignments

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Special assessment (TE, DA, ...)

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Classification improvement

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Observations

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