Mechanical Vibrations and Noise
Objectives
This course aims to provide students with fundamental knowledge in the areas of mechanical vibrations and noise, with a focus on their application in the analysis, design, and optimization of mechanical systems. Specifically, the course intends for students to:
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Understand the vibratory phenomena associated with mechanical vibrations, recognizing their causes and implications;
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Be able to analyze and characterize the oscillatory motion of mechanical systems under free or forced vibration, with or without damping;
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Assess the effects of vibrations on the performance and safety of mechanical systems;
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Apply appropriate vibration control techniques to minimize negative impacts;
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Understand the fundamental concepts related to noise, including its effects on human health and well-being;
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Be familiar with and able to apply methods for noise measurement and control in various contexts.
General characterization
Code
3668
Credits
6.0
Responsible teacher
Pedro Samuel Gonçalves Coelho, Raquel Albuquerque Soares Brás de Almeida
Hours
Weekly - 4
Total - 62
Teaching language
Português
Prerequisites
It is essential that students have acquired knowledge in the curricular units related to Mathematical Analysis and Linear Algebra, as well as in Applied Mechanics I and II, and Solid Mechanics I and II.
Bibliography
“Mechanical Vibrations” (5ª edição no SI de unidades); Singiresu S. Rao, Editora Pearson.
“Fundamentals of Mechanical Vibrations”; S. Graham Kelly, McGraw-Hill.
“Engineering Vibrations”; Daniel J. Inman, Pearson.
"Theoretical and Experimental Modal Analysis”; Maia, Silva, He, Lieven, Lin, Skingle, To, Urgueira, Research Studies Press Ltd.
Teaching method
The teaching methodology of the Mechanical Vibrations and Noise course combines theoretical classes, where concepts are clearly presented with the use of experimental setups or videos, and practical classes, where students solve problems individually or in groups, fostering critical thinking, collaboration, and autonomy in applying the knowledge gained.
Evaluation method
Approval in this Course Unit (CU) can be obtained through Continuous Assessment (CA) or via a Resit Exam. In order to obtain attendance for the CU, the student must complete an Experimental Assignment (EA). This assignment contributes 15% to the final grade in continuous assessment. The components used for the continuous assessment and their respective weightings are as follows:
- (EA) – Experimental Assignment (15%) ⇒ (Grants mandatory attendance for the CU)
- (T1) – 1st Test (40%)
- (T2) – 2nd Test (45%)
The final grade for continuous assessment is determined by the following weighted average:
- Final Grade (CA) = 0.15 EA + 0.40 T1 + 0.45 T2 ≥ 9.5 points
To pass the CU, the student must achieve a final grade in continuous assessment equal to or greater than 9.5 points.
If the student does not pass the CU through continuous assessment but has obtained attendance, they may take the resit exam (E), and will pass if the final grade is equal to or greater than 9.5 points.
- Final Grade (Resit Exam) = 0.15 EA + 0.85 E ≥ 9.5 points
Grades higher than 18 points (in either continuous assessment or resit exam) are subject to an oral examination.
Subject matter
Introduction to vibratory phenomena. Types of dynamic excitations. Modeling and discretization of mechanical systems. Study of vibratory systems with one degree of freedom (1 DOF): mass, springs, and dampers. Derivation of motion equations based on D’Alembert’s Principle, the Principle of Virtual Work, Hamilton’s Principle, and the Principle of Conservation of Mechanical Energy. Application of Lagrange’s equations.
Analysis of the free vibration response of 1 DOF systems, with and without damping. Study of different damping models: viscous, hysteretic, and Coulomb friction. Forced response to harmonic excitations, including unbalanced rotating masses. Concepts of transmissibility and vibration isolation.
Extension to systems with two or more degrees of freedom: determination of natural frequencies and vibration modes. Introduction to vibrations in continuous systems: analysis of longitudinal (bars), transverse (cables and beams), and torsional (shafts) vibrations.
In the noise module, fundamental concepts such as sound pressure, intensity, and power are addressed. Study of the effects of noise on human health. Basic techniques for noise measurement and control are also introduced.