Mechanical Vibrations and Noise


Specific objectives of the UC:

  • understanding of the vibratory phenomenon associated with mechanical vibrations;
  • analysis and characterization of the oscillatory movement of mechanical systems in free or forced vibration, with or without damping;
  •  determination of the effects of vibration on the performance and safety of mechanical systems;
  •  Know how to apply vibration control techniques;
  • Compression of the fundamental concepts associated with noise. Effect of noise on humans. Noise measurement and control techniques-

General characterization





Responsible teacher

Raquel Albuquerque Soares Brás de Almeida


Weekly - 4

Total - 62

Teaching language



Students must have to be acquired knowledge in the UCs of Mathematical Analysis and Linear Algebra, as well as in Applied Mechanics I and II and Solid Mechanics I and II.


Mechanical Vibrations (5ª edição no SI de unidades)

Singiresu S. Rao, Editora Pearson.


António P. Vale Urgueira - Manual de Apoio à Disciplina.


S. Graham  Kelly - Fundamentals of Mechanical Vibrations;  McGraw-Hill.

Engineering Vibrations  - Daniel J. Inman

Teaching method

The teaching of the subject is divided into theoretical lectures of an expository nature in which students are systematically invited to participate and in practical classes where students solve problems applied to situations that are in the field of mechanical engineering, often using didactic simulators.

Evaluation method

Evaluation (AD) or by Exam To obtain frequency to UC the student has to carry out experimental work (TE), outside the faculty. The valuation of this work for the final grade of the distributed evaluation is 15%. The elements used to carry out the distributed evaluation of the students and the percentages affected are as follows:

  • (TE) - Experimental work (15%) ⇒ (Checks the mandatory frequency to the UC))
  •  (T1) - 1st Test (40%)
  •   (T2) - 2nd Test (45%)

The final grade of the distributed evaluation is determined by the following weighted average.

  •     Final grade (AD) = 0.15 TE + 0.40 T1 + 0.45 T2 ≥ 9.5 Values

For the student to obtain approval to UC the result of the final grade (AD) must be greater than or equal to 9.5 values.

If the student does not obtain approval to UC in the distributed evaluation and has obtained frequency to UC can go to the appeal exam (E). The final approval is obtained if the final grade is greater than or equal to 9.5 values.

  •     Final grade (Examination) = 0.15 TE + 0.85 E ≥ 9.5 Values
Obtaining a grade higher than 16 (AD or Exam) will be dependent on an oral exam.

Subject matter


Introduction. Types of dynamic solicitations. Discretization of mechanical systems. Elements of a vibratory system with one degree of freedom. Masses, Springs and dampers. Motion equations. D''Alembert''s Principle, Virtual Works Principle, Hamilton Principle and Principle of Conservation of Mechanical Energy. Free vibration response of undamped and damped system with one degree of freedom. Types of Damping: viscous, hysteretic and Coulomb´s. Response of a system with, one degree of freedom, to a harmonic load with constant amplitude, or due to the existence of unbalanced rotating masses. Transmissibility of movements. Vibration isolation. Periodic and impulsive solicitations. System with two or more degrees of freedom. Determination of natural frequencies and modes of vibration of a system. Continuous systems. Longitudinal vibrations (bars), transversal vibrations (cables and beams) and torsional vibrations (shafts). Fundamental concepts about noise. Sound pressure, intensity and power. Noise effect on humans. Noise measurement and control.


Programs where the course is taught: