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 - 5

Total - Available soon

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

Lectures and problem-solving sessions

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 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 requests. Discretization of mechanical systems. Choice of degrees of freedom. Elements of a vibratory system. Springs and shock absorbers. Equations of motion. Principle of D''Alembert, Virtual Works and Hamilton. Systems with a degree of freedom. Free vibration response, non-damped and with damping. Viscous, hysteretic cushioning and due to dry friction. Response to a harmonic request of constant amplitude and due to the existence of rotating masses. Transmissibility. Vibration isolation. Periodic and impulsive solicitation. System with two degrees of freedom. Natural frequencies and modes of vibration. System with N degrees of freedom. Methods for determining natural frequencies. Continuous systems. Longitudinal, transverse and torsional vibrations. Fundamental concepts about noise. Sound pressure, intensity and power. Effect of noise on humans. Noise measurement and control.


Programs where the course is taught: