Single-Course English 5 ECTS

Mechanical Vibrations

Overall Course Objectives

To provide the students with a theoretical and practical foundation for solving vibration problems related to structures and machines, using analytical and numerical methods. To give the basis for advanced studies in dynamics and vibrations.

Learning Objectives

  • Identify masses, stiffness, energy-dissipation and external forces in some standard mechanical systems.
  • Use Newton’s second law, free body diagrams and the energy method to derive the equations of motion (scalar or matrix-vector form) for simple models of mechanical systems with a finite or infinite number of degrees of freedom.
  • Determine the natural frequencies for mechanical systems with a finite or infinite number of degrees of freedom.
  • Use analytical and numerical methods to solve equations of motion for mechanical systems.
  • Understand and explain eigenfunctions, eigenvectors and eigenvalues.
  • Identify resonance problems for both damped and undamped vibrating mechanical systems.
  • Account for the limitations in the models and methods used, and predict the possible consequences of making simplified assumptions, especially linearization and limitation of the number of degrees of freedom.
  • Use approximate methods to determine natural frequencies.
  • Write technical reports with correct description of theoretical and experimental procedures, in a clear way, using technical terms, giving physical interpretations and evaluations of results.
  • Use the computer software DAMA and MATLAB for solving vibration problems.
  • To give the students a basic background for advanced studies in dynamics and vibrations.
  • Read engineering literature on mechanical vibrations.

Course Content

Equations of motion with initial conditions.

Vibrations of linear single and two degree-of-freedom systems, including free and forced vibrations for translation and rotation with damping and without damping.

Vibration isolators.

Pendulums and mass moment of inertia.

Vibrations of continuous systems: Equations of motion for strings, bars and beams. Boundary and initial conditions. Fourier series, orthogonality, eigenfunctions, eigenvectors and eigenvalues. Whirling shafts and Dunkerley’s formula. Rayleigh’s method and Rayleigh-Ritz method.

Finite Element Methods: Mass and Stiffness matrices and equations of motion for bars and beams expressed in Matrix form.

Introduction to non-linear vibration.

The software “DAMA” will be used as an animation tool, in order to enhance the students’ understanding of the motion and vibration of mechanical systems.

Recommended prerequisites


Teaching Method

The teaching is both project-oriented and problem-based. There are both lectures and exercises. The mandatory project is bases upon experiments with a Frequency Analyzer as well as MATLAB and COMSOL simulations.



Faggruppe: Mekanisk teknologi

See course in the course database.





13 weeks


Engineering Technology


DTU Ballerup Campus

Course code 62643
Course type Graduate Engineer
Semester start Week 35
Semester end Week 48
Days Wed 8-12

7.500,00 DKK