Single-Course English 5 ECTS

Advanced dynamics and vibrations

Overall Course Objectives

Qualify participants to assess, formulate, classify, and solve various problems involving mechanical vibrations and stability. This includes employing advanced and current methods, following relevant scientific literature, and communicating with specialists within the field.

Learning Objectives

  • Identify sources of inertia, stiffness, energy dissipation, external loads, nonlinearity, and instability for specific mechanical systems.
  • Use Newton’s laws and Hamilton’s principle for determining equations of motion for linear and nonlinear mechanical systems having a finite or infinite number of degrees of freedom.
  • Identify potential dynamical phenomena for specific mechanical systems.
  • Set up and solve eigenvalue problems for determining natural frequencies and mode shapes for linerized mechanical systems having a finite or infinite number of degrees of freedom.
  • Use theoretical modal analysis for approximating / discretizing equations of motions for linear or nonlinear mechanical systems having a finite or infinite number of degrees of freedom.
  • Use perturbation analysis for analyzing weakly nonlinear systems having few degrees of freedom.
  • Use simple bifurcation analysis for single-degree-of-freedom systems.
  • Use computer programs for simulating and analyzing nonlinear dynamical systems, including solving nonlinear ordinary differential equations, frequency spectra, phase plane plots, Poincaré maps, and Lyapunov exponents.
  • Give practically useful assessments of frequency response, phase plane, and bifurcation diagrams.
  • Present written problem solutions and reports that are well structured, complete, clear and concise, critically assessing / concluding, and otherwise confirming to accepted standards for written presentation in the subject area.

Course Content

Stability analysis of static and dynamic equilibria for mechanical systems. General eigenvalue theory for mechanical vibration and stability problems. Discretization of continuous systems. Mechanical nonlinearities. Nonlinear oscillations and phenomena (e.g. super- and subharmonic resonance, internal resonance, modal interaction, saturation, amplitude jumps, multi-solutions). Post-critical analysis: perturbation methods and bifurcation theory. Numerical simulation. Model reduction. Vibro-impact. Chaos theory for mechanical systems. Effects of high-frequency excitation. Continuation methods. Computer simulation. Scientific/technical reporting.

Recommended prerequisites

41560/41214/41514/62643/41237/41564, / course in elementary vibration theory. Experience in MATLAB/Maple programming.

Teaching Method

Lectures, demos, problem solving, exercises, project work


See course in the course database.





13 weeks


DTU Lyngby Campus

Course code 41522
Course type Candidate
Semester start Week 5
Semester end Week 19
Days Mon 13-17

7.500,00 DKK