Single-Course English 5 ECTS

E-course in Random Vibrations

Overall Course Objectives

Main objective is to give the student a general understanding of the dynamic response of structures loaded by random loadings like, wind, waves, traffic etc. The focus of the course is on understanding why the response is nearly always normal distributed, and that this naturally leads to the use of correlation functions and spectral densities, and how these quantities should be understood and estimated from real data. The course is based on exercises in Matlab.

Learning Objectives

  • Define and estimate probabilistic quantities like mean values and variances from response data
  • Define correlation and explain how the concept can be used to extract physical information
  • Define auto-correlation and cross-correlation functions and explain how they can be used to extract physical information
  • Use numerical methods to estimate auto-correlation and cross-correlation functions
  • Explain classical Fourier transforms and use digital Fourier transforms to process response data in Matlab
  • Define spectral density functions and explain how they can be used to extract physical information
  • Use numerical methods to estimate spectral density functions
  • Outline and describe the concept of linear systems and use Matlab to perform simple response simulations

Course Content

1. Probalistic description of random responses
2. Correlation and auto correlation functions
3. Cross correlation functions
4. Physical meaning of correlations functions
5. Fourier series and Fourier integral
6. Digital Fourier series
7. Auto spectral density
8. Cross spectral density
9. Response of linear systems
10. Course overview

Recommended prerequisites

41035/41214/11374, Or similar

Teaching Method

Self-paced e-learning with weekly meetings and parallel live webinar. Group work, numerical exercises and problems, computer simulations, portfolio report, final report.

Limited number of seats

Maximum: 100.

Please be aware that this course has a limited number of seats available. If there are too many applicants, a pool will be created for the remainder of the qualified applicants, and they will be selected at random. You will be informed 8 days before the start of the course, whether you have been allocated a spot.

See course in the course database.





3 weeks


DTU Other Campus

Course code 41970
Course type Candidate
Semester start Week 32
Semester end Week 34
Days Mon-fri 8:00-17:00

7.500,00 DKK

Please note that this course has participants limitation. Read more