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. En studerende, der fuldt ud har opfyldt kursets mål, vil kunne:

• 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

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 Newland, David Edward. An introduction to random vibrations, spectral & wavelet analysis. Courier Corporation, 2012.

Brincker, Rune, and Carlos Ventura. Introduction to operational modal analysis. John Wiley & Sons, 2015. (tilgængelig for gratis download for DTU studerende) 21. maj, 2025