Course content

Natural phenomena such as water waves, wind and earthquakes can be modelled as irregular time series, and these are considered as input to systems that have the corresponding forces as output. On the next level these forces are input in a system in which the displacements of a structure is the output. The relationship from input to output is denoted 'transfer function', and from this follows the response spectrum. Further average frequency, average number of peaks of different magnitude, per time unit, and expected maximum response may be determined.

Learning outcome

Knowledge
The candidate should have knowledge of:
- Statistical based methods for the description of the environmental loads and the resulting. response, such as structural displacements of a structure.
- Modelling of a dynamic system using differential equations.
- Establishment of the equations of dynamic equilibrium, the equations of motion.
- The transfer function and the impulse response function for a dynamic system.
- Dynamic response due to irregular stochastic loadings.
- Analysis of time and frequency domains.
- The use of transfer functions.
- Description of stochastic processes.
- Correlations and variance spectra for stochastic processes.
- Response spectra for structures subjected to stochastic loading processes.
- Response statistics for calculation of extreme responses.
- MATLAB.

Skills
The candidate should be able to:
- Establish the dynamic equilibrium equations for systems with few degrees of freedom.
- Use complex numbers in the formulations.
- Calculate the response of the system from a given deterministic load.
- Determine the mean and variance as well as the response spectrum of the system subjected to a stochastic irregular loads.
- Simulate time series of environmental loads.
- Conduct statistical analysis of combined stochastic processes.
- Calculate up-crossing frequencies of stochastic vibrations.

General competence
The candidate has:
- Basic understanding of deterministic and stochastic structural dynamics.
- Depth understanding of the dynamics associated with one degree of freedom dynamic systems.
- A sound basis for further studies in structural dynamics and stochastic loads and response modelling.
- Characterization of structural dynamic properties (eigenfrequencies) in relation to the load characteristics (load spectrum).

Learning methods and activities

Lectures and exercises. The subject is taught in English. If there is a re-sit examination, the examination form may be changed from written to oral.

Compulsory assignments

• Exercises

Recommended previous knowledge

Minimum 30 credits in mathematics and statistics, as well as basic knowledge of mechanics equivalent to the first 2.5 years of Civil and Environmental Engineering studyprogram at NTNU.

Course materials

Textbook, compendium, papers.
A. Naess: An Introduction to Random Vibrations, Compendium available at Department of Civil and Transport Engineering.
Papers and notes by G. Moe distributed via It's learning.

Credit reductions