Random Vibrations and Uncertainty Quantification for Metamaterials 

Objectives
Excitations affecting metamaterials and metastructures, like ambient noise, earthquakes, wind, and ocean waves, are inherently stochastic. This course introduces stochastic processes and random vibrations for modeling and evaluating their stocastic dynamic response. Special attention is given to applications in ambient noise and earthquake engineering. The course deepens understanding of metamaterial and metastructure dynamics, including frequency domain analysis, coherency of inputs, and modal cross-correlations—essential for assessing their effectiveness in applications like energy harvesting and advanced seismic isolation systems.

Topics
Probability theory and random processes
Analysis of discrete and continuous periodic systems
Transfer Matrix method
Correlation and power spectral density functions
Stochastic dynamic analysis of periodic structures subjected to stationary and non-stationary random excitations
Stochastic dynamic analysis of periodic structures subjected to spatially varying excitations

Required Skills
Basic knowledge of mechanics and dynamics of structures

Course Modality and Verification of Learning
The classes will be given in hybrid (i.e., onsite and online) format. The teaching activity includes theoretical lessons, exercises and lab experiments.
The exam consists of a written test with multiple-choice questions on the course topics.