The main purpose of the present work can be divided into two separate objectives. The first one and most important is to study the different computational techniques that are used in the structural vibrations modelling field in both the linear and nonlinear regimes, as well as their methodology of implementation. In particular, this thesis places special emphasis on a specific order-reducing model called hyperreduction. This approach makes use of Machine Learning techniques such as the Singular Value Decomposition to solve an optimization problem that selects the set of reduced elements to be integrated from the entirety of finite elements of the mesh. To do so, several simulations are launched an analysed throughout the study. These simulations intend to estimate the dynamic response that a simple 2D cantilever beam would suffer when subjected under different types of boundary conditions. Such a task is performed thanks to a Finite Element Method based on the Galerkin approximation. With the help of Matlab, the semi-discrete equation of motion that governs the dynamic response of the system can be computationally integrated making use of the Newmark-Bossak scheme and the Newton-Raphson algorithm. The results obtained from the Finite Element study will be compared with the analytical solution deduced from the modal analysis decomposition technique and also with the results obtained from the hyperreduction stage. On the other hand, the second goal of this thesis is to study the dynamic response of the above-mentioned structure when subjected to the action of real wind gusts. This study is included in the list of simulations to be launched in this project. In this sense, the Fast Fourier Transform (FFT) is also employed in order to obtain a continuous representation in the time domain of a discrete data set representing real measurements of wind speed. The main conclusion of this work is that the hyperreduction method is significantly more efficient than a standard Finite Element method since it requires less than 1% of the finite elements of the mesh to integrate the semi-discrete equation of motion, thus contributing to achieving reductions of up to 96% in computational time within an accuracy tolerance of the order of 10−3 . Therefore, this technique is a highly valuable tool in any engineering field that involves simulations with very refined meshes or with complex nonlinear conditions among others, since they require great computational efforts
