Reduced Order Framework for Free Vibration Simulation of Linear and Non-Linear Beam Model

In this article, a reduced order framework as a surrogate model of linear and non-linear beam vibration is presented. The model is constructed based on the proper orthogonal decomposi-tion (POD) method. First, a finite element model has been used to find static and dynamic re-sponses of the considered linear and non-linear beams. Euler-Bernoulli beam elements with two primary variables (deflection and slope) at each node are employed and Hermite cubic interpolation functions are used in FE modelling. Responses to three different static loads are obtained and applying them as initial conditions, time responses of the beam are calculated by the Newmark’s time approximation scheme. Then, a reduced order model extracted from the ensemble under the effect of an arbitrary loading is reconstructed. This approach has been previously proposed by the author for free vibration simulation of linear beam model. The modification of model under effect of new initial condition is performed based on recalcula-tion of eigenvalues. The results obtained from the ROM are showing relative good agreement to the benchmark data for both linear and non-linear models and proving high accuracy of model.