A Surrogate Low-dimensional POD Approach for Free Vibration Simulation of Linear Beam Model

In the present work, a low-dimensional POD model is presented and used in vibration simulation of linear beam model. First, a finite element analysis is used to find static and dynamicresponses of the considered linear beams. Euler-Bernoulli beam elements with two primary variables (deflection and slope) at each node are employed and Hermite cubic interpolationfunctions are used in FE modelling. Responses to three different static load cases are obtainedand applying them as initial conditions, time responses of the beam are calculated by the Newmark's time approximation scheme. A low-dimensional POD model which extractedfrom the ensemble under effect of an arbitrary loading is reconstructed. To apply the modelto simulate response of beam under effect of other loads, POD modal coefficients are updated due to change of initial condition. This modification is performed based on recalculation ofeigenvalues due to new initial condition. The results obtained from the low-dimensionalmodel are showing good agreement to the benchmark data and proving high accuracy ofmodel.

A Surrogate Low-dimensional POD Approach for Free Vibration Simulation of Linear Beam Model Keywords:

Proper orthogonal decomposition , Low-dimensional model , Free vibration , Structural dynamics