Model order reduction of nonlinear Euler-Bernoulli beam

Abstract

Numerical simulations of large-scale models of complex systems are essential to modern research and development. However these simulations are also problematic by requiring excessive computational resources and large data storage. High fidelity reduced order models (ROMs) can be used to overcome these difficulties, but are hard to develop and test. A new framework for identifying subspaces suitable for ROM development has been recently proposed. This framework is based on two new concepts: (1) dynamic consistency which indicates how well does the ROM preserve the dynamical properties of the full-scale model; and (2) subspace robustness which indicates the suitability of ROM for a range of initial conditions, forcing amplitudes, and system parameters. This framework has been tested on relatively low-dimensional systems; however, its feasibility for more complex systems is still unexplored. A 58 degree-of-freedom fixed-fixed nonlinear Euler-Bernoulli beam is studied, where large-amplitude forcing introduces geometrical nonlinearities. The responses of the beam subjected to both harmonic and random loads are obtained using finite difference method. The ROM subspaces are identified using the framework with both Proper Orthogonal Decomposition (POD) and Smooth Orthogonal Decomposition (SOD). POD- and SOD-based ROMs are then compared and fidelity of the new framework is evaluated.