Nonlinear Dynamic Analysis of Cantilever Beam Using POD Based Reduced Order Model

Abstract:

In this paper, a reduced order model is obtained for nonlinear dynamic analysis of a cantilever beam. Nonlinearity in the system is basically due to large deformation. A reduced order model is an efficient method to formulate low order dynamical model which can be obtained from data obtained from numerical technique such as finite element method (FEM). Nonlinear dynamical models are complex with large number of degrees of freedom and hence, are computationally intensive. With formulation of reduced order models (i.e. Macromodels) number of degrees of freedom are reduced to fewer degrees of freedom by using projection based method like Galerkin’s projection, so as to make system computationally faster and cost effective. These macromodels are obtained by extracting global basis functions from fully meshed model runs. Macromodels are generated using technique called proper orthogonal decomposition (POD) which gives good linear fit for the nonlinear systems. Using POD based macromodel, response of system can be computed using fewer modes instead of considering all modes of system. Macromodel is generated to obtain the response of cantilever beam with large deformation and hence, simulation time is reduced by factor of 90 approximately with error of order of 10^-4. Further, method of POD based reduced order model is aplied to beam with different loading conditions to check the robustness of the macromodel. POD based macromodel response gives good agreement with FEA model response for a cantilever beam.

• Periodical: Applied Mechanics and Materials (Volume 786)
• Pages: 398-403
• DOI: https://doi.org/10.4028/www.scientific.net/AMM.786.398
• Online since: August 2015
• Authors: Kulkarni Atul Shankar*, Manoj Pandey
• Keywords: Finite Element Method (FEM), Global Basis Functions, Large Deformation, Nonlinear Dynamics, Proper Orthogonal Decomposition, Reduced Order Model

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