Abstract
AbstractIn civil engineering reduction methods are used for the mechanical design of buildings in order to avoid unnecessary complexity and computational effort especially in the seismic design of structures. The determination of vibration modes by earthquake excitation is carried out by using Ritz vectors instead of eigenvectors. Thus, only the modes of interest are obtained. Furthermore, the Fast Nonlinear Analysis (FNA) method was formulated to easily insert nonlinearities like concentrated damping in a construction model. The main idea is to take the nonlinear forces to the right hand side of the equation of motion. In the context of this work, the FNA method is applied on a finite element model of a clamped beam with a cubic spring that works at the free end of the beam. First, a harmonic excitement is applied and the vibration modes of the system are obtained by using Ritz vectors. Then, a piecewise exact integration method is implemented to iteratively determine the results for displacement, velocity and acceleration of the discretized beam.
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