Premium
Application of the fast nonlinear analysis method on a clamped beam with a cubic spring
Author(s) -
Akar Özge,
Willner Kai
Publication year - 2019
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201900022
Subject(s) - beam (structure) , nonlinear system , ritz method , spring (device) , vibration , finite element method , eigenvalues and eigenvectors , discretization , context (archaeology) , structural engineering , piecewise , normal mode , displacement (psychology) , piecewise linear function , acceleration , mathematics , mathematical analysis , engineering , classical mechanics , physics , acoustics , geology , quantum mechanics , psychology , paleontology , psychotherapist
In 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.