Abstract
This paper applies approximate analytical methods namely Iteration Perturbation Method (IPM), variational approach (VA) and Parameter Expanding Method (PEM) to Single-Degree-Of-Freedom (SDOF) nonlinear oscillation systems. Some numerical cases as dynamic behavior of current-carrying wire-conductors and bucking of a column as well as their comparisons with the exact solutions are presented. Different specific parameters and initial values comprising the mass and stiffness are studied within the current research and excellent accuracy which is the most significant feature of the proposed solutions, is reported for the whole range of oscillation amplitude values.DOI: http://dx.doi.org/10.5755/j01.mech.19.3.4659
Highlights
A one-dimensional composite frame element for nonlinear static and cyclic behavior of concrete-filled steel beam columns is formulated by Valipour and Foster [5].A nonlinear fiber element analysis is presented through the work presented by Liang et al [6] for predicting the ultimate strengths of thin-walled steel box columns with local buckling behavior
The results presented in this paper reveal that these methods are very effective and convenient for conservative nonlinear oscillators
We introduce the variable y du dt, and Eq (5) can be replaced by equivalent system: u t y t ; (6)
Summary
In the last few decades, Single-Degree-OfFreedom (SDOF) oscillator has been widely used to study the behavior of machines used in pile driving, compacting, rock drilling, impact printing and marine structures [1,2,3,4]. We obtain an approximate expression for the periodic solutions to two practical cases [25, 26] of nonlinear SODF oscillation systems, namely oscillation of current-carrying wire in a magnetic field and the model of bucking of a column by means of iteration perturbation method (IPM), variational approach (VA), and perturbation expansion method (PEM). These techniques yield a very rapid convergence using an iteration and lead to high accuracy of the solution. The results presented in this paper reveal that these methods are very effective and convenient for conservative nonlinear oscillators
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