@article{article_397802, title={Nonlinear Oscillations of a Mass Attached to Linear and Nonlinear Springs in Series Using Approximate Solutions}, journal={Celal Bayar University Journal of Science}, volume={14}, pages={201–207}, year={2018}, DOI={10.18466/cbayarfbe.397802}, author={Bostancı, Beyza and Karahan, M. M. Fatih}, keywords={Multiple Scales Lindstedt Poincare (MSLP) method,Nonlinear Oscillation,Nonlinear Stiffness,Perturbation Methods.}, abstract={<div style="text-align:justify;"> <span lang="en-us" style="font-size:10pt;font-family:’Times New Roman’, serif;" xml:lang="en-us">Nonlinear oscillations of a mass with serial linear and nonlinear
stiffness on a frictionless surface is considered. Equation of motion of </span> <span lang="en-us" style="font-size:10pt;font-family:’Times New Roman’, serif;" xml:lang="en-us">the considered </span> <span lang="en-us" style="font-size:10pt;font-family:’Times New Roman’, serif;" xml:lang="en-us">system is obtained. </span> <span lang="en-us" style="font-size:10pt;font-family:’Times New Roman’, serif;" xml:lang="en-us">For analysing of the
system, relatively new perturbation method that is named Multiple Scales
Lindstedt Poincare (MSLP) and classical multiple scales (MS) methods are used.
Both approximate solutions are compared with the numerical solutions for weakly
and strongly nonlinear systems. For weakly nonlinear systems, both approximate
solutions are in excellent agreement with numerical simulations. However, for
strong nonlinearities, MS method is not give reliable results while MSLP method
can provide acceptable solutions with numerical solutions. </span> </div>}, number={2}, publisher={Manisa Celal Bayar University}