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Journals / Celal Bayar Üniversitesi Fen Bilimleri Dergisi / 2018 / Cilt: 14 - Sayı: 2

Nonlinear Oscillations of a Mass Attached to Linear and Nonlinear Springs in Series Using Approximate Solutions

Beyza BOSTANCI
M. M. Fatih KARAHAN
Pages
201–207
Publication Date
2018-06-30
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

However, for strong nonlinearities, MS method is not give reliable results while MSLP method can provide acceptable solutions with numerical solutions.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:Nonlinear oscillations of a mass with serial linear and nonlinear stiffness on a frictionless surface is considered.
📊
Key Findings & Data:Equation of motion of the considered system is obtained.
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Conclusion & Impact:However, for strong nonlinearities, MS method is not give reliable results while MSLP method can provide acceptable solutions with numerical solutions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Multiple Scales Lindstedt Poincare (MSLP) method · Nonlinear Oscillation · Nonlinear Stiffness

Abstract

Nonlinear oscillations of a mass with serial linear and nonlinear stiffness on a frictionless surface is considered. Equation of motion of the considered system is obtained. 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.

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Cite This Article

BOSTANCI, B., KARAHAN, M. M. F. (2018). Nonlinear Oscillations of a Mass Attached to Linear and Nonlinear Springs in Series Using Approximate Solutions. Celal Bayar Üniversitesi Fen Bilimleri Dergisi, Cilt: 14 - Sayı: 2, 201–207. https://ajindex.com/articles/108806

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