Browsing by Subject "Multiple scales methods"

Now showing 1 - 6 of 6
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    A new perturbation algorithm with better convergence properties: Multiple scales lindstedt poincare method
    (Association for Scientific Research, 2009) Pakdemirli M.; Karahan M.M.F.; Boyaci H.
    A new perturbation algorithm combining the Method of Multiple Scales and Lindstedt-Poincare techniques is proposed for the first time. The algorithm combines the advantages of both methods. Convergence to real solutions with large perturbation parameters can be achieved for both constant amplitude and variable amplitude cases. Three problems are solved: Linear damped vibration equation, classical duffing equation and damped cubic nonlinear equation. Results of Multiple Scales, new method and numerical solutions are contrasted. The proposed new method produces better results for strong nonlinearities. © Association for Scientific Research.
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    Forced vibrations of strongly nonlinear systems with multiple scales lindstedt poincare method
    (Association for Scientific Research, 2011) Pakdemirli M.; Karahan M.M.F.; Boyaci H.
    Forced vibrations of duffing equation with damping is considered. Recently developed Multiple Scales Lindstedt-Poincare (MSLP) technique for free vibrations is applied for the first time to the forced vibration problem in search of approximate solutions. For the case of weak and strong nonlinearities, approximate solutions of the new method are contrasted with the usual Multiple Scales (MS) method and numerical simulations. For weakly nonlinear systems, frequency response curves of both perturbation methods and numerical solutions are in good agreement. For strongly nonlinear systems however, results of MS deviate much from the MSLP method and numerical simulations, the latter two being in good agreement. Keywords- Perturbation Methods, Lindstedt Poincare method, Multiple. © Association for Scientific Research.
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    A new perturbation technique in solution of nonlinear differential equations by using variable transformation
    (2014) Elmas N.; Boyaci H.
    A perturbation algorithm using a new variable transformation is introduced. This transformation enables control of the independent variable of the problem. The problems are solved with new transformation: Classical Duffing equation with cubic nonlinear term and a singular perturbation problem. Results of multiple scales, Lindstedt Poincare method, new method and numerical solutions are contrasted.© 2013 Elsevier Inc.
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    Solution of quadratic nonlinear problems with multiple scales Lindstedt-Poincare method
    (Association for Scientific Research, 2015) Pakdemirli M.; Sari G.
    A recently developed perturbation algorithm namely the multiple scales Lindstedt-Poincare method (MSLP) is employed to solve the mathematical models. Three different models with quadratic nonlinearities are considered. Approximate solutions are obtained with classical multiple scales method (MS) and the MSLP method and they are compared with the numerical solutions. It is shown that MSLP solutions are better than the MS solutions for the strongly nonlinear case of the considered models. © 2015, Association for Scientific Research. All rights reserved.
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    Solution of a quadratic nonlinear problem with multiple scales Lindstedt-Poincare method
    (American Institute of Physics Inc., 2015) Pakdemirli M.; SarI G.
    A recently developed perturbation algorithm namely the Multiple Scales Lindstedt-Poincare method (MSLP) is employed to solve an equation with quadratic nonlinearity. Approximate solutions are obtained with classical multiple scales Method (MS) and the MSLP method and they are compared with numerical solutions. It is shown that MSLP solutions are better than the MS solutions for the strongly nonlinear case. © 2015 AIP Publishing LLC.
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    Magnetic field effect on nonlinear vibration of nonlocal nanobeam embedded in nonlinear elastic foundation
    (Techno-Press, 2021) Yapanmiş B.E.; Toǧun N.; Baǧdatli S.M.; Akkoca Ş.
    The history of modern humanity is developing towards making the technological equipment used as small as possible to facilitate human life. From this perspective, it is expected that electromechanical systems should be reduced to a size suitable for the requirements of the era. Therefore, dimensionless motion analysis of beams on the devices such as electronics, optics, etc., is of great significance. In this study, the linear and nonlinear vibration of nanobeams, which are frequently used in nanostructures, are focused on. Scenarios have been created about the vibration of nanobeams on the magnetic field and elastic foundation. In addition to these, the boundary conditions (BC) of nanobeams having clamped-clamped and simple-simple support situations are investigated. Nonlinear and linear natural frequencies of nanobeams are found, and the results are presented in tables and graphs. When the results are examined, decreases the vibration amplitudes with the increase of magnetic field and the elastic foundation coefficient. Higher frequency values and correction terms were obtained in clamped-clamped support conditions due to the structure's stiffening. © 2021 Techno-Press, Ltd.