A Modified Lindstedt–Poincaré Method for a Strongly Nonlinear System with Quadratic and Cubic Nonlinearities
نویسندگان
چکیده
منابع مشابه
A MODIFIED STEFFENSEN'S METHOD WITH MEMORY FOR NONLINEAR EQUATIONS
In this note, we propose a modification of Steffensen's method with some free parameters. These parameters are then be used for further acceleration via the concept of with memorization. In this way, we derive a fast Steffensen-type method with memory for solving nonlinear equations. Numerical results are also given to support the underlying theory of the article.
متن کاملAccuracy Improvement of the Method of Multiple Scales for Nonlinear Vibration Analyses of Continuous Systems with Quadratic and Cubic Nonlinearities
This paper proposes an accuracy improvement of the method of multiple scales MMSs for nonlinear vibration analyses of continuous systems with quadratic and cubic nonlinearities. As an example, we treat a shallow suspended cable subjected to a harmonic excitation, and investigate the primary resonance of themth in-plane mode Ω ≈ ωm in whichΩ and ωm are the driving and natural frequencies, respec...
متن کاملAnalytical Solution for the Forced Vibrations of a Nano-Resonator with Cubic Nonlinearities Using Homotopy Analysis Method
Many of nonlinear systems in the field of engineering such as nano-resonator and atomic force microscope can be modeled based on Duffing equation. Analytical frequency response of this system helps us analyze different interesting nonlinear behaviors appearing in its response due to its rich dynamics. In this paper, the general form of Duffing equation with cubic nonlinearity as well as par...
متن کاملSOLVING NONLINEAR KLEIN-GORDON EQUATION WITH A QUADRATIC NONLINEAR TERM USING HOMOTOPY ANALYSIS METHOD
In this paper, nonlinear Klein-Gordon equation with quadratic term is solved by means of an analytic technique, namely the Homotopy analysis method (HAM).Comparisons are made between the Adomian decomposition method (ADM), the exact solution and homotopy analysis method. The results reveal that the proposed method is very effective and simple.
متن کاملGiant Nonlinear Optical Activity of Achiral Origin in Planar Metasurfaces with Quadratic and Cubic Nonlinearities.
3D chirality is shown to be unnecessary for introducing strong circular dichroism for harmonic generations. Specifically, near-unity circular dichroism for both second-harmonic generation and third-harmonic generations is demonstrated on suitably designed ultrathin plasmonic metasurfaces with only 2D planar chirality. The study opens up new routes for designing chip-type biosensing platform, wh...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Shock and Vibration
سال: 1996
ISSN: 1070-9622,1875-9203
DOI: 10.1155/1996/231241