Journal ArticleDOI
The solution structure of the Düffing oscillator’s transient response and general solution
Keguan Zou,Satish Nagarajaiah +1 more
TLDR
In this paper, a modification of homotopy analysis method (HAM) is developed, and the solution structure of the Duffing oscillator free vibration at different damping levels is put forward based on this modified HAM.Abstract:
A modification of homotopy analysis method (HAM) is developed in this paper. The solution structure of the Duffing oscillator’s free vibration at different damping levels is put forward based on this new modified HAM. Explicit expressions for the fundamental decaying rate and the fundamental frequency are derived. Numerical examples with different initial conditions are calculated to verify the proposed solution structures. The number of terms required to be considered in the modified HAM for yielding satisfactorily accurate solutions is analyzed. The structure of forced and damped Duffing oscillator’s general solution is also put forward and verified.read more
Citations
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Journal ArticleDOI
Analytical study of exact solutions of the nonlinear Korteweg-de Vries equation with space-time fractional derivatives
Jiangen Liu,Yufeng Zhang +1 more
TL;DR: In this article, the exact solutions of the Kortewegde Vries equation with space-time local fractional derivatives were analyzed and the explicit traveling wave solutions including periodic solutions, dark soliton solutions, soliton solution and soliton-like solutions were obtained for the first time.
Journal ArticleDOI
Adjustable template stiffness device and SDOF nonlinear frequency response
TL;DR: In this article, an adjustable template stiffness device (ATSD) is presented, which is made up of precompressed springs attached to rollers, rolling along curved templates that allow adjustment of stiffness as a predetermined function of displacement.
Journal ArticleDOI
Bifurcation and chaotic threshold of Duffing system with jump discontinuities
TL;DR: In this paper, the authors proposed a reasonable compromise based on all of characteristics of the non-smooth homoclinic orbits with the jump discontinuities for the Duffing system with open interval, where the extended Melnikov function is explicitly detected to judge the stable and unstable manifolds whether intersect transversally at any position of trajectory under the perturbation of damping and external forcing.
Journal ArticleDOI
Numerical and Experimental Study of Clearance Nonlinearities Based on Nonlinear Response Reconstruction
Journal ArticleDOI
Closed-form criterion for convergence and stability of pseudo-force method for nonlinear dynamic analysis
Keguan Zou,Satish Nagarajaiah +1 more
TL;DR: In this paper, the authors investigated the convergence of the pseudo-force (PF) method for single and multi-degree of freedom systems with elasto-plastic nonlinearities which involve repeated cycles of loading and unloading.
References
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Book
Perturbation Methods
Ali H. Nayfeh,Vimal Singh +1 more
TL;DR: This website becomes a very available place to look for countless perturbation methods sources and sources about the books from countries in the world are provided.
Book
Introduction to perturbation techniques
TL;DR: In this paper, the authors introduce the notion of forced Oscillations of the Duffing Equation and the Mathieu Equation for weakly nonlinear systems with quadratic and cubic nonlinearities.
Book
Homotopy Analysis Method in Nonlinear Differential Equations
TL;DR: In this paper, a convergence series for Divergent Taylor Series is proposed to solve nonlinear initial value problems and nonlinear Eigenvalue problems with free or moving boundary in heat transfer.
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