Results 121 to 130 of about 436 (168)

2π-Periodic solutions of Duffing's equation

USSR Computational Mathematics and Mathematical Physics, 1986
The common properties of different classes of \(2\pi\)-periodic solutions of Duffing's nonlinear differential equation are investigated analytically and numerically. Generating periodic solutions are examined. The basic properties of \(2\pi\)-periodic solutions are investigated using the nonlinear functional analysis method.
Galaktionova, O. O., Zlatoustov, V. A.
openaire   +2 more sources

Periodic solutions for Duffing equations

Nonlinear Analysis: Theory, Methods & Applications, 1995
The main result proved by the authors in this paper states that if \(k\) is the minimal positive integer such that \((k- 1)^2< A< k^2< B< \infty\), and there exists \(\beta\in C[0, 2\pi]\) such that \(A\leq f_y(x, y)\leq \beta(x)\leq B\) and \(\int^{2\pi}_0 \beta(x) dx< 2\pi A+ 2(B- A)\alpha_k\), where \(\alpha_k\) is the minimal positive root of the ...
Wang, H., Li, Y.
openaire   +2 more sources

Periodic Solutions of Discontinuous Duffing Equations

Qualitative Theory of Dynamical Systems, 2020
The author considers a scalar differential equation of the type \[ x''+g(x)=e(t), \] where \(e:{\mathbb R}\to {\mathbb R}\) is continuous and \(T\)-periodic, and \(g:{\mathbb R}\to {\mathbb R}\) has a discontinuity at the origin, with \(\lim_{x\to0^\pm}g(x)\in {\mathbb R}\) but different.
openaire   +2 more sources

An Alternative Analysis of Duffing’s Equation

SIAM Review, 1992
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +1 more source

Parametric Frequency Analysis of Mathieu–Duffing Equation

International Journal of Bifurcation and Chaos, 2021
The classic linear Mathieu equation is one of the archetypical differential equations which has been studied frequently by employing different analytical and numerical methods. The Mathieu equation with cubic nonlinear term, also known as Mathieu–Duffing equation, is one of the many extensions of the classic Mathieu equation. Nonlinear characteristics
openaire   +1 more source

Experimental mimicry of Duffing's equation

Journal of Sound and Vibration, 1992
Abstract Extensive analytical and numerical investigations have focused on Duffing's equation. However, experimental work, in a mechanics context, has been limited to studying systems the stiffness characteristics of which can be approximated by a non-linear (cubic) restoring force; e.g., a buckled beam excited transversely or a rigid pendulum ...
J.A. Gottwald, L.N. Virgin, E.H. Dowell
openaire   +1 more source

On controllability of Duffing equation

Applied Mathematics and Computation, 2013
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Loi, Nguyen Van, Obukhovskii, Valeri
openaire   +1 more source

The generalized duffing equation with large damping

International Journal of Non-Linear Mechanics, 1968
Abstract The equation x + 2p x + ω 2 0 x + μ n x = 0 where n is an odd integer greater than or equal to 3, x(0) = A0, and x (0) = 0 has received much attention in the literature but always with the restrictions that μ and p are small.
Ludeke, C. A., Wagner, W. S.
openaire   +2 more sources

On Quasi-periodic Perturbations of Duffing Equation

The interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity, 2016
Summary: Quasi-periodic two-frequency perturbations are studied in a system which is close to a nonlinear two-dimensional Hamiltonian one. The example of Duffing equation with a saddle and two separatix loops is considered. Several problems are studied: dynamical behavior in a neighborhood of a resonance level of the unperturbed system, conditions for ...
Morozov, A. D., Dragunov, T. N.
openaire   +1 more source

Duffing equation and action functional

Nonlinear Analysis: Theory, Methods & Applications, 2011
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources