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An Alternative Analysis of Duffing’s Equation
SIAM Review, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Parametric Frequency Analysis of Mathieu–Duffing Equation
International Journal of Bifurcation and Chaos, 2021The 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
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Experimental mimicry of Duffing's equation
Journal of Sound and Vibration, 1992Abstract 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
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On controllability of Duffing equation
Applied Mathematics and Computation, 2013zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Loi, Nguyen Van, Obukhovskii, Valeri
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The generalized duffing equation with large damping
International Journal of Non-Linear Mechanics, 1968Abstract 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.
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On Quasi-periodic Perturbations of Duffing Equation
The interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity, 2016Summary: 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.
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Duffing equation and action functional
Nonlinear Analysis: Theory, Methods & Applications, 2011zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Boundedness of solutions for semilinear duffing equations
Applied Mathematics and Computation, 2002The author studies the boundedness of all solutions of the equation \(x''+n^{2}x+f(x) = p(t)\). The main result is the following theorem: Suppose \(f(x) \in C^{\infty } ({\mathbb R}), p(t)\in C^{6} ({\mathbb R}/2 \pi {\mathbb Z})\). If \(\int^{2\pi }_{0} p(t)e^{-int}dt = 0\) and if \(f(x)\) satisfies the following conditions: the limits \(\lim \limits_{
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Duffing's equation and nonlinear resonance
International Journal of Mathematical Education in Science and Technology, 2003The phenomenon of nonlinear resonance (sometimes called the ‘jump phenomenon’) is examined and second-order van der Pol plane analysis is employed to indicate that this phenomenon is not a feature of the equation, but rather the result of accumulated round-off error, truncation error and algorithm error that distorts the true bounded solution onto an ...
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Solution of the Duffing Equation
1994Consider the Duffing equation with variable excitation and constant coefficients α, β, γ $$\begin{gathered} {\text{u''}} + \alpha u' + \beta u + \gamma {u^3} = \delta (t) \hfill \\ u(0) = {c_0}{\text{ u'(0) = }}{{\text{c}}_1} \hfill \\ \end{gathered} % MathType!End!2!1! $$ δ(t) will be written as a series δ(t) = Σ n=0 ∞ δntn. Let L = d2/dt2. Then
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