Weighted linearization technique for period approximation in large amplitude non-linear oscillations

Agrwal, V.P.; Denman, Harry H.

doi:10.1016/0022-460x(85)90534-6

Cited by 41 publications

(18 citation statements)

References 6 publications

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“…But these methods have certain limitation such as perturbation method is physically sound for weak physical parameter again multiple scale analysis could not produce time dependent behaviour as the method based on averaging the time, The Homotopy analysis method overcome these difficulty but very difficult to implement. There are some non-perturb analytic method such as Weighted linearization method (Agrwal and Denman 1985), Adomian decomposition (Adomian 1988;El-Danaf, Ramadan, and Alaal 2005) method, Laplace Transform method (Alia, Sheikha;Saqiba, and Khanb 2017) vibrational iteration method (He, Wan, and Guo 2004), δ−expansion method (Awrejcewicz, Andrianov, and Manevitch 2012) however all these customary strategies can't guarantee about the convergence of solution series and also those methods cannot be are easily implemented. The present work may excel for the following aspects:…”

Section: Introductionmentioning

confidence: 99%

On Dispersion in Oscillatory Annular Flow Driven Jointly by Pressure Pulsation and Wall Oscillation

Roy

Saha

Debnath

2017

JAFM

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Longitudinal dispersion of solute released in an unsteady flow between two coaxial cylinders is re-examined in the presence of first order chemical kinetics in the bulk flow. The flow unsteadiness is caused by the oscillation of the outer tube around its axis as well as by a periodic pressure gradient. Unlike some previous works, the gap width of the annular tube is used as the typical length scale which is physically meaningful to a greater extent. In order to employ the method of moment, a finite difference implicit scheme has been adopted to solve the Aris integral moment equations arising from the unsteady convective diffusion equation for all time periods. The individual and combined effects of different velocity components resulting from steady and timedependent parts of the driving forces are examined and they are identified based on their functionality. In any flow situation, wall factor is found to have a larger contribution in velocity as well as in dispersion compared to the pressure factor. The behaviour of dispersion coefficient with the variation of radius ratio, bulk flow reaction parameter, and frequency parameters have been examined. Dispersion coefficient is found to diminish with the increase of the reaction-rate in the bulk flow, whereas the effect of the radius ratio on the dispersion coefficient is fixed by the form of the velocity distribution. The axial distributions of mean concentration are approximated using Hermite polynomial representation from the first four central moments for a range of different reaction-rate parameters. It has been found that, irrespective of the flow situation, the peak of the concentration distribution decreases with the increase in reaction rate parameter.

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Section: Introductionmentioning

confidence: 99%

On Dispersion in Oscillatory Annular Flow Driven Jointly by Pressure Pulsation and Wall Oscillation

Roy

Saha

Debnath

2017

JAFM

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“…The following remarks are important to set the number of terms of the power series expansion of Equations (5) and (6) that provides an invariant polynomial expression which describes the shapes of the invariant manifolds that are related to the system's nonlinear normal modes [21,38,42]: (a) Odd terms arise in the right-hand term (RHT) of the invariant polynomial expressions of Equations (5) and (6) if the restoring forces of the dynamic system are described by an invariant odd polynomial expression.…”

Section: Transformation Techniquementioning

confidence: 99%

“…(b) If the restoring forces of the original system have mixed-parity nonlinearities, then even and odd terms arise in the RHT invariant polynomial expressions of Equations (5) and (6). (c) Velocity-dependent terms arise mainly in the RHT of the invariant polynomial expressions of Equations (5) and (6) in order to capture not only the effective trend of the system's nonlinearities responsible for displaying amplitude-dependent nonlinear mode shapes, but also to take into account decay rate effects.…”

Section: Transformation Techniquementioning

confidence: 99%

“…(c) Velocity-dependent terms arise mainly in the RHT of the invariant polynomial expressions of Equations (5) and (6) in order to capture not only the effective trend of the system's nonlinearities responsible for displaying amplitude-dependent nonlinear mode shapes, but also to take into account decay rate effects.…”

Section: Transformation Techniquementioning

confidence: 99%

“…Minorsky [1], Caughey [2], Iwan [3,4], Sinha and Srinivasan [5], Agrwal and Denman [6], Yuste and Sánchez [7,8], Cai [9], Farzaneh and Tootoonchi [10], and many others have reported approaches that replace linear and nonlinear dynamic systems by equivalent ones with known solutions that are closed to the original system, which produce the same oscillations that appear in the original equations of motion. .…”

Section: Introductionmentioning

confidence: 99%

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Lyapunov Equivalent Representation Form of Forced, Damped, Nonlinear, Two Degree-of-Freedom Systems

et al. 2018

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Featured Application: The qualitative and quantitative dynamic behavior of two degree-offreedom nonlinear systems can be studied by using their corresponding decoupled one degree of freedom Duffing type equivalent representation forms in the sense of Lyapunov, with the advantage of capturing amplitude-dependent nonlinear mode shapes.Abstract: The aim of this paper focuses on finding equivalent representation forms of forced, damped, two degree-of-freedom, nonlinear systems in the sense of Lyapunov by using a nonlinear transformation approach that provides decoupled, forced, damped, nonlinear equations of the Duffing type, under the assumption that the driving frequency and the external forces are equal in both systems. The values of Lyapunov characteristic exponents (LCEs), Lyapunov largest exponents (LLE), and time-amplitude and frequency-amplitude curves computed from numerical integration solutions, indicate that the decoupled Duffing-type equations are equivalent, in the sense of Lyapunov, to the original dynamic system, since both set of motion equations tend to have the same qualitative and quantitative behaviors.

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Introduction

Marinca¹,

Herişanu²

2015

The Optimal Homotopy Asymptotic Method

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Weighted linearization technique for period approximation in large amplitude non-linear oscillations

Cited by 41 publications

References 6 publications

On Dispersion in Oscillatory Annular Flow Driven Jointly by Pressure Pulsation and Wall Oscillation

On Dispersion in Oscillatory Annular Flow Driven Jointly by Pressure Pulsation and Wall Oscillation

Lyapunov Equivalent Representation Form of Forced, Damped, Nonlinear, Two Degree-of-Freedom Systems

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