Nonlinear Vertical Vibration of Tension Leg Platforms with Homotopy Analysis Method

2015 ◽  
Vol 7 (3) ◽  
pp. 357-368 ◽  
Author(s):  
Arash Reza ◽  
Hamid M. Sedighi
Keyword(s):  
Differential Equation ◽  
Homotopy Analysis Method ◽  
Equations Of Motion ◽  
Closed Form Solution ◽  
Added Mass ◽  
Form Solution ◽  
Analysis Method ◽  
Homotopy Analysis ◽  
Mass Coefficient ◽  
Added Mass Coefficient

AbstractOne of the useful methods for offshore oil exploration in the deep regions is the use of tension leg platforms (TLP). The effective mass fluctuating of the structure which due to its vibration can be noted as one of the important issues about these platforms. With this description, dynamic analysis of these structures will play a significant role in their design. Differential equations of motion of such systems are nonlinear and providing a useful method for its analysis is very important. Also, the amount of added mass coefficient has a direct effect on the level of nonlinearity of partial differential equation of these systems. In this study, Homotopy analysis method has been used for closed form solution of the governing differential equation. Linear springs have been used for modeling the stiffness of this system and the effects of torsion, bending and damping of water have been ignored. In the study of obtained results, the effect of added mass coefficient has been investigated. The results show that increasing of this coefficient decreases the bottom amplitude of fluctuations and the system frequency. The obtained results from this method are in good agreement with the published results on the valid articles.

A Homotopy Analysis Method for the Option Pricing PDE in Post-Crash Markets

2014 ◽  
Vol 2 (3-4) ◽  
pp. 45-50
Author(s):  
Youssef El-Khatib
Keyword(s):  
Differential Equation ◽  
Financial Crisis ◽  
Option Pricing ◽  
Homotopy Analysis Method ◽  
Closed Form Solution ◽  
Form Solution ◽  
Analysis Method ◽  
European Option ◽  
Homotopy Analysis ◽  
Crash Model

AbstractWe investigate a solution for the option pricing partial differential equation (PDE) in a market suffering from a financial crisis. The post-crash model assumes that the volatility is stochastic. It is an extension of the famous Black and Scholes model. Therefore, the option pricing PDE for the crisis model is a generalization of the Black and Scholes PDE. However, to the best knowledge, it does not have a closed form solution for the general case. In this paper, we provide a solution for the pricing PDE of a European option during financial crisis using the homotopy analysis method.

Flight Performance Analysis of Hybrid Airship Considering Added Mass Effects

2018 ◽  
Vol 140 (11) ◽  
Author(s):  
Lanchuan Zhang ◽  
Mingyun Lv ◽  
Cong Sun ◽  
Junhui Meng
Keyword(s):  
Mass Matrix ◽  
Equations Of Motion ◽  
Coefficient Matrix ◽  
Prolate Spheroid ◽  
Added Mass ◽  
Flight Performance ◽  
Mass Coefficient ◽  
Computational Fluid Dynamics Cfd ◽  
Added Mass Coefficient ◽  
Cfd Method

In this paper, an analysis is applied to a hybrid airship considering the added mass. First, based on the dynamic mesh technology, a computational fluid dynamics (CFD) method is employed to obtain the added mass coefficient matrix. Through a validation process using the 6:1 prolate spheroid, the 6 × 6 added mass matrix of hybrid airship is obtained. After a dynamic modeling, the equations of motion with added mass are developed. Through the linearization based on small perturbation, the linearized longitude model is used to simulate the dynamic response of a trim condition. The take-off and landing performance has been analyzed and affected by the added mass. The result shows an obvious vertical destabilizing trend on the hybrid airship dynamics due to the added mass and the inertial effect has little influence on the vehicle during the take-off and landing.

scholarly journals On the Solutions of Fractional Cauchy Problem Featuring Conformable Derivative

2018 ◽  
Vol 22 ◽  
pp. 01045 ◽  
Author(s):  
Mehmet Yavuz ◽  
Necati Özdemir
Keyword(s):  
Differential Equation ◽  
Cauchy Problem ◽  
Exact Solutions ◽  
Detailed Analysis ◽  
Analytical Solutions ◽  
Homotopy Analysis Method ◽  
Analysis Method ◽  
Conformable Derivative ◽  
Homotopy Analysis ◽  
Fractional Cauchy Problem

In this study, we have obtained analytical solutions of fractional Cauchy problem by using q-Homotopy Analysis Method (q-HAM) featuring conformable derivative. We have considered different situations according to the homogeneity and linearity of the fractional Cauchy differential equation. A detailed analysis of the results obtained in the study has been reported. According to the results, we have found out that our obtained solutions approach very speedily to the exact solutions.

Optimum Path of a Flying Object with Exponentially Decaying Density Medium

2009 ◽  
Vol 64 (7-8) ◽  
pp. 431-438 ◽  
Author(s):  
Said Abbasbandy ◽  
Mehmet Pakdemirli ◽  
Elyas Shivanian
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Homotopy Analysis Method ◽  
Analysis Method ◽  
Dimensionless Form ◽  
Optimum Path ◽  
Homotopy Analysis

AbstractIn this paper, a differential equation describing the optimum path of a flying object is derived. The density of the fluid is assumed to be exponentially decaying with altitude. The equation is cast in to a dimensionless form and the exact solution is given. This equation is then analyzed by homotopy analysis method (HAM). The results showed in the figures reveal that this method is very effective and convenient.

Studying Dynamic Pull-In Behavior of Microbeams by Means of the Homotopy Analysis Method

2008 ◽  
Author(s):  
Mahdi Moghimi Zand ◽  
S. Ahmad Tajalli ◽  
Mohammad Taghi Ahmadian
Keyword(s):  
Differential Equation ◽  
Homotopy Analysis Method ◽  
Nonlinear Partial Differential Equation ◽  
Nonlinear Ordinary Differential Equation ◽  
Strong Nonlinearity ◽  
Analysis Method ◽  
Solution Methods ◽  
Homotopy Analysis ◽  
Fringing Field ◽  
Fringing Field Effect

In this study, the homotopy analysis method (HAM) is used to study dynamic pull-in instability in microbeams considering different sources of nonlinearity. Electrostatic actuation, fringing field effect and midplane stretching causes strong nonlinearity in microbeams. In order to investigate dynamic pull-in behavior, using Galerkin’s decomposition method, the nonlinear partial differential equation of motion is reduced to a single nonlinear ordinary differential equation. The obtained equation is solved analytically in time domain using HAM. The problem is studied by two separate manners: direct use of HAM and indirect use of HAM in conjunction with He’s Modified Lindstedt-Poincare´ Method. To demonstrate the effectiveness of the solution methods, results are compared with those in literature. The comparison between obtained results and those available in literature shows good agreement.

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