Artificial Parameter Perturbation Method and Parameter-Expansion Method Used in Accurate Prediction of the Ring-Spinning Balloon in Zero Air Drag

2010 ◽  
Author(s):  
Rong Yin ◽  
Yang Liu ◽  
Hongbo Gu
Keyword(s):  
Perturbation Method ◽  
Expansion Method ◽  
Accurate Prediction ◽  
Ring Spinning ◽  
Parameter Perturbation ◽  
Air Drag ◽  
Parameter Expansion ◽  
Parameter Perturbation Method ◽  
Artificial Parameter ◽  
Parameter Expansion Method

Determination of the Limit Cycle by He’s Parameter-Expansion for Oscillators in a u3 / (1 + u2) Potential

2007 ◽  
Vol 62 (7-8) ◽  
pp. 396-398 ◽  
Author(s):  
Li-Na Zhang ◽  
Lan Xu
Keyword(s):  
Exact Solutions ◽  
Limit Cycle ◽  
Limit Cycles ◽  
Expansion Method ◽  
Nonlinear Oscillators ◽  
Mathematical Tool ◽  
Parameter Expansion ◽  
Parameter Expansion Method ◽  
Powerful Mathematical Tool

This paper applies He’s parameter-expansion method to determine the limit cycle of oscillators in a u3/(1+u2) potential. The results are compared with the exact solutions. This shows that the method is a convenient and powerful mathematical tool for the search of limit cycles of nonlinear oscillators.

scholarly journals Application of Multi-Parameter Perturbation Method to Functionally-Graded, Thin, Circular Piezoelectric Plates

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 342 ◽  
Author(s):  
Xiao-Ting He ◽  
Zhi-Xin Yang ◽  
Yang-Hui Li ◽  
Xue Li ◽  
Jun-Yi Sun
Keyword(s):  
Perturbation Method ◽  
Electrical Potential ◽  
Functionally Graded ◽  
Parameter Perturbation ◽  
Graded Materials ◽  
Cylindrical Coordinate ◽  
Stress Functions ◽  
Perturbation Parameters ◽  
Parameter Perturbation Method ◽  
Piezoelectric Plates

In this study, a multi-parameter perturbation method is used for the solution of a functionally-graded, thin, circular piezoelectric plate. First, by assuming that elastic, piezoelectric, and dielectric coefficients of the functionally-graded materials vary in the form of the same exponential function, the basic equation expressed in terms of two stress functions and one electrical potential function are established in cylindrical coordinate system. Three piezoelectric coefficients are selected as perturbation parameters, and the established equations are solved by the multi-parameter perturbation method, thus obtaining up to first-order perturbation solutions. The validity of the perturbation solution obtained is verified by numerical simulations, based on layer-wise theory. The perturbation process indicates that adopting three piezoelectric coefficients as perturbation parameters follows the basic idea of perturbation theory—i.e., if the piezoelectricity may be regarded as a kind of introduced disturbance, the zero-order solution of the disturbance system corresponds exactly to the solution of functionally-graded plates without piezoelectricity. The result also indicates that the deformation magnitude of piezoelectric plates is smaller than that of plates without piezoelectricity, due to the well-known piezoelectric stiffening effect.

scholarly journals Higher-Order Solutions of Coupled Systems Using the Parameter Expansion Method

2009 ◽  
Vol 2009 ◽  
pp. 1-20 ◽  
Author(s):  
S. S. Ganji ◽  
M. G. Sfahani ◽  
S. M. Modares Tonekaboni ◽  
A. K. Moosavi ◽  
D. D. Ganji
Keyword(s):  
Exact Solution ◽  
Order Approximation ◽  
Expansion Method ◽  
Higher Order ◽  
Coupled Systems ◽  
Parameter Expansion ◽  
Analytical Technique ◽  
First Approximation ◽  
Mass Spring ◽  
Parameter Expansion Method

We consider periodic solution for coupled systems of mass-spring. Three practical cases of these systems are explained and introduced. An analytical technique called Parameter Expansion Method (PEM) was applied to calculate approximations to the achieved nonlinear differential oscillation equations. Comparing with exact solutions, the first approximation to the frequency of oscillation produces tolerable error 3.14% as the maximum. By the second iteration the respective error became 1/5th, as it is 0.064%. So we conclude that the first approximation of PEM is so benefit when a quick answer is required, but the higher order approximation gives a convergent precise solution when an exact solution is required.

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