scholarly journals Higher accuracy analytical approximations to nonlinear oscillators with discontinuity by energy balance method

2017 ◽  
Vol 7 ◽  
pp. 2104-2110 ◽  
Author(s):  
M. Helal Uddin Molla ◽  
M.S. Alam
Keyword(s):  
Energy Balance ◽  
Nonlinear Oscillators ◽  
Balance Method ◽  
Energy Balance Method ◽  
Analytical Approximations

scholarly journals ANALYSIS OF NONLINEAR OSCILLATORS WITH U FORCE BY HE’S ENERGY BALANCE METHOD

2008 ◽  
Vol 3 ◽  
pp. 57-66 ◽  
Author(s):  
Mehdi Akbarzade ◽  
Davoodi Domiri Ganji ◽  
Mohammad Hadi Pashaei
Keyword(s):  
Energy Balance ◽  
Nonlinear Oscillators ◽  
Balance Method ◽  
Energy Balance Method

scholarly journals High-Order Energy Balance Method to Nonlinear Oscillators

2012 ◽  
Vol 2012 ◽  
pp. 1-7 ◽  
Author(s):  
Seher Durmaz ◽  
Metin Orhan Kaya
Keyword(s):  
Energy Balance ◽  
Order Approximation ◽  
Duffing Oscillator ◽  
Nonlinear Oscillators ◽  
High Order ◽  
Balance Method ◽  
Third Order ◽  
Energy Balance Method ◽  
Relative Errors ◽  
Third Order Approximation

Energy balance method (EBM) is extended for high-order nonlinear oscillators. To illustrate the effectiveness of the method, a cubic-quintic Duffing oscillator was chosen. The maximum relative errors of the frequencies of the oscillator read 1.25% and 0.6% for the first- and second-order approximation, respectively. The third-order approximation has an accuracy as high as 0.008%. Excellent agreement of the approximated frequencies and periodic solutions with the exact ones is demonstrated for several values of parameters of the oscillator.

Dynamics research of Fangzhu’s nanoscale surface

2021 ◽  
pp. 146134842110527
Author(s):  
Pinxia Wu ◽  
Weiwei Ling ◽  
Xiumei Li ◽  
Xichun He ◽  
Liangjin Xie
Keyword(s):  
Energy Balance ◽  
Analytical Solutions ◽  
Numerical Experiments ◽  
Fractal Model ◽  
Balance Method ◽  
Transform Method ◽  
Energy Balance Method ◽  
Collection Rate ◽  
Fractal Derivative ◽  
Approximate Analytical Solutions

In this paper, we mainly focus on a fractal model of Fangzhu’s nanoscale surface for water collection which is established through He’s fractal derivative. Based on the fractal two-scale transform method, the approximate analytical solutions are obtained by the energy balance method and He’s frequency–amplitude formulation method with average residuals. Some specific numerical experiments of the model show that these two methods are simple and effective and can be adopted to other nonlinear fractal oscillators. In addition, these properties of the obtained solution reveal how to enhance the collection rate of Fangzhu by adjusting the smoothness of its surfaces.

Sign in / Sign up

Export Citation Format

Share Document