scholarly journals APPROXIMATE ANALYTICAL SOLUTIONS TO NONLINEAR OSCILLATIONS OF NON-NATURAL SYSTEMS USING HE'S ENERGY BALANCE METHOD

2008 ◽  
Vol 5 ◽  
pp. 43-54 ◽  
Author(s):  
Davoodi Domiri Ganji ◽  
Salim Karimpour ◽  
Seyedreza Seyedaliza Ganji
Keyword(s):  
Energy Balance ◽  
Analytical Solutions ◽  
Nonlinear Oscillations ◽  
Balance Method ◽  
Energy Balance Method ◽  
Natural Systems ◽  
Approximate Analytical Solutions

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.

Fluctuation and Frequency of the Oscillators with Exponential Spring Using Accurate Approximate Analytical Solutions

2021 ◽  
pp. 2150036
Author(s):  
A. G. Davodi ◽  
H. Rezazadeh ◽  
Waleed Adel ◽  
A. Bekir ◽  
D. D. Ganji
Keyword(s):  
Energy Balance ◽  
Analytical Solutions ◽  
Horizontal Plane ◽  
Homotopy Perturbation Method ◽  
Governing Equations ◽  
Energy Balance Method ◽  
Homotopy Perturbation ◽  
Approximate Analytical Solutions ◽  
A Minor ◽  
Artificial Parameter

This paper examines the fluctuation and frequency of the motion of a homogeneous solid on a horizontal plane on an exponential crisscross spring. The governing equations of this oscillator are investigated using a modified Homotopy Perturbation method, Energy balance method and artificial parameter–Linstedt–Poincare’ method. A comparison of solutions shows that the fluctuation and frequency of the system solved by the presented methods are effective with a minor error of 0.1%.

Nonlinear Oscillations Analysis of the Elevator Cable in a Drum Drive Elevator System

2015 ◽  
Vol 7 (1) ◽  
pp. 43-57 ◽  
Author(s):  
H. Askari ◽  
D. Younesian ◽  
Z. Saadatnia
Keyword(s):  
Energy Balance ◽  
Closed Form ◽  
Natural Frequency ◽  
Governing Equation ◽  
Nonlinear Oscillations ◽  
Quadratic Function ◽  
Balance Method ◽  
Closed Form Expression ◽  
Energy Balance Method ◽  
Elevator Cable

AbstractThis paper aims to investigate nonlinear oscillations of an elevator cable in a drum drive. The governing equation of motion of the objective system is developed by virtue of Lagrangian’s method. A complicated term is broached in the governing equation of the motion of the system owing to existence of multiplication of a quadratic function of velocity with a sinusoidal function of displacement in the kinetic energy of the system. The obtained equation is an example of a well-known category of nonlinear oscillators, namely, non-natural systems. Due to the complex terms in the governing equation, perturbation methods cannot directly extract any closed form expressions for the natural frequency. Unavoidably, different non-perturbative approaches are employed to solve the problem and to elicit a closed-form expression for the natural frequency. Energy balance method, modified energy balance method and variational approach are utilized for frequency analyzing of the system. Frequency-amplitude relationships are analytically obtained for nonlinear vibration of the elevator’s drum. In order to examine accuracy of the obtained results, exact solutions are numerically obtained and then compared with those obtained from approximate closed-form solutions for several cases. In a parametric study for different nonlinear parameters, variation of the natural frequencies against the initial amplitude is investigated. Accuracy of the three different approaches is then discussed for both small and large amplitudes of the oscillations.

scholarly journals A distributed snowmelt prediction model in mountain areas based on an energy balance method

1994 ◽  
Vol 19 ◽  
pp. 107-113 ◽  
Author(s):  
Takeshi Ohta
Keyword(s):  
Energy Balance ◽  
Prediction Model ◽  
Deciduous Forest ◽  
Balance Method ◽  
Evergreen Forest ◽  
Snowmelt Runoff ◽  
Mountain Areas ◽  
Mountain Area ◽  
Energy Balance Method ◽  
Surface Cover

A distributed snowmelt prediction model was developed for a mountain area. Topography of the study area was represented by a digital map. Cells On the map were divided into three surface-cover types; deciduous forest, evergreen forest and deforested area. Snowmelt rates for each cell were calculated by an energy balance method. Meteorological elements were estimated separately in each cell according to topographical characteristics and surface-cover type. Distributions of water equivalent of snow cover were estimated by the model. Snowmelt runoff in the watershed was also simulated by snowmelt rates calculated by the model. The model showed thai the snowmelt period and snowmelt runoff after timber harvests would be about two weeks earlier than under the forest-covered condition.

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