scholarly journals HE'S ENERGY BALANCE METHOD TO EVALUATE THE EFFECT OF AMPLITUDE ON THE NATURAL FREQUENCY IN NONLINEAR VIBRATION SYSTEMS

2008 ◽  
Vol 4 ◽  
pp. 143-154 ◽  
Author(s):  
Hamed Babazadeh ◽  
Davoodi Domiri Ganji ◽  
Mehdi Akbarzade
Keyword(s):  
Energy Balance ◽  
Nonlinear Vibration ◽  
Natural Frequency ◽  
Balance Method ◽  
Energy Balance Method

Dynamics of n Coupled Double Pendula Suspended to the Moving Beam

2014 ◽  
Vol 14 (08) ◽  
pp. 1440028 ◽  
Author(s):  
Piotr Koluda ◽  
Piotr Brzeski ◽  
Przemyslaw Perlikowski
Keyword(s):  
Energy Balance ◽  
Periodic Solutions ◽  
Natural Frequency ◽  
Balance Method ◽  
Energy Balance Method ◽  
Analytical Analysis ◽  
Stability Properties ◽  
Moving Beam ◽  
The Stability

We consider the synchronization of n self-excited double pendula. For such pendula hanging on the same beam, different synchronous configurations can be obtained (in-phase and anti-phase states). An approximate analytical analysis allows to derive the synchronization condition and explain the observed types of synchronization for any number of coupled double pendula. The energy balance method is used to show how the energy between the pendula is transferred via the oscillating beam allowing their synchronization. We compute periodic solutions for n = 2, 3, 4, 5 coupled double pendula, based on analytical predictions. For all obtained periodic solutions, we investigate how the stability properties change with the varying natural frequency of the beam.

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.

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.

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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