Solution of nonlinear cubic-quintic Duffing oscillators using He’s Energy Balance Method

In this study, He＇s Energy Balance Method （EBM） was applied to solve strong nonlinear Duffing oscillators with cubic-quintic nonlinear restoring force. The complete EBM solution procedure of the cubic-quintic Duffing oscillator equation is presented. For illustration of effectiveness and convenience of the EBM, different cases of cubic-quintic Duffing oscillator with different parameters of α,β and y were compared with the exact solution. We found that the solutions were valid for small as well as large amplitudes of oscillation. The results show that the EBM is very convenient and precise, so it can be widely appli- cable in engineering and other sciences.

The Spatial Sensitivity Analysis of Evapotranspiration using Penman-Monteith Method at Grid Scale

The need to allocate the existing water in a sustainable manner, even with the projected population growth, has made to assess the consumptive use or evapotranspiration (ET), which determines the irrigation demand. As underscored in the literature, Penman-Monteith method which is a combination of aerodynamic and energy balance method is widely used and accepted as the method of estimation of ET. However, the application of Penman-Monteith relies on many climate parameters such as relative humidity, solar radiation, temperature, and wind speed. Therefore, there exists a need to determine the parameters that are most sensitive and correlated with dependent variable (i.e., ET), to strengthen the knowledge base. However, the sensitivity of ET using Penman-Monteith is oftentimes estimated using meteorological data from climate stations. Such estimation of sensitivity may vary spatially and thus there exists a need to estimate sensitivity of ET spatially. Thus, in this paper, based on One-AT-A-Time (OAT) method, a spatial sensitivity tool that can geographically encompass all the best available climate datasets to produce ET and its sensitivity at different spatial scales is developed. The spatial tool is developed as a Python toolbox in ArcGIS using Python, an open source programming language, and the ArcPy site-package of ArcGIS. The developed spatial tool is demonstrated using the meteorological data from Automated Weather Data Network in Nebraska in 2010. To summarize the outcome of the sensitivity analysis using OAT method, sensitivity indices are developed for each raster cell. The demonstration of the tool shows that, among the considered parameters, the computed ET using Penman-Monteith is highly sensitive to solar radiation followed by temperature for the state of Nebraska, as depicted by the sensitivity index. The computed sensitivity index of wind speed and the relative humidity are not that significant compared to the sensitivity index of solar radiation and temperature.

Comparative Study on Methods for Computing Soil Heat Storage and Energy Balance in Arid and Semi-Arid Areas

Observations collected in the Badan Jaran desert hinterland and edge during 19-23 August 2009 and in the Jinta Oasis during 12-16 June 2005 are used to assess three methods for calculating the heat storage of the5-20-cm soil layer.The methods evaluated include the harmonic method,the conduction-convection method,and the temperature integral method.Soil heat storage calculated using the harmonic method provides the closest match with measured values.The conduction-convection method underestimates nighttime soil heat storage.The temperature integral method best captures fluctuations in soil heat storage on sub-diurnal timescales,but overestimates the amplitude and peak values of the diurnal cycle.The relative performance of each method varies with the underlying land surface.The land surface energy balance is evaluated using observations of soil heat flux at 5-cm depth and estimates of ground heat flux adjusted to account for soil heat storage.The energy balance closure rate increases and energy balance is improved when the ground heat flux is adjusted to account for soil heat storage.The results achieved using the harmonic and temperature integral methods are superior to those achieved using the conduction-convection method.

SURFACE IMBALANCE ENERGY CALCULATED AND ANALYZED WITH THE DATA OF EBEX-2000

Mainly.three methods have been developed to calculate turbulence heat flux.They are eddy covariance method,Bowen ratio/energy balance method and aerodynamic method.In this paper, all the three methods have been used to calculate sensible heat flux,latent heat flux and imbalance energy near the surface with the experiment data of EBEX-2000.Then comparisons of the three methods and some possible explanations of the surface imbalance energy are given.

A Spatial Evapotranspiration Tool at Grid Scale

The drastic decline in groundwater table and many other detrimental effects in meeting irrigation demand, and the projected population growth have force to evaluate consumptive use or evapo-transpiration (ET), the rate of liquid water transformation to vapor from open water, bare soil, and vegetation, which determines the irrigation demand. As underscored in the literature, Pen-man-Monteith method which is based on aerodynamic and energy balance method is widely used and accepted as the method of estimation of ET. However, the estimation of ET is oftentimes carried out using meteorological data from climate stations. Therefore, such estimation of ET may vary spatially and thus there exists a need to estimate ET spatially at different spatial or grid scales/resolutions. Thus, in this paper, a spatial tool that can geographically encompass all the best available climate datasets to produce ET at different spatial scales is developed. The spatial tool is developed as a Python toolbox in ArcGIS using Python, an open source programming language, and the ArcPy site-package of ArcGIS. The developed spatial tool is demonstrated using the meteorological data from Automated Weather Data Network in Nebraska in 2010.

Aeolian vibration control measures for ground wires of Han River long span transmission lines

Long span ultra-high voltage(UHV) transmission lines have serious aeolian vibration problems. To control these vibrations,we improved the energy balance method in the following aspects:the wind power input,the conductor self-damping,and the damper dissipated power. Meanwhile,we built a theoretical mechanical model of β wire dampers and derived energy dissipation calculation formulae. This permits the vibration energy dissipated by β wire dampers can be considered in the energy balance method. Then,we developed a computer program based on the improved energy balance method using Matlab,and analyzed UHV long span ground wires of the Han River long span project in P. R. China. The results show that the combination of β wire dampers and Stockbridge dampers can reduce vibration of UHV long span transmission lines,which provides a reference for research and construction of UHV engineering projects.

On abundant wave structures of the unsteady korteweg-de vries equation arising in shallow water

The aim of this paper is to study the unsteady korteweg-de vries equation that plays an important role in describing the shallow water.Two analytical techniques namely the Sardar-subequation method and the energy balance method are employed to seek the abundant traveling wave solutions for the first time.By these two methods,plenty of traveling wave solutions such as the bright solitary wave solutions,dark solitary wave solutions,singular periodic wave solutions and perfect periodic wave solution that expressed in terms of the generalized hyperbolic functions,generalized trigonometric functions and the cosine function are obtained.Finally,the dynamic behaviors of the solutions are described through the 3D plot and 2D curve.The results in this paper demonstrate that the proposed methods are powerful and effective to construct the traveling wave solutions of the nonlinear evolution equations in ocean engineering and science.

Nonlinear vibration of an elastically restrained tapered beam

This paper presents the analytical simulation of an elastically restrained tapered cantilever beam using the energy balance method(EBM) and the iteration perturbation method(IPM).To assess the accuracy of solutions,we compare the results with the harmonic balance method(HBM).The obtained results from EBM and IPM are in excellent agreement with HBM results.The results show that both methods can be easily extended to other nonlinear oscillations and it can be predicted that both methods can be found widely applicable in engineering and physics.

CHAOTIC ANALYSIS OF SUBHARMONIC RESONANT WAVES IN UNDAMPED AND DAMPED STRINGS

The chaotic phenomena of subharmonic resonant waves in undamped and damped strings are investigated in this paper. The model consistS of a constant-tension, stretched string whose partial differential equation is derived by taking into account its exact configuration. Simplification via a Taylor series expansion of the curvature term and then employing the Galerkin method, an ordinary differential equation for the nonlinear dyamics is obtained. For the undamped case, we can formulate the Hamiltonian energy form of the conservative string, under the influence of an external periodic excitation. This permits the subharmonic resonant condition for this system to be derived. We truncate the resulting infinite number of subharmonic resonant waves to just two waves by renormalizing the Hamiltonian energy function near the subharmonic resonant orbit of the system. Adopting the renormalization group technique for the nit6raction of the two subharmonic resonant waves, an approximate chaotic condition associated with the subharmonic resonance of this system is determined. For the case fo the damped string, the minimum condition for the bifurcation of the subharmonic resonant wave is computed using the incremental energy balance method. For model verification, we carried out numerical simulations and they show good agreement with our analytical results.

Nonlinear dynamic analysis of a punctual charge in the electric field of a charged ring via modified frequency-amplitude formulation

In this paper,two types of frequency amplitude fomulation method are initially utilized to obtain frequency-amplitude relationship of nonlinear vibration of a punctual charge in the electric field of a charged ring.In order to obtain the nonlinear natural frequency of the considered system,Reng-Gui and Geng-Cai modified methods are implemented.A table is also prepared to provide a brief review of recent development of nonlinear differential equations.The coectness of the obtained results is compared with those obtained from harmonic balance method(HBM)and energy balance method(EBM).A numerical simulation is caied out to investigate the accuracy of the used methods.In accordance with it,the relative errors of the employed approaches are numerically and analytically found based on the exact numerical solutions.It is exposed that the exerted approaches are very reliable and applicable for solving the nonlinear differential equations.