Large-amplitude nonlinear free vibrations of functionally graded plates with porous imperfection: A novel approach based on energy balance method

2020 ◽  
Vol 246 ◽  
pp. 112367
Author(s):  
Ke Xie ◽  
Yuewu Wang ◽  
Hongpan Niu ◽  
Hongyong Chen
Keyword(s):  
Energy Balance ◽  
Large Amplitude ◽  
Free Vibrations ◽  
Functionally Graded ◽  
Balance Method ◽  
Functionally Graded Plates ◽  
Energy Balance Method ◽  
Novel Approach

scholarly journals CESSATION OF FREE VIBRATIONS OF A NONLINEAR ELASTIC SYSTEM DUE TO VISCOUS RESISTANCE

2021 ◽  
pp. 69-75
Author(s):  
Vasiliy Olshanskiy ◽  
Stanislav Olshanskiy
Keyword(s):  
Energy Balance ◽  
Finite Number ◽  
Power Law ◽  
Dry Friction ◽  
Free Vibrations ◽  
Balance Method ◽  
Viscous Resistance ◽  
Energy Balance Method ◽  
Number Of Cycles ◽  
The Impact

The paper deals with free vibrations of a system with power-law nonlinear elasticity subjected to power-law viscous resistance. The relation between the nonlinearity indices is determined when the impact of the viscous resistance force causes the vibrations to die away. In this case the vibrations are limited in time i.e. consist of a finite number of cycles analogous to a system with Coulomb dry friction. The research exploits the energy balance method. The periodic Ateb-functions are used to obtain an approximate formula for the work of dissipative force over a semi-cycle of vibrations. A recursive power-law equation for the vibration swings is derived from the condition of equality of the work to the potential energy change. By analyzing the change of the coefficient in the equation, which is related to the change of the semi-cycle number as well as the vibration swings, the condition for the equation to have no positive root is determined, which means that the vibrations die away. The condition is formulated in the form of an inequality. It is shown to generalize the results previously known. The theoretical inferences are verified by numerical integration of the nonlinear differential equation of motion. It is shown that under the conditions proposed in the paper the free vibrations consist of a finite number of cycles even if dry friction is absent from the system. Special cases are highlighted, when the approximate energy balance method results into exact computational formulae. The length of the cycles increases during the motion since it depends on the swing of damped vibrations in the essentially nonlinear system with rigid force characteristics considered.

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.

Bowen Ratio Energy Balance Method

2015 ◽  
pp. 397-405 ◽  
Author(s):  
Leo J. Fritschen ◽  
Charles L. Fritschen
Keyword(s):  
Energy Balance ◽  
Bowen Ratio ◽  
Balance Method ◽  
Energy Balance Method ◽  
Ratio Energy

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.

Technology of Protection Against the Dynamic Effect of Nuclear Pipe Rupture

2017 ◽  
Author(s):  
Feng He ◽  
Feng Yuan ◽  
Honglei Ai ◽  
Xinjun Wang ◽  
Xifeng Lu ◽  
...  
Keyword(s):  
Finite Element ◽  
Energy Balance ◽  
Nuclear Power ◽  
Dynamic Method ◽  
Plastic Hinge ◽  
Dynamic Effect ◽  
Element Model ◽  
High Energy ◽  
Balance Method ◽  
Energy Balance Method

The special safety facilities and important equipment, etc. of the nuclear power plant will be damaged due to the whipping nuclear high-energy piping after the rupture, and more serious further damage will be caused. In this paper, the process and method of protection analysis of the nuclear high-energy piping rupture have been given from four aspects. The four aspects are location of high-energy piping break, the jet thrust, whipping behavior analysis, and protection analysis of whipping. On the basis of the traditional energy balance method, the method is improved by considering the energy absorbed by the plastic hinge of the piping and the change in the direction of the jet thrust. And then, the comparisons among the traditional energy balance method, the improved energy balance method, and the 3-D finite element dynamic method have been carried out. The deformation of the whip limiter analyzed by the traditional energy balance method is 20.31% larger than which analyzed by the improved energy balance method, and the deformation of the whip limiter analyzed by the 3-D finite element dynamic method is 30.59% smaller than which analyzed by the improved energy balance method. For the first time, a 3-D finite element model according to the true arrangement of the pipe and the whip limiter model are built to simulate the process of whipping not in the plane, considering the energy dissipation of the whip limiter. For the pipe whipping not in the plane and protecting against the pipe rupture by whip limiter, there is no good way to carry out the protection analysis of the piping rupture in the past. Now, the problem can be solved by the 3-D finite element dynamic method.

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