The three‐dimensional Fourier series method for the calculation of stress and strain: Application to strained‐layer structures

1994 ◽  
Vol 75 (10) ◽  
pp. 4963-4968 ◽  
Author(s):  
David A. Faux ◽  
Jonathan Gill
Keyword(s):  
Fourier Series ◽  
Three Dimensional ◽  
Stress And Strain ◽  
Series Method ◽  
Strained Layer ◽  
Fourier Series Method ◽  
Layer Structures

Initial design of low-thrust trajectories based on the Bezier curve-based shaping approach

2020 ◽  
Vol 234 (11) ◽  
pp. 1825-1835
Author(s):  
Zichen Fan ◽  
Mingying Huo ◽  
Naiming Qi ◽  
Ce Zhao ◽  
Ze Yu ◽  
...  
Keyword(s):  
Fourier Series ◽  
Three Dimensional ◽  
Initial Approximation ◽  
Mission Design ◽  
Bézier Curve ◽  
Design Stage ◽  
Bezier Curve ◽  
Series Method ◽  
Low Thrust ◽  
Fourier Series Method

This paper presents a method to use the Bezier curve to rapidly generate three-dimensional low-thrust trajectories, which can provide a suitable initial approximation to be used for more accurate trajectory optimal control tools. Two missions, from Earth to Mars and the asteroid Dionysus, are considered to evaluate the performance of the method. In order to verify the advantages of this method, it is compared with the finite Fourier series method. Numerical results show that the Bezier method can get better performance index in shorter computation time compared with the finite Fourier series method. The applicability of the solution obtained by Bezier method is evaluated by introducing the obtained solution into the Gauss pseudospectral method as an initial guess. The simulation results show that the Bezier method can rapidly generate a very suitable three-dimensional initial trajectory for the optimal solver. This is very important for rapid evaluation of the feasibility of a large number of low-thrust flight schemes in the preliminary mission design stage.

scholarly journals 1-D heat conduction in a fractal medium: A solution by the local fractional Fourier series method

2013 ◽  
Vol 17 (3) ◽  
pp. 953-956 ◽  
Author(s):  
Yuzhu Zhang ◽  
Aimin Yang ◽  
Xiao-Jun Yang
Keyword(s):  
Heat Transfer ◽  
Fourier Series ◽  
Heat Conduction ◽  
Local Heat Transfer ◽  
Local Heat ◽  
Series Method ◽  
Heat Transfer Mechanism ◽  
Basic Properties ◽  
Fractal Medium ◽  
Fourier Series Method

In this communication 1-D heat conduction in a fractal medium is solved by the local fractional Fourier series method. The solution developed allows relating the basic properties of the fractal medium to the local heat transfer mechanism.

Development of the Low Cost Harmonic and Power Instrument by Using Fourier Series Method with Microcontroller

2014 ◽  
Vol 492 ◽  
pp. 519-525
Author(s):  
Napat Watjanatepin ◽  
Chaiyant Boonmee ◽  
Yutthana Kantaphayao
Keyword(s):  
Fourier Series ◽  
Power Factor ◽  
Measurement Errors ◽  
Single Phase ◽  
Low Cost ◽  
Electrical Power ◽  
Quality Measurement ◽  
Series Method ◽  
Electrical Parameters ◽  
Fourier Series Method

The objective of this paper is to present the application of microcontroller dsPIC30F6012A to measure the harmonics current and electrical power by using the Fourier series method to calculate the electrical parameters. This design is to develop the low cost harmonics instrument and to focus on working with the single phase AC system. The prototype was then developed to measure the harmonics current and power factor, and the result was compared with the standard instrument. The result is that most electrical parameters have the measurement errors of less than 4.0%. However, this idea could be developed so that it applies in the related work with the power quality measurement.

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