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Fourier series
About: Fourier series is a research topic. Over the lifetime, 16548 publications have been published within this topic receiving 322486 citations.
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60 citations
TL;DR: In this paper, it was shown that the same co-ordinates and estimated errors are obtained by the method of least squares and by appropriately weighted Fourier series (corrected for finite summation).
Abstract: Recent work by Cruickshank on the accuracy of atomic co-ordinates obtained in Fourier syntheses is here related to that of Cochran on the connexions between the least-squares and Fourier methods. Except when the atomic peaks are not resolved, it is shown that the same co-ordinates and estimated errors are obtained by the method of least squares and by appropriately weighted Fourier series (corrected for finite summation). An expression is obtained for the relative accuracies of the weighted and unweighted Fourier methods.
60 citations
TL;DR: An essential element of the proof of the maximum principles is an estimation for the value of the Riemann-Liouville fractional derivative of a function at its maximum point that is established in this paper for a wider space of functions compared to those used in previous publications.
60 citations
TL;DR: In this paper, the dynamics analysis of FGP circular, annular and sector plates with general elastic restraints is performed in a unified form for the first time, and the overall theoretical model is based on the first order shear deformation theory.
Abstract: In this paper, the dynamics analysis of functionally graded porous (FGP) circular, annular and sector plates with general elastic restraints is performed in a unified form for the first time. The overall theoretical model is based on the first order shear deformation theory. The kinetic energy and potential energy function of the plates are unified representation of five kinds of displacement admissible function. Then, each of displacement admissible function is expanded as a modified Fourier series to obtain general elastic restraints. Lastly, the solutions are obtained by using the variational operation. The convergence and accuracy of the present modeling are validated by comparing its results with those available in the literature and FEM results. Based on that, a series of innovative results are also highlighted in the text, which may be as the basic data for other algorithm research in the future.
60 citations
TL;DR: In this paper, the authors provided an exact solution for the size dependent buckling and post-buckling behavior of functionally graded (FG) micro-beams with arbitrary boundary conditions which are subjected to combined thermo-mechanical loading.
60 citations