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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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TL;DR: In this article, a new size-dependent quasi-3D plate theory is presented for wave dispersion analysis of functionally graded nanoplates while resting on an elastic foundation and under the hygrothermaal environment.
Abstract: In this paper, a new size-dependent quasi-3D plate theory is presented for wave dispersion analysis of functionally graded nanoplates while resting on an elastic foundation and under the hygrothermaal environment. This quasi-3D plate theory considers both thickness stretching influences and shear deformation with the variations of displacements in the thickness direction as a parabolic function. Moreover, the stress-free boundary conditions on both sides of the plate are satisfied without using a shear correction factor. This theory includes five independent unknowns with results in only five governing equations. Size effects are obtained via a higher-order nonlocal strain gradient theory of elasticity. A variational approach is adopted to owning the governing equations employing Hamilton\'s principle. Solving analytically via Fourier series, these equations gives wave frequencies and phase velocities as a function of wave numbers. The validity of the present results is examined by comparing them with those of the known data in the literature. Parametric studies are conducted for material composition, size dependency, two parametric elastic foundation, temperature and moisture differences, and wave number. Some conclusions are drawn from the parametric studies with respect to the wave characteristics.

64 citations

Journal ArticleDOI
TL;DR: In this paper, a unified Jacobi-Ritz method is presented and implemented to study the free vibration analysis of coupled composite laminated axis-symmetric doubly-curved revolution shell structures with general boundary conditions.

64 citations

Posted Content
Mark A. Iwen1
TL;DR: In this paper, modified variants of the sparse Fourier transform algorithms from [14] are presented which improve on the approximation error bounds of the original algorithms. And simple methods for extending the improved sparse transform algorithms to higher dimensional settings are developed.
Abstract: In this paper modified variants of the sparse Fourier transform algorithms from [14] are presented which improve on the approximation error bounds of the original algorithms. In addition, simple methods for extending the improved sparse Fourier transforms to higher dimensional settings are developed. As a consequence, approximate Fourier transforms are obtained which will identify a near-optimal k-term Fourier series for any given input function, $f : [0, 2 pi] -> C, in O(k^2 \cdot D^4)$ time (neglecting logarithmic factors). Faster randomized Fourier algorithm variants with runtime complexities that scale linearly in the sparsity parameter k are also presented.

64 citations

Journal ArticleDOI
TL;DR: Simulations are provided to demonstrate precise detection of component frequencies and weights in short data records, coping with missing or unequally spaced data, and recovery of signals heavily contaminated with noise.
Abstract: In this paper a technique is examined for obtaining accurate and parsimonious sinusoidal series representations of biological time-series data, and for resolving sinusoidal signals in noise. The technique operates via a fast orthogonal search method discussed in the paper, and achieves economy of representation by finding the most significant sinusoidal frequencies first, in a least squares fit sense. Another reason for the parsimony in representation is that the identified sinusoidal series model is not restricted to frequencies which are commensurate or integral multiples of the fundamental frequency corresponding to the record length. Biological applications relate to spectral analysis of noisy time-series data such as EEG, ECG, EMG, EOG, and to speech analysis. Simulations are provided to demonstrate precise detection of component frequencies and weights in short data records, coping with missing or unequally spaced data, and recovery of signals heavily contaminated with noise. The technique is also shown to be capable of higher frequency resolution than is achievable by conventional Fourier series analysis.

64 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023270
2022702
2021511
2020510
2019589
2018580