Discrete Fourier Series Expansion Research Articles

Computer Algorithms for Pseudo-Formal Linearization Method Based on Discrete Fourier Series Expansion and Nonlinear Observer

Computer Algorithms for Pseudo-Formal Linearization Method Based on Discrete Fourier Series Expansion and Nonlinear Observer

Application of discrete Fourier series to the stress analysis of shell structures

A method for the solution of problems associated with determination of the stress state of shells of revolution using a discrete Fourier-series method is proposed. In the present work the classical theory based on Kirchhoff-Lova hypotheses is used to describe the stress state of shells. The problem of determination of the stress state of a shell with variable parameters along a generatrix is reduced to the solution of the system of partial differential equations. Discrete Fourier series are the set of functions defined on a discrete set of points. This method allows one to reduce the dimension of the problem and to solve it by the numerical Godunov’s method of discrete orthogonalization. As the approach based on application of a discrete Fourier-series for the functions set on a discrete ensemble of points is used, the curvilinear grid with an equal step on a meridian is plotted on the shell surface. The circles obtained are broken into equal amounts. This yields a set of virtual shell elements. It is recognized that the value of distributed loads on this set of virtual elements is known. We suggest to approximate loads using a discrete Fourier series expansion in cosines and sines, which makes it possible to describe any asymmetric loading. Examples of application of analytical and discrete Fourier series to calculation of isotropic and the orthotrophic of shells are given. The errors in approximating the given functions are defined by discrete series. For all the problems the necessary number of harmonics is determined. On necessary retention of the quantity of summable harmonics, the approximating function describes rather precisely various external superficial loading modes. The approximation error obtained by the Fourier series expansion method proposed here is insignificant, and this provides a description of any asymmetric loading. Application of discrete Fourier series makes it possible to reduce the dimension of the problem and to determine the stress state of shells of revolution.

Modal analysis of a vibrating string via electromagnetic field excitation

An electromagnetic field (EM) generating device (“EBow”) was used to excite a fixed string held in tension between two boundaries on a custom-built apparatus in the style of a monochord. A high-speed camera was used to visualize and record the vibration of the string across the length of the string for every EBow position. The data sets were analyzed to create amplitude vs time graphs. Every excitation position was found to result into a different mode of vibration that emphasized fundamental, second, third, and fourth eigenmodes. Each mode resulted in a distinct displacement pattern, which was found to follow curve fits with R<+>2<+> values ranging from 0.94 to 0.99. The recorded amplitudes also agreed with expected nodal and anti-nodal positions for every observed mode signifying the data were robust. A discrete Fourier series expansion was performed on the polynomial fits and yielded simple second-order expressions (including a damping term) which are in agreement with the expected excitation models for a fixed string.

Total Harmonic Distortion and Content Rate of Spatial Modal Information for Haptic Parallel Motion Analysis

In this paper, two kinds of evaluation index for the haptic motion analysis in parallel multiple degrees—of—freedom (MDOF) system are proposed. At first, the spatial modal decomposition method based on discrete Fourier series expansion (DFS) is presented. Spatial modal information expresses a motion element that corresponds to a specific physical action. The spatial modal information can mathematically be defined by the Fourier coefficients. Then, this paper proposes the total harmonic distortion (THD) and the content rate of the haptic modal information as motion evaluation indexes. THD of the spatial modal information can evaluate the complexity of the human motion and/or the deformability of the contact environment. Content rate of the spatial modal information can evaluate the priority of motion element. Some experimental results on the bilateral motion control of a parallel five DOF haptic system are shown, in order to confirm the utility of the proposed indexes.

Motion Mode Decomposition Based on Discrete Fourier Series Expansion

In recent years, several methods for decomposing the whole motion of a parallel multi-degrees-of-freedom (MDOF) system into motion modes have been proposed. A motion mode is a motion element that corresponds to a specific physical action, such as grasping, manipulating, and rotating. Modal decomposition is effective for the expression and analysis of a complicated motion. However, conventional methods can extract motion modes only if the arrangement of actuators in the system has spatial linearity and symmetry. Therefore, the actuators cannot be arranged arbitrarily when the conventional methods are applied. In order to solve this problem, a novel method for modal decomposition is proposed; this method is based on the discrete Fourier series expansion. The proposed method is applied to a parallel MDOF bilateral system in which the arrangement of actuators is spatially asymmetric. Finally, the validity of the proposed method is confirmed on the basis of the experimental results.

Elastic properties of wood-strand composites with undulating strands

The following study examines the effects that undulating strands have on the elastic behavior of a wood-strand composite. A discrete Fourier series expansion was used to empirically describe the experimentally measured strand undulation paths. A fiber undulation model was used to predict elastic properties as a function of strand waviness using the empirical path descriptions. Strand undulation was shown to degrade Young's modulus of yellow-poplar laminates in both tension and compression, with more severe effects in compression. Experimental results from compression tests were in good agreement with the predictions based on the analytical model for maximum undulatory angles of 4 and 8°.

Application of discrete Fourier series to the finite element stress analysis of axi‐symmetric solids

AbstractThis paper describes an efficient formulation, based on a discrete Fourier series expansion, for the analysis of axi‐symmetric solids subjected to non‐symmetric loading. In contrast to the commonly adopted continuous Fourier series approach, the discrete Fourier series representation has largely overcome problems such as the presence of Gibb's phenomenon and the lack of conformity of elements. The computational advantage over a fully three‐dimensional formulation is illustrated. Finally, the method is demonstrated through a finite element study of rigid caissons founded in both elastic and elasto‐plastic soils.

Finite element analysis of elastic-plastic layered soil using discrete fourier series expansion : Runesson, K; Booker, J R Int J Num Meth Engng, V19, N4, April 1983, p473–478

Finite element analysis of elastic-plastic layered soil using discrete fourier series expansion : Runesson, K; Booker, J R Int J Num Meth Engng, V19, N4, April 1983, p473–478

Finite element analysis of elastic‐plastic layered soil using discrete Fourier series expansion

AbstractA method is developed which basically concerns how to reduce the necessary storage and cost of solving a set of algebraic equations arising from applying the initial stress technique to the analysis of a uniformly layered elastic‐plastic soil. Advantage is taken of the geometrical symmetry of the problem and the consequent symmetry of the stiffness matrix. The nodal values are expanded in a discrete Fourier series so that a two‐dimensional problem is reduced to a number of one‐dimensional problems.

Automated measurement of bioelectric impedance at very low frequencies

An on-line real-time system utilizing a simple package of dedicated hardware in conjunction with a small computer for measuring two-terminal electrical impedance is described. Operating efficiently from 0.005 to 500 Hz, it covers most of the interesting range for bioelectrode, organ, and tissue studies in electrocardiography, encephalography, myography, and other electrographic researches. The impedance to be measured is driven sinusoidally at a constant current chosen by the operator. By sampling the voltage and the associated current at appropriate paired times during one electrical cycle, coefficients for a discrete Fourier series expansion are obtained in a form which makes calculation of real and imaginary impedance components, DC offset, and harmonic content very simple. Results are displayed on a television-type raster for immediate evaluation and may then be recorded on high-speed tape for subsequent detailed analysis.