Vibration Characteristics of Unsaturated Runways Under Moving Aircraft Loads

The dynamic vibrations of airport runways induced by moving aircraft loads are semi-analytically studied in this paper. The airport runway consists of an infinite Kirchhoff plate, an elastic base course, and an unsaturated poroelastic half-space. The aircraft loads are modeled according to the mechanical properties of the main landing gear of the A380 civil airliner. The governing equations of the whole system are solved in the wavenumber domain using the double Fourier transform. Then the results in the spatial domain are obtained by applying the inverse double Fourier transform. Various parameters including the observation location, soil saturation, load speed, load frequency, and pavement rigidity on the vibration characters of the whole system are investigated. It is found that all these effects are crucial, and the increase of soil saturation leads to a larger maximum vertical displacement and lower critical speed.

Harmonics of Double-fed Wind Power System with Grid-Tied Dual-PWM Converter

To fill the gaps of the double-fed wind power system, this paper conducts a study for the scarcity and integration of social resources. The LF harmonics on the DC and grid sides are surveyed based on the double Fourier transform algorithm, in conjunction with the power balance theory. A study model has also been built herein. The findings show that the calculated values of the HF harmonic components in the DFIG rotor current almost coincide with the simulation results, regardless of whether the wind velocity is 7 m/s or 19 m/s. When the three-phase voltage of the grid is unbalanced, the stator current contains the grid side basebands with LF harmonics of odd times, among which, the fundamental frequency of triple grid side baseband is the most distinct. It is thus clear that the simulation can capture relevant voltage and current data for the wind power system running in the balance and unbalanced states of grid voltages. it is therefore proved that the theoretical analysis is accurate and reliable.

Detection of Large-Scale Noisy Multi-Periodic Patterns with Discrete Double Fourier Transform. II. Study of Correlations Between Patterns

The discrete double Fourier transform (DDFT) was developed to search for large-scale multi-periodic patterns in the presence of noise and is based on detection of the equidistant series of harmonics generated by the periodic patterns in the discrete Fourier transform (DFT) spectra. As DDFT retains all generic features of the Fourier transform, the corresponding pattern correlation function (PCF) related to DDFT can be introduced similarly to the data correlation function (DCF) related to DFT on the basis of the Wiener–Khinchin relationship. Peaks in PCF indicate the number of periodic patterns in a dataset under analysis and have direct correspondence with the counterpart peaks in the DFT spectrum. The close correspondence between positions of the peaks in the PCF and DFT spectra strongly enhances statistical significance of detected periodicities. Similar PCFs can also be defined for the cepstrum transform. The combined DFT–DCF and DDFT–PCF technique was applied to the detection of cycles in geomagnetic activity using disturbance storm-time (Dst) index. In addition to the known 27-day, semiannual and 11-year cycles of geomagnetic activity, we have also found the annual cycle of activity. The results were compared with those obtained by the cepstrum transform. A multiple cross-check makes the combined technique much more efficient and robust in comparison with the detection based on a unique particular method.

Three-dimensional generalized thermoelasticity with variable thermal conductivity

In this paper, a three-dimensional model of the generalized thermoelasticity with one relaxation time and variable thermal conductivity is constructed. The resulting nondimensional governing equations, together with the Laplace and double Fourier transform techniques have been applied to a three-dimensional half-space subjected to thermal loading with rectangular pulse and traction free surface. The inverses of double Fourier transforms and Laplace transforms have been obtained numerically. Numerical results for the temperature increment, the invariant stress, the invariant strain, and the displacement are represented graphically. The variability of thermal conductivity has significant effects on all the studied fields.

Analytical Solutions for Steady-State Multiwell Aquifer Tests in Rectangular Aquifers by Using Double Fourier Transform: A Case Study in the Ordos Plateau, China

Straightforward solutions have long been expected for the analysis of multiwell aquifer tests. In this paper, we derive series analytical solutions of steady-state groundwater flow in a rectangular-shaped aquifer with pumping/injection wells for both confined and unconfined conditions. Double Fourier Transform (DFT) technique is applied to deal with different combinations of impermeable and specified head boundaries on sides. The obtained solutions are compact and concise in mathematics and flexible in terms of well number, well locations, and pumping/injection rates. Hatoucaidang, a groundwater resource field in the Ordos Plateau, Northwestern China, is introduced as a field case study, where a multiwell aquifer test was conducted. One of the analytical solutions derived herein is used to estimate hydraulic conductivities by applying a direct calculation method and a least square estimation method regarding observed versus calculated drawdowns. By comparing with nearby single-well pumping tests, the reliability of the derived analytical solutions is proven. This study facilitates utilizing the multiwell aquifer test to analyze the general behavior of groundwater movement in aquifer systems.

Detection of Large-Scale Noisy Multi-Periodic Patterns with Discrete Double Fourier Transform

In many processes, the variations in underlying characteristics can be approximated by noisy multi-periodic patterns. If large-scale patterns are superimposed by a noise with long-range correlations, the detection of multi-periodic patterns becomes especially challenging. To solve this problem, we developed a discrete double Fourier transform (DDFT). DDFT is based on the equidistance property of harmonics generated by multi-periodic patterns in the discrete Fourier transform (DFT) spectra. As the large-scale patterns generate long enough equidistant series, they can be detected by the iteration of the primary DFT. DDFT is defined as Fourier transform of intensity spectral harmonics or of their functions. It comprises widely used cepstrum transform as a particular case. We present also the relevant analytical criteria for the assessment of the statistical significance of peak harmonics in DDFT spectra in the presence of noise. DDFT technique was tested by extensive numerical simulations. The practical applications of the DDFT technique are illustrated by the analysis of variations in solar wind speed related to solar rotation and by the study of large-scale multi-periodic patterns in DNA sequences. The latter application can be considered as a generic example for the general spectral analysis of symbolic sequences. The results are compared with those obtained by the cepstrum transform. The mutual combination of DFT and DDFT provides an efficient technique to search for noisy large-scale multi-periodic patterns.

Self-equilibrated stresses in the system composed of a covering layer + spatially locally curved reinforcing layer + half-space

The system composed of a face covering layer + spatially locally curved substrate reinforcing layer + half-space is taken into consideration. It is presumed that this framework is compressed at infinity by uniformly distributed normal forces and it is required to establish the self-equilibrated normal stresses in that, caused by locally curved of the substrate reinforcing layer. The matching boundary and contact value problem is defined within the scope of 3-D geometrically non-linear exact equations. Formulated problem?s solution is introduced with the series form of small parameter which represents the degree of the aforesaid locally curving. These series? zeroth and first approximation are ascertained with the utilization of double Fourier transform. The original of values that are searching is ascertained numerically. Corresponding numerical outcomes about the self-equilibrated normal stress caused by this spatially local curving are presented and discussed.

Stress distribution caused by co-phase locally spatially curved layers in an infinite elastic body under bi-axial compression

In the present paper, the stress distribution is studied in an infinite elastic body, reinforced by an arbitrary number of non-intersecting co-phase locally spatially curved filler layers under bi-axial compression is studied. It is assumed that this system is loaded at infinity with uniformly distributed normal forces with intensity p1(p3) acting in the direction which is parallel to the layers? location planes. It is required to determine the self-equilibrated stresses within, caused by the spa?tially local curving of the layers. The corresponding boundary and contact value problem is formulated within the scope of geometrically non-linear exact 3-D equations of the theory of elasticity by utilizing of the piece-wise homogeneous body model. The solution the formulated problem is represented with the series form of the small parameter which characterizes the degree of the aforementioned local curving. The boundary-value problems for the zeroth and the first approximations of these series are determined with the use of the exponential double Fourier transform. The original of the sought values is determined numerically. Consequently, in the present investigation, the effect of the local curving on the considered interface stress distribution is taken into account within the framework of the geometrical non-linear statement. The numerical results related to the considered interface stress distribution and to the influence of the problem parameters on this distribution are given and discussed.