Explicit solutions to nonlinear Chen–Lee–Liu equation

In this work, a generalized [Formula: see text]-expansion method has been used for solving the nonlinear Chen–Lee–Liu equation. This method is a more common, general, and powerful mathematical algorithm for finding the exact solutions of nonlinear partial differential equations (NPDEs), where [Formula: see text] follows the Jacobi elliptic equation [Formula: see text], and we let [Formula: see text] be a fourth-order polynomial. Many new exact solutions such as the hyperbolic, rational, and trigonometric solutions with different parameters in terms of the Jacobi elliptic functions are obtained. The distinct solutions obtained in this paper clearly explain the importance of some physical structures in the field of nonlinear phenomena. Also, this method deals very well with higher-order nonlinear equations in the field of science. The numerical results described in the plots were obtained by using Maple.

Static analysis of wind turbine blade using 1D FE model

The study presents a unique technique to determine the static response of wind turbine (WT) blade. A 1D Finite element (FE) beam model of WT blade is developed using thin-walled beam theory coupled with PreComp tool used to compute crosssectional stiffness with elastic coupling effects. A realistic 9.2 m long, WT blade is developed using different aerofoils with fourth order polynomial variation for twisting angle of blade span. Three different aerfoil sections NREL S818, NREL S825, and NACA 2412 are employed in the current study. For validation, the results of 1D model developed using MATLAB are compared with that of 3D WT blade model which is analyzed in ANSYS using NuMAD..

Optical Simulation and Experimental Assessment with Time–Walk Correction of TOF–PET Detectors with Multi-Ended Readouts

As a commonly used solution, the multi-ended readout can measure the depth-of-interaction (DOI) for positron emission tomography (PET) detectors. In the present study, the effects of the multi-ended readout design were investigated using the leading-edge discriminator (LED) triggers on the timing performance of time-of-flight (TOF) PET detectors. At the very first, the photon transmission model of the four detectors, namely, single-ended readout, dual-ended readout, side dual-ended readout, and triple-ended readout, was established in Tracepro. The optical simulation revealed that the light output of the multi-ended readout was higher. Meanwhile, the readout circuit could be triggered earlier. Especially, in the triple-ended readout, the light output at 0.5 ns was observed to be nearly twice that of the single-ended readout after the first scintillating photon was generated. Subsequently, a reference detector was applied to test the multi-ended readout detectors that were constructed from a 6 × 6 × 25 mm3 LYSO crystal. Each module is composed of a crystal coupled with multiple SiPMs. Accordingly, its timing performance was improved by approximately 10% after the compensation of fourth-order polynomial fitting. Finally, the compensated full-width-at-half-maximum (FWHM) coincidence timing resolutions (CTR) of the dual-ended readout, side dual-ended readout, and triple-ended readout were 216.9 ps, 231.0 ps, and 203.6 ps, respectively.

Exact Single Traveling Wave Solutions for Generalized Fractional Gardner Equations

In this paper, the classification of all single traveling wave solutions to generalized fractional Gardner equations is presented by utilizing the complete discrimination system method. Under the fractional traveling wave transformation, generalized fractional Gardner equations can be reduced to an ordinary differential equations. All possible exact traveling wave solutions are given through the complete discrimination system of the fourth-order polynomial. Moreover, graphical representations of different kinds of the exact solutions reveal that the method is of significance for searching the exact solutions to generalized fractional Gardner equations.

Reliability Analysis on Fatigue Life of Turbine Disk Regarding for the Correlation Between Divided Zones

Failure of a turbine disk may occur in multiple parts of the disk. It should be taken into consideration that during the process of failure, the failure risk of other relevant parts tend to increase due to the change of stress state of the disk. Therefore, the failure risks of different parts are related. This paper puts forward a reliability analysis method considering the failure correlation between different zones of the disk. Firstly, the dependence between the low cycle fatigue (LCF) of the whole turbine disk and the LCF of each zone is considered in building a multivariate reliability model based on Copula function theory. With utilizing the sample points obtained by finite element method (FEA), the multidimensional maximum likelihood theory is used to estimate the parameters in the marginal distribution of turbine disk life and the correlation coefficients in the Copula model, and to quantify the failure correlation between each zone of the turbine disk. With regard to the lifetime output of different zones, fourth-order polynomial high-precision surrogate models are established, which greatly improves the efficiency of Monte Carlo simulation. Eventually, the LCF life reliability analysis of GH720Li turbine disk is performed.

Damage detection of long-span bridge structures based on response surface model

In order to solve the problem of high risk and low precision of existing damage detection methods for long-span Bridges, a new method based on fourth-order polynomial response surface model is proposed. Response surface model is constructed by using fourth order polynomial function. The parameters of the finite element model of the bridge are modified according to the response surface model. Based on the finite element model, the modal strain energy before and after the damage of the element was calculated, and the damage index of the element was obtained, so as to realize the damage detection of the long-span bridge structure. Experimental results show that the proposed method can accurately detect the damage location of long-span Bridges under different damage conditions, and the detection error of damage degree is less than 1%, which has a broad application prospect.

Optimization of the shaping function of a tapered piezoelectric energy harvester using tabu continuous ant colony system

During the past years, the development of piezoelectric energy harvesters is extensively increased for providing the required energy of sensor nodes. It has been proven that changing the beam’s cross-section along its length direction may lead to extract more power with less mass. In this article, a hybrid metaheuristic algorithm called tabu continuous ant colony system is employed to optimize the tapered piezoelectric energy harvester in a fast and course manner. The exponential and fourth-order polynomial functions are considered as shaping functions for tapering the beam’s width along its length direction. An experiment is also set up to evaluate the performance of the optimization algorithm for the case of exponential shaping function. Finally, the algorithm is applied to optimize the voltage and power per mass of both shaping functions of the tapered piezoelectric energy harvester at the specified excitation frequency.

World Records in Half-Marathon Running by Sex and Age

The relationship between age and elite marathon race times is well investigated, but little is known for half-marathon running. This study investigated the relationship between half-marathon race times and age in 1-year intervals by using the world single age records in half-marathon running and the sex difference in performance from 5 to 91 years in men and 5 to 93 years in women. We found a fourth-order polynomial relationship between age and race time for both women and men. Women achieve their best half-marathon race time earlier in life than men, 23.89 years compared with 28.13 years, but when using a nonlinear regression analysis, the age of the fastest race time does not differ between men and women, with 26.62 years in women and 26.80 years in men. Moreover, the sex difference in half-marathon running performance increased with advancing age.