Numerical Study of the Vibrations of Beams with Variable Stiffness under Impulsive or Harmonic Loading

The behavior of beams with variable stiffness subjected to the action of variable loadings (impulse or harmonic) is analyzed in this paper using the successive approximation method. This successive approximation method is a technique for numerical integration of partial differential equations involving both the space and time, with well-known initial conditions on time and boundary conditions on the space. This technique, although having been applied to beams with constant stiffness, is new for the case of beams with variable stiffness, and it aims to use a quadratic parabola (in time) to approximate the solutions of the differential equations of dynamics. The spatial part is studied using the successive approximation method of the partial differential equations obtained, in order to transform them into a system of time-dependent ordinary differential equations. Thus, the integration algorithm using this technique is established and applied to examples of beams with variable stiffness, under variable loading, and with the different cases of supports chosen in the literature. We have thus calculated the cases of beams with constant or variable rigidity with articulated or embedded supports, subjected to the action of an instantaneous impulse and harmonic loads distributed over its entire length. In order to justify the robustness of the successive approximation method considered in this work, an example of an articulated beam with constant stiffness subjected to a distributed harmonic load was calculated analytically, and the results obtained compared to those found numerically for various steps (spatial h and temporal τ ¯ ) of calculus, and the difference between the values obtained by the two methods was small. For example for ( h=1/8 , τ ¯ =1/ 64 ), the difference between these values is 17%.

轴承用20CrMoH钢S-N疲劳曲线的拟合

为了合理并高效地设计20CrMoH钢轴类零件的安全服役应力,根据轴类零件使用工况用标准旋转疲劳试样进行了旋转弯曲疲劳试验,并采用Parabola曲线模型拟合了中寿命区到长寿命区的中值S-N曲线以及在0.1%失效概率和95%置信度条件下的P-S-N曲线,最后利用疲劳应用统计学,对线性数学模型和Parabola曲线模型两种拟合方法进行了对比。初步研究发现:无论是在50%失效概率还是在0.1%失效概率、95%置信度条件下,与线性数学模型拟合方法相比,Parabola曲线模型拟合得到的S-N曲线结果均具有较高的相关系数,在中、低应力区有着较为保守的疲劳寿命估计,而在高应力区也更贴近原始数据。

Non-Linear Response of Tethers Subjected to Parametric Excitation in Submerged Floating Tunnels

For the study of the non-linear response of inclined tethers subjected to parametric excitation in submerged floating tunnels, a theoretical model for coupled tube-tether vibration is developed. Upon the assumption that the static equilibri- um position of the tether is a quadratic parabola, the governing differential equations of the tether motion are derived by use of the Hamihon principle. An approximate numerical solution is obtained by use of Galerkin method and Runge-kutta method. The results show that, when the static equilibrium position of the tether is assumed to be. a quadratic parabola, the tether sag effect on its vibration may be reflected; the tether sag results in the asymmetry of tether vibration amplitude ; for the reduction of the tether amplitude, the buoyant unit weight of the tether should approach to zero as far as possible during the design.

GREEN FUNCTIONS FOR A DECAGONAL QUASICRYSTALLINE MATERIAL WITH A PARABOLIC BOUNDARY

This investigation presents the Green functions for a decagonal quasicrystalline ma- terial with a parabolic boundary subject to a line force and a line dislocation by means of the complex variable method. The surface Green functions are treated as a special case, and the explicit expressions of displacements and hoop stress at the parabolic boundary are also given. Finally, the stresses and displacements induced by a phonon line force acting at the origin of the lower half-space are presented.

Multiply Charged Anions,Maximum Charge Acceptance,and Higher Electron Affinities of Molecules,Superatoms,and Clusters

The addition of electrons to form gas-phase multiply charged anions(MCAs)normally requires sophisticated experiments or calculations.In this work,the factors stabilizing the MCAs,the maximum electron uptake of gas-phase molecules,X,and the electronic stability of MCAs X^(Q-),are discussed.The drawbacks encountered when applying computational and/or conceptual density functional theory(DFT)to MCAs are highlighted.We develop and test a different model based on the valence-state concept.As in DFT,the electronic energy,E(N,v_(ex)),is a continuous function of the average electron number,N,and the external potential,v_(ex),of the nuclei.The valence-state-parabola is a second-order polynomial that allows extending E(N,v_(ex))to dianions and higher MCAs.The model expresses the maximum electron acceptance,Q_(max),and the higher electron affinities,A_Q,as simple functions of the firstelectron affinity,A_1,and the ionization energy,I,of the"ancestor"system.Thus,the maximum electron acceptance is Q_(max,calc)=1+12A_1/7(I-A_1).The ground-state parabola model of the conceptual DFT yields approximately half of this value,and it is termed Q_(max,GS)=?+A_1/(I-A_1).A large variety of molecules are evaluated including fullerenes,metal clusters,super-pnictogens,super-halogens(OF_3),super-alkali species(OLi_3),and neutral or charged transition-metal complexes,AB_(m )L_n^(0/+/-).The calculated second electron affinity A_(2,calc)=A_1-(7/12)(I-A_1)is linearly correlated to the literature references A_(2,lit) with a correlation coefficient R=0.998.A_2 or A_3 values are predicted for further 24 species.The appearance sizes,n_(ap)^(3-),of triply charged anionic clusters and fullerenes are calculated in agreement with the literature.

Devanagari Handwriting Grading System Based on Curvature Features

Grading of writers in perspective of their handwriting is a challenging task owing to various writing styles of different individuals.This paper presents a framework for grading of Devanagari writers in perspective of their handwriting.This framework of grading can be useful in conducting the handwriting competitions and then deciding the winners on the basis of an automated process.Selecting the set of features is a challenging task for implementing a handwriting grading system of particular language.In this paper,curvature features,namely,parabola curve fitting and power curve fitting have been considered for extracting the vital information of writers,which can be helpful in grading the writers.For obtaining the classification score,k-NN classifier has been considered in the present work.Four printed Devanagari font styles,namely,Devlys,Krishna,Krutidev,and Utsaah have been considered for train the proposed model of handwriting evaluation.For evaluating the effectiveness of the proposed framework,we have conducted a mock test of 75 Devanagari writers(Left handed and Right handed)and noticed that the proposed framework performing well suitable for conducting the handwriting competition of Devanagari text writers.This work is also newly in the ground of Devanagari text recognition.

A Study on Tooth Deformation of Parabola Tooth Belt by Complex Function Computation

An solution to tooth deformation of parabola tooth belt has been obtainedby complex function method of plane elastic theory,with the tooth deformation specifiedand the middle line between neighboring teeth displaced.The law governing the toothdeformation under load and the effect of deformation on distribution of load are analysed aswell.Computer software has been compiled on the basis of this way of solution and anaccurate way of calculation is provided for study on tooth deformation and loaddistribution.

Kink wave determined by parabola solution of a nonlinear ordinary differential equation

By finding a parabola solution connecting two equilibrium points of a planar dynamical system, the existence of the kink wave solution for 6 classes of nonlinear wave equations is shown. Some exact explicit parametric representations of kink wave solutions are given. Explicit parameter conditions to guarantee the existence of kink wave solutions are determined.

Characterization of ion irradiated silicon surfaces ablated by laser-induced breakdown spectroscopy

Low energy metallic ions, generated by a Q-switched Nd：YAG laser （1064-nm wavelength, 10-mJ energy, 9-nm 12-ns-pulse width, 1011 W/cm2 intensity） irradiated on a silicon substrate to modify various properties, such as electrical, morphological, and structural modifications. Thomson parabola technique is used to calculate the energy of these metallic ions whereas the electrical conductivity is calculated with the help of Four-point probe. Interestingly circular tracks forming chain like damage trails are produced via these energetic ions which are carefully examined by optical microscopy. It is observed that excitation, ionization, and cascade collisions are responsible for surface modifications of irradiated samples. Four-point probe analysis revealed that the electrical conductivity of substrate has reduced with increasing trend of atomic number of irradiated metallic ions （A1, Ti, Cu, and Au）. The x-ray diffraction analysis elucidated the crystallographic changes leading to reduction of grain size of N-type silicon substrate, which is also associated with the metallic ions used. The decreasing trend of conductivity and grain size is due to thermal stresses, scattering effect, structural imperfections, and non-uniform conduction of energy absorbed by substrate atoms after the ion irradiation.

Optical terminal analysis of a multigrating tiled compressor in a PW-class CPA-laser

In the highest-power chirped-pulse amplification lasers, the pulse must be stretched in time, amplified, compressed in a grating compressor and subsequently focused by off-axis parabola to obtain a high peak power. In the optical terminal, the temporal and spatial effects of mismatched multigrating tiled compressor on the far-field pulse are critical factors to be analysed. In this paper, a k-space raytracing model is proposed for the temporal and spatial analyses of possible errors in a four-grating single-pass tiled compressor. The results show that the last grating affects mainly the partial focal spot, while the middle two gratings affect the temporal waveform, and the partial focal spot needs much higher error control than that in the temporal domain in a picosecond pulse compression.

Simulating of marble subjected to uni-axial loading using index-parabola damage model

The limitations of several existing classical rock damage models were critically appraised. Thereafter, a description of a new model to estimate the response of rock was provided. The results of an investigation lead to the development and confirmation of a new index parabola damage model. The new model is divided into two parts, fictitious damage and real damage and bordered by the critical damage point. In fictitious damage, the damage variable follows the index distribution, while in the real damage a parabolic distribution is used. Thus, the so called index parabola damage model is derived. The proposed damage model is applied to simulate the damage procedure of marble under uni axial loading. The results of the tests show that the proposed model is in excellent agreement with experimental data, in particular the nonlinear characteristic of rock deformation is adequately represented. [

Comparative Analysis of Parabolic Bootlace Lens and Conventional Lens Approach

In this paper, parabolic refocusing lens is designed for the same requirements as Rotman lens. Comparison of results obtained with the parabolic refocusing lens with those obtained for the Rotman lens is also given.

A Novel Subpixel Curved Edge Localization Method

With the high-speed development of digital image processing technology, machine vision technology has been widely used in automatic detection of industrial products. A large amount of products can be treated by computer instead of human in a shorter time. In the process of automatic detection, edge detection is one of the most commonly used methods. But with the increasing demand for detection precision,traditional pixel-level methods are difficult to meet the requirement, and more subpixel level methods are in the use. This paper presents a new method to detect curved edge with high precision. First, the target area ratio of pixels near the edge is computed by using one-dimensional edge detection method. Second, parabola is used to approximately represent the curved edge. And we select appropriate parameters to obtain accurate results. This method is able to detect curved edges in subpixel level, and shows its practical effectiveness in automatic measure of products with arc shape in large industrial scene.

Geometric meanings of the parameters on rational conic segments

Using algebraic and geometric methods,functional relationships between a point on a conic segment and its corresponding parameter are derived when the conic segment is presented by a rational quadratic or cubic Bézier curve.That is,the inverse mappings of the mappings represented by the expressions of rational conic segments are given.These formulae relate some triangular areas or some angles,determined by the selected point on the curve and the control points of the curve,as well as by the weights of the rational Bézier curve.Also,the relationship can be expressed by the corresponding parametric angles of the selected point and two endpoints on the conic segment,as well as by the weights of the rational Bézier curve.These results are greatly useful for optimal parametrization,reparametrization,etc.,of rational Bézier curves and surfaces.

Spatial pattern of grassland aboveground biomass and its environmental controls in the Eurasian steppe

Vegetation biomass is an important component of terrestrial ecosystem carbon stocks. Grasslands are one of the most widespread biomes worldwideplaying an important role in global carbon cycling. Thereforestudying spatial patterns of biomass and their correlations to environment in grasslands is fundamental to quantifying terrestrial carbon budgets. The Eurasian steppean important part of global grasslandsis the largest and relatively well preserved grassland in the world. In this studywe analyzed the spatial pattern of aboveground biomass（AGB）and correlations of AGB to its environment in the Eurasian steppe by meta-analysis. AGB data used in this study were derived from the harvesting method and were obtained from three data sources（literatureglobal NPP database at the Oak Ridge National Laboratory Distributed Active Archive Center（ORNL）some data provided by other researchers）. Our results demonstrated that：（1） as for the Eurasian steppe overallthe spatial variation in AGB exhibited significant horizontal and vertical zonality. In detailAGB showed an inverted parabola curve with the latitude and with the elevationwhile a parabola curve with the longitude. In additionthe spatial pattern of AGB had marked horizontal zonality in the Black Sea-Kazakhstan steppe subregion and the Mongolian Plateau steppe subregionwhile horizontal and vertical zonality in the Tibetan Plateau alpine steppe subregion.（2） Of the examined environmental variablesthe spatial variation of AGB was related to mean annual precipitation（MAP）mean annual temperature（MAT）mean annual solar radiation（MAR）soil Gravel contentsoil p H and soil organic content（SOC） at the depth of 0–30 cm. NeverthelessMAP dominated spatial patterns of AGB in the Eurasian steppe and its three subregions.（3） A Gaussian function was found between AGB and MAP in the Eurasian steppe overallwhich was primarily determined by unique patterns of grasslands and environment in the Tibetan Plateau. AGB was significantly positively related to MAP in the Black Sea-Kazakhstan steppe subregion（elevation 〈 3000 m）the Mongolian Plateau steppe subregion（elevation 〈 3000 m） and the surface（elevation ≥ 4800 m） of the Tibetan Plateau. Neverthelessthe spatial variation in AGB exhibited a Gaussian function curve with the increasing MAP in the east and southeast margins（elevation 〈 4800 m） of the Tibetan Plateau. This study provided more knowledge of spatial patterns of AGB and their environmental controls in grasslands than previous studies only conducted in local regions like the Inner Mongolian temperate grasslandthe Tibetan Plateau alpine grasslandetc.

Nuclear mass parabola and its applications

We propose a method for extracting the properties of the isobaric mass parabola based on the total doubleβ-decay energies of isobaric nuclei.Two important parameters of the mass parabola,the location of the mostβ-stable nuclei ZA and the curvature parameter bA,are obtained for 251 A values,based on the total doubleβ-decay energies of nuclei compiled in the AME2016 database.The advantage of this approach is that the pairing energy term PA caused by the odd-even variation can be removed in the process,as well as the mass excess M(A,ZA)of the most stable nuclide for the mass number A,which are employed in the mass parabolic fitting method.The Coulomb energy coefficient ac=0.6910 MeV is determined by the mass difference relation for mirror nuclei,and the symmetry energy coefficient is also studied by the relation asym(A)=025 bAZA.