Quadratic Distribution Research Articles

An improved enhanced solid shell element for static and buckling analysis of shell structures

This paper presents an improved higher order solid shell element for static and buckling analysis of laminated composite structures based on the enhanced assumed strain (EAS). The transverse shear strain is divided into two parts: the first one is independent of the thickness coordinate and formulated by the assumed natural strain (ANS) method; the second part is an enhancing part, which ensures a quadratic distribution through the thickness. This allows removing the shear correction factors and improves the accuracy of transverse shear stresses. In addition, volumetric locking is completely avoided by using the optimal parameters in the EAS method. The formulated finite element is implemented to study the static and buckling behavior of shell structures and to investigate the influence of some parameters on the buckling load. Comparisons of numerical results with those extracted from literature show the acceptable performance of the developed element.

Inverse synthetic aperture radar imaging of targets with complex motions based on modified chirp rate–quadratic chirp rate distribution for cubic phase signal

For targets with complex motions, the time-varying Doppler frequency deteriorates inverse synthetic aperture radar (ISAR) images. After range alignment and phase adjustment, azimuth echoes in a range cell can be modeled as multicomponent cubic phase signals (CPSs). The chirp rate and the quadratic chirp rate of the CPS are identified as the causes of the time-varying Doppler frequency; thus, it is necessary to estimate these two parameters correctly to obtain a well-focused ISAR image. The parameter-estimation algorithm based on the modified chirp rate-quadratic chirp rate distribution (M-CRQCRD) is proposed for the CPS and applied to the ISAR imaging of targets with complex motions. The computational cost of M-CRQCRD is low, because it can be implemented by the fast Fourier transform (FFT) and the nonuniform FFT easily. Compared to two representative parameter-estimation algorithms, the M-CRQCRD can acquire a higher antinoise performance due to the introduction of an optimal lag-time. Through simulations and analyses for the synthetic radar data, the effectiveness of the M-CRQCRD and the imaging algorithm based on the M-CRQCRD are verified.

Rank-size distributions of Chinese cities: Macro and micro patterns

A large number of studies have been conducted to find a better fit for city rank-size distributions in different countries. Many theoretical curves have been proposed, but no consensus has been reached. This study argues for the importance of examining city rank-size distribution across different city size scales. In addition to focusing on macro patterns, this study examines the micro patterns of city rank-size distributions in China. A moving window method is developed to detect rank-size distributions of cities in different sizes incrementally. The results show that micro patterns of the actual city rank-size distributions in China are much more complex than those suggested by the three theoretical distributions examined (Pareto, quadratic, and q-exponential distributions). City size distributions present persistent discontinuities. Large cities are more evenly distributed than small cities and than that predicted by Zipf’s law. In addition, the trend is becoming more pronounced over time. Medium-sized cities became evenly distributed first and then unevenly distributed thereafter. The rank-size distributions of small cities are relatively consistent. While the three theoretical distributions examined in this study all have the ability to detect the overall dynamics of city rank-size distributions, the actual macro distribution may be composed of a combination of the three theoretical distributions.

The Onset of Convection in a Horizontal Porous Layer with Spatially Non-Uniform Internal Heating

We have used linear instability theory to determine the condition for the onset of convection in an internally heated horizontal layer, occupied by a porous medium, when the source strength varies in the vertical direction. Some paradigmatic special cases are investigated. In particular, we investigated linear, quadratic and concentrated source strength distributions. Stability is increased in those situations in which the region where the basic temperature gradient is destabilizing is of small extent.

Free vibration analysis of a debonded curved sandwich beam

Abstract In this paper, a high order theory is developed to study the free vibration response of a debonded curved sandwich beam. Since the real contact condition at the debonded region is nonlinear, two linear “with contact” and “without contact” models are employed. The Lagrange's principle and the Rayleigh-Ritz method are employed to derive and solve the governing equations. The model regards the radial and circumferential rigidities of the core. For this purpose, quadratic polynomial distributions across the core's height are proposed for its displacement components. The high order model is validated by finite element simulation in ANSYS Workbench. It will be shown that the quadratic distributions can effectively be used for a debonded curved beam comparing to other possible distributions such as a linear pattern which has been previously suggested for an undamaged beam. The analyses demonstrate that curvature angle and boundary conditions play important roles in the vibration response of a curved beam. Also, the results show that the debond effect on natural frequencies is approximately identical for flat and curved beams.

Crashworthiness performance of conical tubes with nonlinear thickness distribution

Crashworthiness performance of conical tubes with various thickness distributions are investigated in the present work. Specimens are fabricated by tube shrinking process and axial crushing tests are carried out to study their energy absorption characteristics. The potential and benefit of tube shrinking to improve crashworthiness performance of tubes are analyzed. Both thickness increase and material hardening during tube shrinking lead to up to 120% increase in energy absorption with even less structural mass. Although the peak force of tubes is increased after shrinking, the load uniformity is still improved due to larger increase in mean crushing force. Numerical simulations are also conducted for tubes with quadratic thickness distributions. The material hardening during fabrication is included and the numerical results compare well with experiment. In addition, crashworthiness optimization of conical tubes with nonlinear thickness distribution is performed by surrogate method. Influences of relevant thickness parameters on performance of the structure are analyzed.

Application of modified Dugdale model to two pairs of collinear cracks with coalesced yield zones

In this paper, a modified Dugdale’s approach has been presented to arrest four straight collinear quasi-static cracks with coalesced yield zones. An infinite elastic perfectly plastic plate, containing four cracks, is subjected to uniform stresses applied at infinite boundary of the plate. As a result, yield zones develop at each crack tip. On increasing the stresses, yield zones between two pairs of cracks get coalesced and after that at each internal crack tip. In order to detain propagation of cracks, a quadratic yield stress distribution is applied on the rims of the yield zones. This distribution enables to investigate the residual strength of an infinite plate, when the plate fails at a stress which is well below the yield stress of the plate. Muskhelishvili’s complex variable technique is use to solve the stated problem. Analytical expressions for stress intensity factor and crack-tip opening displacements are established. The results validate with previously published works.

Variable Optical Delay Line Using Discrete Harmonic Oscillation in Waveguide Lattices

This paper proposes a variable optical delay line based on the discrete harmonic oscillation in the waveguide lattice with a quadratic distribution of coupling coefficients. Theoretical analysis and numerical simulation have shown that the device design can achieve a time delay of up to 10 ns, with the resolution of 0.5 ns, and the 3-dB bandwidth over the whole C-band. It allows a data packet of up to 17 bits at the rate of 100 Gb/s. In this design, the propagation path is folded by up to five times (or ten times for the one-port design). Compared with the conventional fiber-delay-line buffer, this design has a small footprint (about 10 mm × 0.5 mm). A group of them can be paralleled and cascaded within a small area (e.g., 20 copies into 1 cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ) as enabled by the microfabrication. With further optimization, this design has a potential for interconnecting and signal processing applications in optical communications and computing.

A New Reassigned Spectrogram Method in Interference Detection for GNSS Receivers.

Interference detection is very important for Global Navigation Satellite System (GNSS) receivers. Current work on interference detection in GNSS receivers has mainly focused on time-frequency (TF) analysis techniques, such as spectrogram and Wigner–Ville distribution (WVD), where the spectrogram approach presents the TF resolution trade-off problem, since the analysis window is used, and the WVD method suffers from the very serious cross-term problem, due to its quadratic TF distribution nature. In order to solve the cross-term problem and to preserve good TF resolution in the TF plane at the same time, in this paper, a new TF distribution by using a reassigned spectrogram has been proposed in interference detection for GNSS receivers. This proposed reassigned spectrogram method efficiently combines the elimination of the cross-term provided by the spectrogram itself according to its inherent nature and the improvement of the TF aggregation property achieved by the reassignment method. Moreover, a notch filter has been adopted in interference mitigation for GNSS receivers, where receiver operating characteristics (ROCs) are used as metrics for the characterization of interference mitigation performance. The proposed interference detection method by using a reassigned spectrogram is evaluated by experiments on GPS L1 signals in the disturbing scenarios in comparison to the state-of-the-art TF analysis approaches. The analysis results show that the proposed interference detection technique effectively overcomes the cross-term problem and also keeps good TF localization properties, which has been proven to be valid and effective to enhance the interference detection performance; in addition, the adoption of the notch filter in interference mitigation has shown a significant acquisition performance improvement in terms of ROC curves for GNSS receivers in jamming environments.

Mechanical characterization and inclusion based boundary element modeling of lightweight concrete containing foam particles

This paper investigates the effective material properties of lightweight concrete containing polymer foam particles through both experiments and numerical modeling. Different volume fractions of foam particles have been added to cement paste to fabricate lightweight concrete samples. To interpret the experimental results, an inclusion method based boundary integral equation has been proposed. The effect of the material mismatch between the foam particles and the cement matrix can be simulated by an eigenstrain, which is a fictitious nonmechanical strain. Due to the interaction between particles and boundary effect, the eigenstrain on a particle is not uniform. An asymptotic analysis shows that a quadratic distribution of the eigenstrain over each particle provides very good accuracy. Since the discretization of particles is not needed due to applying an analytic form of eigenstrain field, a large number of spherical inhomogeneities can be simulated and the local field can be calculated in a lightweight concrete sample. The formulation has been implemented in a software package for the simulation of material samples and has been verified with the finite element method for two top-down particles embedded in a cylinder. The simulation results based on idealized microstructure exhibit a very good agreement with the experimental results of the effective elastic moduli. A simple and empirical study also predicts the strengths of the composites very well. The developed algorithm can be used for virtual mechanical experiments of particulate composites.

An Improved Time-Frequency Analysis Method in Interference Detection for GNSS Receivers.

In this paper, an improved joint time-frequency (TF) analysis method based on a reassigned smoothed pseudo Wigner–Ville distribution (RSPWVD) has been proposed in interference detection for Global Navigation Satellite System (GNSS) receivers. In the RSPWVD, the two-dimensional low-pass filtering smoothing function is introduced to eliminate the cross-terms present in the quadratic TF distribution, and at the same time, the reassignment method is adopted to improve the TF concentration properties of the auto-terms of the signal components. This proposed interference detection method is evaluated by experiments on GPS L1 signals in the disturbing scenarios compared to the state-of-the-art interference detection approaches. The analysis results show that the proposed interference detection technique effectively overcomes the cross-terms problem and also preserves good TF localization properties, which has been proven to be effective and valid to enhance the interference detection performance of the GNSS receivers, particularly in the jamming environments.

Dynamics Analysis of Spatial Multibody System With Spherical Joint Wear

The influence of the spherical joint with clearance caused by wear on the dynamics performance of spatial multibody system is predicted based on the Archard's wear model and equations of motion of multibody systems. First, the function of contact deformation and load acting on the spherical joint with clearance is derived based on the improved Winkler elastic foundation model and Hertz quadratic pressure distribution assumption. On this basis, considering the influence of clearance size and wear state on the contact stiffness between spherical joint elements, an improved contact force model is proposed by Lankarani–Nikravesh contact force model and improved stiffness coefficient that is the slope of the function of contact deformation and load. Second, due to the complexity for that wear impacts on the surface topography of contact bodies, an approximate calculation method of contact area with respect to the clearance spherical joint is provided for simplifying the computational process of contact pressure in the Archard's wear model. Subsequently, the contact pressure between contact bodies is calculated by the improved contact force model and approximate contact area (ICFM–ACA), which is verified via finite element method (FEM). Moreover, the dynamics model of spatial four bar mechanism considering spherical joint with clearance caused by wear is formulated using equations of motion of multibody systems. Finally, the wear depth of spherical joint with clearance is predicted via two different kinds of contact pressure based on the Archard's wear model (one is from the ICFM–ACA and the other is from FEM), respectively. The numerical simulation results show that the improved contact force model and proposed approximate contact area are correctness and validity for predicting wear in the spherical joint with clearance. Simultaneously, the effect of the spherical joint with clearance caused by wear on the dynamics performance of spatial four bar mechanism is analyzed.

Propagation of anomalous vortex beams in strongly nonlocal nonlinear media

The propagation properties of anomalous vortex beams in strongly nonlocal nonlinear media are investigated. Two equivalent analytical expressions for the evolution of anomalous vortex beams are obtained. It is found that the input power plays a key role in the beam evolutions. Selecting a proper input power, the beam width can be broadened or be compressed periodically, even it can keep invariant during propagation. The beam order and the topological charge mainly influence the intensity evolution and the phase evolution, respectively. The evolution period, the beam width, the phase distribution and the intensity distribution are discussed in detail. The results can also be generalized to other equivalent physical systems, such as an optical fractional Fourier transform system or a medium with a quadratic graded refractive index distribution.

Low Temperature Properties of Inhomogeneous Magnetic Multilayers

System of two magnetic layers with nonuniform distribution of anisotropy parameter and exchange coupled by nonmagnetic spacer is studied by means of the Green function approach. Our attention is focussed on the elementary excitations and low temperature magnetisation behavior. The spin wave parameter B in the Bloch law T 3/2 is found as an oscillatory function of a spacer thickness. The e ects of damping leading to non-zero line-width of ferromagnetic resonance peaks are also taken into account. As a result the dependence of resonance line-width on parameters characterizing system under consideration is obtained for the case of uniform anisotropy parameter and for quadratic distribution of this parameter in magnetic layers, respectively.

Variable gradient refractive index engineering: design, growth and electro-deflective application of KTa1−xNbxO3

A variable gradient refractive index material is proposed, utilizing the controllable quadratic electro-optic coefficient distribution in single crystals of KTa1−xNbxO3.

Torsion of functionally graded nonlocal viscoelastic circular nanobeams

The elastostatic problem of functionally graded circular nanobeams under torsion, with nonlocal elastic behavior proposed by Eringen, is preliminarily formulated. Exact solutions are detected for nanobeams with arbitrary axial gradations of elastic properties and radially quadratic distributions of shear moduli. Extension of the treatment to nonlocal viscoelastic composite circular nanobeams is then performed. An effective solution procedure based on Laplace transform is developed, providing a new correspondence principle in nonlocal viscoelasticity for functionally graded materials. Displacements, shear strains and stresses are established for nonlocal viscoelastic nanobeams made of periodic fiber-reinforced materials, with polymeric matrix described by a Maxwell model connected in series with a Voigt model.

Manipulation of orbital angular momentum beams based on space diffraction compensation

We put forward a technique to manipulate the size of orbital angular momentum (OAM) beams based on space diffraction compensation. Paraxial Fresnel diffraction which carries a negative spatial quadratic phase distribution can be regarded as a negative diffractive effect. To compensate the negative diffraction, we employ a 4f Fourier lens system containing a phase mask to generate an inverse quadratic phase. The size of OAM beams can be easily controlled by designing the phase mask profile without changing the OAM. The applications of space diffraction compensation in OAM demultiplexing, ring fiber coupling for OAM beams and optical manipulation of micro particles are also discussed.

A New Generalization of Quadratic Hazard Rate Distribution

For the first time, a five-parameter distribution, called the kumaraswamy quadratic hazard rate distribution is defined and studied. The new distribution contains as special models some well-known distributions discussed in lifetime literature, such as the Linear failure rate, Exponential and Rayleigh distributions, among several others. We obtain the moments, moment generating and quantile functions. We discuss the method of maximum likelihood to estimate the model parameters and determine the observed information matrix. A real data sets illustrate the importance and flexibility of the proposed models. Normal 0 false false false EN-US X-NONE AR-SA

A two-point boundary value formulation of a mean-field crowd-averse game

We consider a population of “crowd-averse” dynamic agents controlling their states towards regions of low density. This represents a typical dissensus behavior in opinion dynamics. Assuming a quadratic density distribution, we first introduce a mean-field game formulation of the problem, and then we turn the game into a two-point boundary value problem. Such a result has a value in that it turns a set of coupled partial differential equations into ordinary differential equations.

Lifespan development of attentiveness in domestic dogs: drawing parallels with humans.

Attention is pivotal to consciousness, perception, cognition, and working memory in all mammals, and therefore changes in attention over the lifespan are likely to influence development and aging of all of these functions. Due to their evolutionary and developmental history, the dog is being recognized as an important species for modeling human healthspan, aging and associated diseases. In this study, we investigated the normal lifespan development of attentiveness of pet dogs in naturalistic situations, and compared the resulting cross-sectional developmental trajectories with data from previous studies in humans. We tested a sample of 145 Border collies (6 months to 14 years) with humans and objects or food as attention attractors, in order to assess their attentional capture, sustained and selective attention, and sensorimotor abilities. Our results reveal differences in task relevance in sustained attentional performance when watching a human or a moving object, which may be explained by life-long learning processes involving such stimuli. During task switching we found that dogs’ selective attention and sensorimotor abilities showed differences between age groups, with performance peaking at middle age. Dogs’ sensorimotor abilities showed a quadratic distribution with age and were correlated with selective attention performance. Our results support the hypothesis that the development and senescence of sensorimotor and attentional control may be fundamentally interrelated. Additionally, attentional capture, sustained attention, and sensorimotor control developmental trajectories paralleled those found in humans. Given that the development of attention is similar across humans and dogs, we propose that the same regulatory mechanisms are likely to be present in both species. Finally, this cross-sectional study provides the first description of age group changes in attention over the lifespan of pet dogs.