Solving the Optimal Control Problems of Nonlinear Duffing Oscillators By Using an Iterative Shape Functions Method

In the optimal control problem of nonlinear dynamical system,the Hamiltonian formulation is useful and powerful to solve an optimal control force.However,the resulting Euler-Lagrange equations are not easy to solve,when the performance index is complicated,because one may encounter a two-point boundary value problem of nonlinear differential algebraic equations.To be a numerical method,it is hard to exactly preserve all the specified conditions,which might deteriorate the accuracy of numerical solution.With this in mind,we develop a novel algorithm to find the solution of the optimal control problem of nonlinear Duffing oscillator,which can exactly satisfy all the required conditions for the minimality of the performance index.A new idea of shape functions method(SFM)is introduced,from which we can transform the optimal control problems to the initial value problems for the new variables,whose initial values are given arbitrarily,and meanwhile the terminal values are determined iteratively.Numerical examples confirm the high-performance of the iterative algorithms based on the SFM,which are convergence fast,and also provide very accurate solutions.The new algorithm is robust,even large noise is imposed on the input data.

The choosing of reproducing kernel particle shape function with mathematic proof

Many mechanical problems can be induced from differential equations with boundary conditions; there exist analytic and numerical methods for solving the differential equations. Usually it is not so easy to obtain analytic solutions. So it is necessary to give numerical solutions. The reproducing kernel particle （RKP） method is based on the Carlerkin Meshless method. According to the Sobolev space and Fourier transform, the RKP shape function is mathematically proved in this paper.

ON THE SELECTION OF SHAPE FUNCTION SPACES OF TRIANGULAR PLATE ELEMENTS

Using the method of undetermined coefficients, we construct a set of shape function spaces of nine-node triangular plate elements converging for any meshes, which generalize Spect's element and Veubeke's element.

Modeling unbalanced rotor system with continuous viscoelastic shaft by frequency-dependent shape function

A reduced-order dynamic model for an unbalanced rotor system is developed, taking the coupling between torsional and lateral vibrations into account. It is assumed that a shaft is regarded as a continuous viscoelastic shaft with unbalanced and small deformation properties. The equations of motion for the torsional and lateral vibrations are derived using Lagrange's approach with the frequency-dependent shape function. The rotor torsional vibration is coupled with the lateral vibrations by unbalance elements in a way of excitations. Simulation and experiment results show clearly that the torsional vibration has strong impact on the rotor lateral vibrations, and it causes subharmonic and superharmonic excitations through unbalance elements, which leads to the superharmonic resonances in the lateral vibrations. This model with low-order and high accuracy is suitable for rotor dynamic analysis in real time simulation as well as for active vibration control syntheses.

Digital Image Correlation Using Specific Shape Function for Stress Intensity Factor Measurement

The stress intensity factor (SIF) is a critical parameter associated with the fracture behaviour of materials. In this paper, we select the displacement function around a crack tip as the shape function of the digital image correlation (DIC), which makes it possible to directly calculate the SIF by the correlation scheme. Moreover, we use a non-rectangular subset, which can reduce the influence of plastic deformation and crack width on the DIC measurement accuracy. We measured the SIF of a mode I crack in a super-hard aluminium alloy specimen to verify the performance of the proposed method. Our experimental results show that a DIC with a specific shape function can be used to accurately and efficiently calculate the SIF. Furthermore, we also present a practical application of our proposed method for determining the SIF, crack propagation angle and crack tip displacement. © 2017, Tianjin University and Springer-Verlag Berlin Heidelberg.

Effects of galactooligosaccharide glycation on the functional properties of soy protein isolate and its application in noodles

Soybean protein has high nutritional value, but its functional properties are easily affected by external factors,which limits its application in food industry. In the study, soybean protein isolate(SPI) was modified by dry heat glycation of galactooligosaccharides(GOS). The gel properties, antioxidant properties and structural changes of SPI-GOS conjugates were investigated. The application of SPI-GOS conjugates in noodles was also explored. The results observed that the glycation degree of SPI increased with the increasing reaction time. SDS-PAGE and spectral analysis showed the changes of spatial conformation of SPI after glycation. The antioxidant activity of SPI increased after glycation and DPPH radical scavenging activity of SPI-GOS peaked at 48 h of reaction. The hardness, elasticity and resilience of soybean protein gel reached their relative maximum at 48 h, 48 h and 12 h of glycation reaction, respectively. Moreover, the appropriate addition of glycated SPI improved the quality of noodles. The noodles with 4% addition of SPI-GOS had higher hardness, elasticity and tensile properties. This study will provide an effective method to modify soybean protein and expand the use of soybean protein in food industry.

Improving comprehensive properties of Cu-11.9Al-2.5Mn shape memory alloy by adding multi-layer graphene carried by Cu_(51)Zr_(14)inoculant particles

In order to improve the comprehensive properties of the Cu-11.9Al-2.5Mn shape memory alloy(SMA),multilayer graphene(MLG)carried by Cu_(51)Zr_(14)inoculant particles was incorporated and dispersed into this alloy through preparing the preform of the cold-pressed MLG-Cu_(51)Zr_(14)composite powders.In the resultant novel MLG/Cu-Al-Mn composites,MLG in fragmented or flocculent form has a good bonding with the Cu-Al-Mn matrix.MLG can prevent the coarsening of grains of the Cu-Al-Mn SMA and cause thermal mismatch dislocations near the MLG/Cu-Al-Mn interfaces.The damping and mechanical properties of the MLG/Cu-Al-Mn composites are significantly improved.When the content of MLG reaches 0.2 wt.%,the highest room temperature damping of 0.0558,tensile strength of 801.5 MPa,elongation of 10.8%,and hardness of HV 308 can be obtained.On the basis of in-depth observation of microstructures,combined with the theory of internal friction and strengthening and toughening theories of metals,the relevant mechanisms are discussed.

Effect of Exchange-Correlation Functional on the Structural, Mechanical, and Optoelectronic Properties of Orthorhombic RbSrBr3 Perovskite

In the present study, the effect of the exchange-correlation functional on the structural, mechanical, and optoelectronic properties of orthorhombic RbSrBr3 perovskite has been investigated using various functionals in Density Functional Theory (DFT) with the CASTEP code. The optimized lattice parameters are quite similar for all the functionals. The electronic properties have shown that RbSrBr3 perovskite is a wide direct band gap compound with a band gap energy ranging from 4.296 eV to 4.494 eV for all the functionals. The mechanical parameters like elastic constants, Young’s modulus, Shear modulus, Poisson’s ratio, Pugh’s ratio, and an anisotropic factor reveal that the RbSrBr3 perovskite has ductile behavior and an anisotropic nature which signifies the mechanical stability of the compound. The Debye temperature might withstand lattice vibration heat. High absorption coefficient (>104 cm−1), high optical conductivity, and very low reflectivity have been found in the RbSrBr3 perovskite for all functions. The computed findings on the RbSrBr3 perovskite suggested that the presented studied material is potentially applicable for photodetector and optoelectronic devices.

Application of Pomegranate Rind Extract for Improvement of Functional Properties of Various Materials—A Critical Review

Pomegranate rind is abundantly available as a waste material. Pomegranate Rind Extract (PRE) can be applied to cotton fabrics for its natural colours, as a mordanting agent and also for imparting certain functional properties such as fire retardancy and antimicrobial properties. This paper reviews the feasibility of Pomegranate Rind Extract to improve the functional properties of cellulosic fabrics. Studies show that varying concentrations and higher temperatures that were used to apply the extract on the fabric, resulted in enhanced functional properties. At a particular concentration, the treated fabric showed a 15 times lower burning rate in comparison with the control fabric. Also, antimicrobial efficacy has been observed against Gram-positive and Gram-negative bacteria. Due to the natural colouring material, it can be used as a natural dye on cotton material. The fire retardancy of pomegranate rind extract was tested on jute material under varying alkalinity. Research has indicated that pomegranate rind extract could be used to dye polyamide as well. The rubbing and wash fastness of the finished fabrics is good. The light fastness was fair, and its antibacterial efficiency against tested bacteria was good.

Changes of structure and functional properties of rice protein in the fresh edible rice during the seed development

It has been reported that fresh edible rice has more bioactive compounds and its protein is easier to digest and has lower hypoallergenic than mature rice. In this paper, the changes in structure and functional properties of proteins at five different stages, including early milky stage(EMS), middle milky stage(MMS), late milky stage(LMS), waxy ripe stage(WS)and ripening stage(RS), during the seed development were investigated. It was found that with the seed developing, the molecular weight of fresh rice protein gradually become larger while the secondary structure changed from the highest content of disordered structure at MMS to the highest content of ordered structure at RS, which affect the surface hydrophobicity and then the functional properties of proteins, including foaming properties, emulsifying properties and oil holding capacity. Fresh rice protein at MMS has the strongest surface hydrophobicity while fresh edible rice protein at RS has the strongest oil holding capability. The results of our study can provide a theoretical basis for the application of fresh rice protein in the food industry and help to develop new fresh edible rice food.

Investigation of the structural, electronic and mechanical properties of CaO–SiO_(2) compound particles in steel based on density functional theory

CaO–SiO_(2)compounds compromise one of the most common series of oxide particles in liquid steels, which could significantly affect the service performance of the steels as crack initiation sites. However, the structural, electronic, and mechanical properties of the compounds in CaO–SiO_(2)system are still not fully clarified due to the difficulties in the experiments. In this study, a thorough investigation of these properties of CaO–SiO_(2)compound particles in steels was conducted based on first-principles density functional theory. Corresponding phases were determined by thermodynamic calculation, including gamma dicalcium silicate(γ-C2S), alpha-prime(L) dicalcium silicate(αL′-C2S), alpha-prime(H) dicalcium silicate(αH′-C2S), alpha dicalcium silicate(α-C2S), rankinite(C3S2), hatrurite(C3S), wollastonite(CS), and pseudowollastonite(Ps-CS). The results showed that the calculated crystal structures of the eight phases agree well with the experimental results. All the eight phases are stable according to the calculated formation energies, and γ-C2S is the most stable. O atom contributes the most to the reactivity of these phases. The Young’s modulus of the eight phases is in the range of 100.63–132.04 GPa. Poisson’s ratio is in the range of0.249–0.281. This study provided further understanding concerning the CaO–SiO_(2)compound particles in steels and fulfilled the corresponding property database, paving the way for inclusion engineering and design in terms of fracture-resistant steels.

Experimental study on thermal and mechanical properties of tailings-based cemented paste backfill with CaCl_(2)·6H_(2)O/expanded vermiculite shape stabilized phase change materials

CaCl_(2)·6H_(2)O/expanded vermiculite shape stabilized phase change materials(CEV)was prepared by atmospheric impregnation method.Using gold mine tailings as aggregate of cemented paste backfill(CPB)material,the CPB with CEV added was prepared,and the specific heat capacity,thermal conductivity,and uniaxial compressive strength(UCS)of CPB with different cement-tailing ratios and CEV addition ratios were tested,the influence of the above variables on the thermal and mechanical properties of CPB was analyzed.The results show that the maximum encapsulation capacity of expanded vermiculite for CaCl_(2)·6H_(2)O is about 60%,and the melting and solidification enthalpies of CEV can reach 98.87 J/g and 97.56 J/g,respectively.For the CPB without CEV,the specific heat capacity,thermal conductivity,and UCS decrease with the decrease of cement-tailing ratio.For the CPB with CEV added,with the increase of CEV addition ratio,the specific heat capacity increases significantly,and the sensible heat storage capacity and latent heat storage capacity can be increased by at least 10.74%and 218.97%respectively after adding 12%CEV.However,the addition of CEV leads to the increase of pores,and the thermal conductivity and UCS both decrease with the increase of CEV addition.When cement-tailing ratio is 1:8 and 6%,9%,and 12%of CEV are added,the 28-days UCS of CPB is less than 1 MPa.Considering the heat storage capacity and cost price of backfill,the recommended proportion scheme of CPB material presents cement-tailing ratio of 1:6 and 12%CEV,and the most recommended heat storage/release temperature cycle range of CPB with added CEV is from 20 to 40℃.This work can provide theoretical basis for the utilization of heat storage backfill in green mines.

Pectin fractions extracted sequentially from Cerasus humilis:Their compositions,structures,functional properties and antioxidant activities

Three pectin fractions(water-soluble fraction(WSF),chelator-soluble fraction(CSF),and sodium carbonatesoluble fraction(NSF))were obtained from Chinese dwarf cherry(Cerasus humilis)fruits.All of them were branched low methoxylated pectins with an amorphous or partially nanocrystalline nature and eight neutral monosaccharides(arabinose and galactose were most abundant).WSF,CSF and NSF had a degree of methylation(DM)of 35.82%,14.85%and 7.13%,uronic acid(UA)content of 76.02%,83.71%and 69.01%,and total protein content of 2.4%,2.1%and 8.8%,respectively.Their molecular weights were 340.31,330.16 and 141.31 kg/mol,respectively(analyzed by gel permeation chromatography(GPC)).WSF,CSF and NSF exhibited good rheological,thermal,emulsifying,emulsion-stabilizing,water-adsorbing,oil-binding,cholesterol-binding and antioxidant properties.NSF had the highest emulsifying,emulsion stabilizing,water-/oil-/cholesterol-binding and antioxidant capacities,followed by CSF.NSF had the highest viscosity(406.77 m Pa·s),flowability,and resistance to heat-induced changes/damage,which may be related to its lowest polydispersity index,DM and UA content and highest protein content.The three pectin fractions with desirable characteristics can be used as food additives/ingredients and dietary supplements.

Experimental Evaluation of Thermal Conductivity and Other Thermophysical Properties of Nanofluids Based on Functionalized (-OH) Mwcnt Nanoparticles Dispersed in Distilled Water

A possible way to increase thermal conductivity of working fluids, while keeping pressure drop at acceptable levels, is through nanofluids. Nanofluids are nano-sized particles dispersed in conventional working fluids. A great number of materials have potential to be used in nanoparticles production and then in nanofluids;one of them is Multi-Walled Carbon Nano Tubes (MWCNT). They have thermal conductivity around 3000 W/mK while other materials used as nanoparticles like CuO have thermal conductivity of 76.5 W/mK. Due to this fact, MWCNT nanoparticles have potential to be used in nanofluids production, aiming to increase heat transfer rate in energy systems. In this context, the main goal of this paper is to evaluate from the synthesis to the experimental measurement of thermal conductivity of nanofluid samples based on functionalized (-OH) MWCNT nanoparticles. They will be analyzed nanoparticles with different functionalization degrees (4% wt, 6% wt, and 9% wt). In addition, it will be quantified other thermophysical properties (dynamic viscosity, specific heat and specific mass) of the synthetized nanofluids. So, the present work can contribute with experimental data that will help researches in the study and development of MWCNT nanofluids. According to the results, the maximum increment obtained in thermal conductivity was 10.65% in relation to the base fluid (water).

Functional properties,antioxidant activity and in-vitro digestibility characteristics of brown and polished rice flours of Indian temperate region

The present investigation was aimed to study functional properties,antioxidant activity and in-vitro digestibility characteristics of brown and polished flours obtained from four rice cultivars(SR-4,K-39,Mushq Budij and Zhag)of Kashmir.Brown rice flours had higher total dietary fibre(3.08%-3.68%),oil absorption(116.0%-139.0%),emulsion capacity(4.78%-9.52%),emulsion stability(87.46%-99.93%)and resistant starch content(6.80%-9.00%)than polished flours.However,polished flours presented greater water absorption(102.0%-122.0%),foaming capacity(8.00%-13.63%),apparent amylose(19.16%-22.62%),peak(2260.0-2408.0 cP),trough(1372.0-1589.0 cP)and breakdown(714.0-978.0 cP)viscosities than their brown counterparts.Brown rice flours depicted highest total phenolic content(4.40-6.40 mg GAE/g)and inhibition of lipid peroxidation(19.50%-33.20%).However,equilibrium starch hydrolysis percentage(C∞)and predicted glycemic index of brown rice flours were lower than their polished counterparts.Among rice cultivars,brown Zhag flour had the highest total dietary fibre(3.68%),emulsion capacity(9.52%),emulsion stability(99.93%),resistant starch(9.00%),DPPH radical scavenging activity(85.45%)and inhibition of lipid peroxidation(33.20%),respectively.Emulsion capacity and emulsion stability were positively correlated with protein content of rice flours.However,peak,trough,breakdown and setback viscosities were negatively correlated with protein and fat contents of rice flour.The present investigation will be helpful in identifying nutritive role of rice flours from studied cultivars in human diet.

High-throughput calculations combining machine learning to investigate the corrosion properties of binary Mg alloys

Magnesium(Mg)alloys have shown great prospects as both structural and biomedical materials,while poor corrosion resistance limits their further application.In this work,to avoid the time-consuming and laborious experiment trial,a high-throughput computational strategy based on first-principles calculations is designed for screening corrosion-resistant binary Mg alloy with intermetallics,from both the thermodynamic and kinetic perspectives.The stable binary Mg intermetallics with low equilibrium potential difference with respect to the Mg matrix are firstly identified.Then,the hydrogen adsorption energies on the surfaces of these Mg intermetallics are calculated,and the corrosion exchange current density is further calculated by a hydrogen evolution reaction(HER)kinetic model.Several intermetallics,e.g.Y_(3)Mg,Y_(2)Mg and La_(5)Mg,are identified to be promising intermetallics which might effectively hinder the cathodic HER.Furthermore,machine learning(ML)models are developed to predict Mg intermetallics with proper hydrogen adsorption energy employing work function(W_(f))and weighted first ionization energy(WFIE).The generalization of the ML models is tested on five new binary Mg intermetallics with the average root mean square error(RMSE)of 0.11 eV.This study not only predicts some promising binary Mg intermetallics which may suppress the galvanic corrosion,but also provides a high-throughput screening strategy and ML models for the design of corrosion-resistant alloy,which can be extended to ternary Mg alloys or other alloy systems.

Effect of lipid peroxidation on the allergenicity and functional properties of soybeanβ-conglycinin(7S)and glycinin(11S)

This study aimed to analyze the effect of lipid peroxidation on the allergenicity and functional properties of soybeanβ-conglycinin(7 S)and glycinin(11 S).Oxidation complexes were determined using the lipid peroxidation method.Functional properties were analyzed based on emulsifying and foaming properties.The potential allergenicity was evaluated by in vitro and in vivo methods.The results found that oxidation altered structures of the proteins and resulted in the formation of cross-linked protein polymers.The emulsion and foaming properties of the proteins were improved after oxidation.The IgE-binding capacity of 7 S and11 S reduced after oxidation.KU812 cell assays showed that both histamine and IL-4 release decreased after oxidation treatment.A mouse model showed that oxidation reduced the IgE,IgG,and IgG1 levels,as well as reduced histamine and mMCP-1 release in serum,which might suppress the allergic reaction.In conclusion,the lipid peroxidation treatment likely causes changes to the functional properties of soybean,decreasing the potential allergenicity of 7 S and 11 S.

Disparities in tree mortality among plant functional types(PFTs)in a temperate forest:Insights into size-dependent and PFT-specific patterns

Tree mortality significantly influences forest structure and function,yet our understanding of its dynamic patterns among a range of tree sizes and among different plant functional types(PFTs)remains incomplete.This study analysed size-dependent tree mortality in a temperate forest,encompassing 46 tree species and 32,565 individuals across different PFTs(i.e.,evergreen conifer vs.deciduous broadleaf species,shade-tolerant vs.shade-intolerant species).By employing all-subset regression procedures and logistic generalized linear mixed-effects models,we identified distinct mortality patterns influenced by biotic and abiotic factors.Our results showed a stable mortality patte rn in eve rgreen conifer species,contrasted by a declining pattern in deciduous broadleaf and shadetolerant,as well as shade-intolerant species,across size classes.The contribution to tree mortality of evergreen conifer species shifted from abiotic to biotic factors with increasing size,while the mortality of deciduous broadleaf species was mainly influenced by biotic factors,such as initial diameter at breast height(DBH)and conspecific negative density.For shade-tolerant species,the mortality of small individuals was mainly determined by initial DBH and conspecific negative density dependence,whereas the mortality of large individuals was subjected to the combined effect of biotic(competition from neighbours)and abiotic factors(i.e.,convexity and pH).As for shade-intolerant species,competition from neighbours was found to be the main driver of tree mortality throughout their growth stages.Thus,these insights enhance our understanding of forest dynamics by revealing the size-dependent and PFT-specific tree mortality patterns,which may inform strategies for maintaining forest diversity and resilience in temperate forest ecosystems.

Structure,electronic,and nonlinear optical properties of superalkaline M_(3)O(M=Li,Na)doped cyclo[18]carbon

Cyclo[18]carbon has received considerable attention thanks to its novel geometric configuration and special electronic structure.Superalkalis have low ionization energy.Doping a superalkali in cyclo[18]carbon is an effective method to improve the optical properties of the system because considerable electron transfer occurs.In this paper,the geometry,bonding properties,electronic structure,absorption spectrum,and nonlinear optical(NLO)properties of superalkaline M_(3)O(M=Li,Na)-doped cyclo[18]carbon were studied by using density functional theory.M_(3)O and the C_(18) rings are not coplanar.The C_(18) ring still exhibits alternating long and short bonds.The charge transfer between M_(3)O and C_(18) forms stable[M_(3)O]+[C_(18)]-ionic complexes.C_(18)M_(3)O(M=Li,Na)shows striking optical nonlinearity,i.e.,their first-and second-order hyperpolarizability(βvec andγ||)increase considerably atλ=1907 nm and 1460 nm.

Wave propagation of a functionally graded plate via integral variables with a hyperbolic arcsine function

Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagation of the waves in plates.This work aims to explore the effects of changing compositional characteristics and the volume fraction of the constituent of plate materials regarding the wave propagation response of thick plates of FGM.This model is based on a higher-order theory and a new displacement field with four unknowns that introduce indeterminate integral variables with a hyperbolic arcsine function.The FGM plate is assumed to consist of a mixture of metal and ceramic,and its properties change depending on the power functions of the thickness of the plate,such as linear,quadratic,cubic,and inverse quadratic.By utilizing Hamilton’s principle,general formulae of the wave propagation were obtained to establish wave modes and phase velocity curves of the wave propagation in a functionally graded plate,including the effects of changing compositional characteristics of materials.