Efficient semi-analytical methods for the vibration response of and acoustic radiation from a periodical orthogonally rib-stiffened plate

In order to theoretically predict and analyze the vibration response and acoustic radiation characteristics of a periodical orthogonally rib-stiffened plate,its vibro-acoustic equations of an underwater infinite model are established.The rib-stiffened plate is stimulated by a harmonic plane pressure.By using the Fourier transforms,Poisson’s summation formula and space harmonic method,the structural vibration response and acoustic radiation pressure are expressed as functions of displacement harmonic components.Efficient semi-analytical methods are proposed in this work,and then approximate solutions for finite terms of the harmonic components are obtained by employing the truncation technique.Effects of the vibration response,rib spacing and torsional moment of the ribs on the radiation pressure are examined,and the validity of the present methods is also verified.Theoretical results show that the torsional moment of the ribs affects the modal frequencies of the stiffened plate,which should not be neglected in engineering applications with high precision requirement.With attachment of the ribs to the thin plate,its far field radiation pressure can be reduced in the low frequency range by adjusting rib spacing and cross sectional size of the ribs.

REFINEMENTS OF THE NORM OF TWO ORTHOGONAL PROJECTIONS

In this paper,some refinements of norm equalities and inequalities of combination of two orthogonal projections are established.We use certain norm inequalities for positive contraction operator to establish norm inequalities for combination of orthogonal projections on a Hilbert space.Furthermore,we give necessary and sufficient conditions under which the norm of the above combination of o`rthogonal projections attains its optimal value.

Optimal Design of High-Speed Partial Flow Pumps using Orthogonal Tests and Numerical Simulations

To investigate the influence of structural parameters on the performances and internal flow characteristics of partial flow pumps at a low specific speed of 10000 rpm,special attention was paid to the first and second stage impeller guide vanes.Moreover,the impeller blade outlet width,impeller inlet diameter,blade inclination angle,and number of blades were considered for orthogonal tests.Accordingly,nine groups of design solutions were formed,and then used as a basis for the execution of numerical simulations(CFD)aimed at obtaining the efficiency values and heads for each design solution group.The influence of impeller geometric parameters on the efficiency and head was explored,and the“weight”of each factor was obtained via a range analysis.Optimal structural parameters were finally chosen on the basis of the numerical simulation results,and the performances of the optimized model were verified accordingly(yet by means of CFD).Evidence is provided that the increase in the efficiency and head of the optimized model was 12.11%and 23.5 m,respectively,compared with those of the original model.

Dynamically enhanced Autler–Townes splitting by orthogonal XUV fields

Based on numerical solutions of the time-dependent Schr ¨odinger equation, we theoretically investigate the photoelectron spectrum of hydrogen atoms ionized by a pair of ultrashort, intense, and orthogonally polarized laser pulses with a relative time delay in a pump–probe configuration. The pump pulse resonantly excites electrons from the 1s and 2p levels,inducing Rabi oscillations. The resulting dynamically enhanced Autler–Townes(AT) splitting is observed in the photoelectron energy spectrum upon interaction with the second probe pulse. In contrast to the previous parallel-polarization scheme, the proposed orthogonal-polarization configuration enables the resolution of dynamically enhanced AT splitting over a considerably wider range of probe photon energies.

Manipulating the electron dynamics in the non-sequential double ionization process of Ar atoms by an orthogonal two-color laser field

Electron dynamics during non-sequential double ionization(NSDI) is one of the most attractive areas of research in the field of laser–atom or laser–molecule interaction. Based on the classic two-dimensional model, we study the process of NSDI of argon atoms driven by a few-cycle orthogonal two-color laser field composed of 800 nm and 400 nm laser pulses. By changing the relative phase of the two laser pulses, a localized enhancement of NSDI yield is observed at 0.5πand 1.5π, which could be attributed to a rapid and substantial increase in the number of electrons returning to the parent ion within extremely short time intervals at these specific phases. Through the analysis of the electron–electron momentum correlations within different time windows of NSDI events and the angular distributions of emitted electrons in different channels, we observe a more pronounced electron–electron correlation phenomenon in the recollision-induced ionization(RII) channel. This is attributed to the shorter delay time in the RII channel.

Optimization of Center of Gravity Position and Anti-Wave Plate Angle of Amphibious Unmanned Vehicle Based on Orthogonal Experimental Method

When the amphibious vehicle navigates in water,the angle of the anti-wave plate and the position of the center of gravity greatly influence the navigation characteristics.In the relevant research on reducing the navigation resistance of amphibious vehicles by adjusting the angle of the anti-wave plate,there is a lack of scientific selection of parameters and reasonable research of simulation results by using mathematical methods,and the influence of the center of gravity position on navigation characteristics is not considered at the same time.To study the influence of the combinations of the angle of the anti-wave plate and the position of the center of gravity on the resistance reduction characteristics,a numerical calculation model of the amphibious unmanned vehicle was established by using the theory of computational fluid dynamics,and the experimental data verified the correctness of the numerical model.Based on this numerical model,the navigation characteristics of the amphibious unmanned vehicle were studied when the center of gravity was located at different positions,and the orthogonal experimental design method was used to optimize the parameters of the angle of the anti-wave plate and the position of the center of gravity.The results show that through the parameter optimization analysis based on the orthogonal experimental method,the combination of the optimal angle of the anti-wave plate and the position of the center of gravity is obtained.And the numerical simulation result of resistance is consistent with the predicted optimal solution.Compared with the maximum navigational resistance,the parameter optimization reduces the navigational resistance of the amphibious unmanned vehicle by 24%.

Optimization of short-circuit transition parameters of Q235B steel GMAW based on orthogonal gray relational analysis

In gas metal arc welding(GMAW)process,the short-circuit transition was the most typical transition observed in molten metal droplets.This paper used orthogonal tests to explore the coupling effect law of welding process parameters on the quality of weld forming under short-circuit transition,the design of 3 factors and 3 levels of a total of 9 groups of orthogonal tests,welding current,welding voltage,welding speed as input parameters:effective area ratio,humps,actual linear power density,aspect ratio,Vickers hardness as output paramet-ers(response targets).Using range analysis and trend charts,we can visually depict the relationship between input parameters and a single output parameter,ultimately determining the optimal process parameters that impact the single output index.Then combined with gray the-ory to transform the three response targets into a single gray relational grade(GRG)for analysis,the optimal combination of the weld mor-phology parameters as follows:welding current 100 A,welding voltage 25 V,welding speed 30 cm/min.Finally,validation experiments were conducted,and the results showed that the error between the gray relational grade and the predicted value was 2.74%.It was observed that the effective area ratio of the response target significantly improved,validating the reliability of the orthogonal gray relational method.

Optimization of Extraction Process of Fagopyri Dibotryis Rhizoma by Orthogonal Experiment

[Objectives]To optimize the water extraction process of Fagopyri Dibotryis Rhizoma.[Methods]The entropy weight method was used to determine the weight of epicatechin extraction rate and dry extract rate and calculate the comprehensive score.The water extraction process of Fagopyri Dibotryis Rhizoma was optimized by orthogonal design with the comprehensive score as the indicator and the amount of water,extraction time and extraction times as the factors.[Results]The optimum extraction process of Fagopyri Dibotryis Rhizoma was as follows:adding 10 times of water,extracting 3 times,and extracting for 60 min each time.[Conclusions]The optimized extraction process is stable and feasible,and can be used for the extraction of Fagopyri Dibotryis Rhizoma.

Flow of micropolar fluid between two orthogonally moving porous disks

The unsteady, laminar, incompressible, and two-dimensional flow of a mi- cropolar fluid between two orthogonally moving porous coaxial disks is considered. The extension of von Karman＇s similarity transformations is used to reduce the governing partial differential equations （PDEs） to a set of non-linear coupled ordinary differential equations （ODEs） in the dimensionless form. The analytical solutions are obtained by employing the homotopy analysis method （HAM）. The effects of various physical param- eters such as the expansion ratio and the permeability Reynolds number on the velocity fields are discussed in detail.

Controlling the contributions to high-order harmonic generation from different nuclei of N_2 with an orthogonally polarized two-color laser field

The generation of high-order harmonic and the attosecond pulse of the N2 molecule with an orthogonally polarized two-color laser field are investigated by the strong-field Lewenstein model.We show that the control of contributions to high-order harmonic generation（HHG） from different nuclei is realized by properly selecting the relative phase.When the relative phase is chosen to be φ= 0.4π,the contribution to HHG from one nucleus is much more than that from another.Interference between two nuclei can be suppressed greatly; a supercontinuum spectrum of HHG appears from 40 e V to125 e V.The underlying physical mechanism is well explained by the time–frequency analysis and the semi-classical threestep model with a finite initial transverse velocity.By superposing several orders of harmonics,an isolated attosecond pulse with a duration of 80 as can be generated.

A Stable Wavelength Operation Ho:YAG Laser with Orthogonally Polarized Pump

A stable wavelength operation Ho:YAG laser dual-pumped by two orthogonally polarized Tm:YLF lasers is reported. Under the cw operation mode, a laser output power of 24 W is measured. The corresponding opticaloptical conversion efficiency is 44.75% and the slope efficiency is 50.12%. Under the Q-switched operation mode,the output maximum average power is 22.8 W at the re-frequency of 6 kHz. The corresponding optical-optical conversion efficiency and slope efficiency are 42.64% and 48.01%, respectively. The output central wavelength is 2090.73 nm, the linewidth is 0.40 nm, and the beam quality is M^2< 1.6. Moreover, the shift of the output central wavelength is less than 0.01 nm, and the linewidth shift is also less than 0.01 nm.

The vibroacoustic response and sound absorption performance of multilayer, microperforated rib-stiffened plates

The vibroacoustic response and sound absorption performance of a structure composed of multilayer plates and one rigid back wall are theoretically analyzed. In this structure, all plates are two-dimensional, microperforated, and periodically rib-stiffened. To investigate such a structural system, semianalytical models of one-layer and multilayer plate structures considering the vibration effects are first developed. Then approaches of the space harmonic method and Fourier transforms are applied to a one-layer plate, and finally the cascade connection method is utilized for a multilayer plate structure. Based on fundamental acoustic formulas, the vibroacoustic responses of microperforated stiffened plates are expressed as functions of a series of harmonic amplitudes of plate displacement, which are then solved by employing the numerical truncation method. Applying the inverse Fourier transform, wave propagation, and linear addition properties, the equations of the sound pressures and absorption coefficients for the one-layer and multilayer stiffened plates in physical space are finally derived. Using numerical examples, the effects of the most important physical parameters-for example, the perforation ratio of the plate, sound incident angles, and periodical rib spacing-on sound absorption performance are examined. Numerical results indicate that the sound absorption performance of the studied structure is effectively enhanced by the flexural vibration of the plate in water. Finally, the proposed approaches are validated by comparing the results of stiffened plates of the present work with solutions from previous studies.

A novel orthogonally linearly polarized Nd:YVO_4 laser

We presented a novel orthogonally linearly polarized Nd：YVO4 laser. Two pieces of a-cut grown-together composite YVO4/Nd：YVO4 crystals were placed in the resonant cavity with the c-axis of the two crystals orthogonally. The polarization and power performance of the orthogonally polarized laser were investigated. A 26.2-W orthogonally linearly polarized laser was obtained. The power ratio between the two orthogonally polarized lasers was varied with the pump power caused by the polarized mode coupling. The longitudinal modes competition and the corresponding variable optical beats were also observed from the orthogonally polarized laser. We also adjusted the crystals with their c-axis parallele to each other, and a 40.7-W linearly polarized TEM00 laser was obtained, and the beam quality factors were Mx^2 = 1.37 and My^2 = 1.25.

A General Model for Analysis of Sound Radiation from Orthogonally Stiffened Laminated Composite Plates

A general theoretical model is developed to investigate the sound radiation from an infinite orthogonally stiffened plate under point excitation force. The plate can be metallic or composite, and fluid loading is also considered in the research. The first order shear deformation theory is used to account for the transverse shear deformation. The motion of the equally spaced stiffeners is examined by considering their bending vibrations and torsional movements. Based on the periodic structure theory and the concepts of the equivalent dynamic flexibility of the plate, the generalized vibro-acoustic equation of the model is obtained by applying the Fourier transform method. The generalized model that can be solved numerically is validated by comparing model predictions with the existing results. Numerical calculations are performed to investigate the effects of the location of the excitation, the spacing of the stiffeners, the plate thickness, the strengthening form and the fiber orientation on the sound radiation characteristic of the orthogonaUy stiffened plate, and some practical conclusions are drawn from these parameter studies.

Selecting the Technology of Sodium Silicate Modified Poplar with the Highest Performance by Fuzzy Orthogonal Method

Sodium silicate modification can improve the overall performance of wood.The modification process has a great influence on the properties of modified wood.In this study,a new method was introduced to analyze the wood modification process,and the properties of modified wood were studied.Poplar wood was modified with sodium silicate by vacuum-pressure impregnation.After screening using single-factor experiments,an orthogonal experiment was carried out with solution concentration,impregnation time,impregnation pressure,and the cycle times as experimental factors.The modified poplar with the best properties was selected by fuzzy mathematics and characterized by SEM,FT-IR,XRD and TG.The results showed that some lignin and hemicellulose were removed from the wood due to the alkaline action of sodium silicate,and the orderly crystal area of poplar became disorderly,resulting in the reduction of crystallinity of the modified poplar wood.FT-IR analysis showed that sodium silicate was hydrolyzed to form polysilicic acid in wood,and structural analysis revealed the formation of Si-O-Si and Si-O-C,indicating that sodium silicate reacted with fibers on the wood cell wall.TG-DTG curves showed that the final residual mass of modified poplar wood increased from 25%to 67%,and the temperature of the maximum loss rate decreased from 343℃ to 276℃.The heat release and smoke release of modified poplar wood decreased obviously.This kind of material with high strength and fire resistance can be used in the outdoor building and indoor furniture.

Ultrafast photoionization of ions and molecules by orthogonally polarized intense laser pulses: Effects of the time delay

We present the photoelectron momentum distributions(PMDs) and the photoelectron angular distributions(PADs) of He+ ions, aligned H2+ molecules and N2 molecules by intense orthogonally polarized laser pulses. Simulations are performed by numerically solving the corresponding two-dimensional time-dependent Schr?dinger equations(TDSEs) within the single-electron approximation frame. Photoelectron momentum distributions and photoelectron angular distributions present different patterns with the time delays Td, illustrating the dependences of the PMDs and PADs on the time delays by orthogonally polarized laser pulses. The evolution of the electron wavepackets can be employed to describe the intensity of the PADs from the TDSE simulations for N2 molecules.

The investigation of multiple factors on elastic anisotropy of artificial shale based on the orthogonal experiment

Elastic anisotropy of shales is critical to accurate constraints for rock physical models,quantitative interpretation and hydraulic fracturing.However,the causes of elastic anisotropy of shales are very complicated,and the understanding of how multiple influence factors affect the elastic anisotropy of shales is still not clear.Hence,the orthogonal experiment,as an effective multiple factors experimental method,is adopted in this study to analyze the effect of multiple factors for shale elastic anisotropy.Three factors,clay content,organic matter(OM)content and compaction stress are selected as independent variables,the orthogonal test table L_(16)(4^(3))with four levels for each factor is adopted.According to the designed orthogonal table,sixteen artificial shales are constructed based on the cold-pressing method,and all the dry artificial shales are measured by the ultrasonic measurements.The influence of each factor on the elastic anisotropy and the sensitivity orders of three factors are obtained using the range analysis.The orders of sensitivity for selected factors follow the sequence clay content>compaction stress>OM content for velocity anisotropy parameters.The compaction mechanism of artificial shales is also discussed by the compaction factor,which are positively correlated with the velocity anisotropy parameters.The clay platelets orientation distribution function(ODF)of samples is evaluated by a theoretical model,the ODF coefficients are significantly affected by the clay content and compaction stress,and W200 are much more sensitive to these factors than W400.The results can provide a critical rock physics basis for quantitative interpretation and reservoir prediction of the low-maturity or maturity shale reservoir.

The formation of orthogonal joint systems and cuboidal blocks:New insights gained from flat-lying limestone beds in the region of Havre-Saint-Pierre(Quebec,Canada)

Vertical orthogonal joints are a common feature in shallow crustal rocks.There are several competing theories for their formation despite the ubiquity.We examined the exceptional exposures of orthogonal joints in flat-lying Ordovician limestone beds from the Havre-Saint-Pierre Region in Quebec,Canada(north shore of Saint-Lawrence River)to test conceptual models of joint formation in a natural setting.In the region,the spacing of cross-joints is consistently larger than the spacing of systematic joints by a factor of 1.5 approximately.The joint-spacing-to-bed-thickness ratios(s/t)are much larger in these beds(s/t=4.3 for systematic joints,and 6.4 for cross-joints)than those in higher strained strata along the south shore of the Saint-Lawrence River(s/t=1),highlighting the effect of tectonic strain in decreasing fracture spacing and block size.The high values of s/t indicate that cross-joint formation was unlikely caused by a switch from compression to tension once a critical s/t ratio for systematic joints was reached(as hypothesized in previous studies).We proposed a new model for the formation of orthogonal joint systems where the principal stress axes locally switch during the formation of systematic fractures.The presence of ladder-shaped orthogonal joints suggests a state of effective stress withσ_(1)^(∗)≫0>σ_(2)^(∗)>σ_(3)^(∗)and whereσ_(2)^(∗)-σ_(3)^(∗)is within the range of fracture strength variability at the time of fracture.This research provides a new mechanical model for the formation of orthogonal joint systems and cuboidal blocks.

A Spider Monkey Optimization Algorithm Combining Opposition-Based Learning and Orthogonal Experimental Design

As a new bionic algorithm,Spider Monkey Optimization(SMO)has been widely used in various complex optimization problems in recent years.However,the new space exploration power of SMO is limited and the diversity of the population in SMO is not abundant.Thus,this paper focuses on how to reconstruct SMO to improve its performance,and a novel spider monkey optimization algorithm with opposition-based learning and orthogonal experimental design(SMO^(3))is developed.A position updatingmethod based on the historical optimal domain and particle swarmfor Local Leader Phase(LLP)andGlobal Leader Phase(GLP)is presented to improve the diversity of the population of SMO.Moreover,an opposition-based learning strategy based on self-extremum is proposed to avoid suffering from premature convergence and getting stuck at locally optimal values.Also,a local worst individual elimination method based on orthogonal experimental design is used for helping the SMO algorithm eliminate the poor individuals in time.Furthermore,an extended SMO^(3)named CSMO^(3)is investigated to deal with constrained optimization problems.The proposed algorithm is applied to both unconstrained and constrained functions which include the CEC2006 benchmark set and three engineering problems.Experimental results show that the performance of the proposed algorithm is better than three well-known SMO algorithms and other evolutionary algorithms in unconstrained and constrained problems.

Generation of quasi-chirp-free isolated attosecond pulses from atoms under the action of orthogonal two-color combined pulse of fundamental frequency and higher intensity second harmonic fields

The intrinsic chirp of high-order harmonic generation is an important factor limiting the production of ultrashort attosecond pulses.Based on numerically solving the time-dependent Schrodinger equation,the generation process of highorder harmonic from the He atom under the action of orthogonal two-color combined pulse of fundamental frequency and higher intensity second harmonic fields is studied.In this paper,we propose to achieve quasi-chirp-free isolated attosecond pulses by superimposing a higher second-harmonic field on the orthogonal direction of the fundamental frequency field.It is found that the high-energy part of its harmonic emission exhibits small chirp characteristics,which can be used to synthesize isolated attosecond pulses.Through the analysis of the wave packets evolution and the classical motion trajectories of the electron,it is demonstrated that the quasi-chirp-free harmonic can be attributed to the simultaneous return of electrons ionized at different times to the parent particle.The influence of the relative phase of the two pulses on the harmonics is further analyzed,and it is observed that this phenomenon is sensitive to the relative phase,but it can still generate isolated attosecond pulses within a certain phase.