Transient responses of double-curved sandwich two-layer shells resting on Kerr's foundations with laminated three-phase polymer/GNP/fiber surface and auxetic honeycomb core subjected to the blast load

This work uses refined first-order shear theory to analyze the free vibration and transient responses of double-curved sandwich two-layer shells made of auxetic honeycomb core and laminated three-phase polymer/GNP/fiber surface subjected to the blast load.Each of the two layers that make up the double-curved shell structure is made up of an auxetic honeycomb core and two laminated sheets of three-phase polymer/GNP/fiber.The exterior is supported by a Kerr elastic foundation with three characteristics.The key innovation of the proposed theory is that the transverse shear stresses are zero at two free surfaces of each layer.In contrast to previous first-order shear deformation theories,no shear correction factor is required.Navier's exact solution was used to treat the double-curved shell problem with a single title boundary,while the finite element technique and an eight-node quadrilateral were used to address the other boundary requirements.To ensure the accuracy of these results,a thorough comparison technique is employed in conjunction with credible statements.The problem model's edge cases allow for this kind of analysis.The study's findings may be used in the post-construction evaluation of military and civil works structures for their ability to sustain explosive loads.In addition,this is also an important basis for the calculation and design of shell structures made of smart materials when subjected to shock waves or explosive loads.

A Two-Layer Encoding Learning Swarm Optimizer Based on Frequent Itemsets for Sparse Large-Scale Multi-Objective Optimization

Traditional large-scale multi-objective optimization algorithms(LSMOEAs)encounter difficulties when dealing with sparse large-scale multi-objective optimization problems(SLM-OPs)where most decision variables are zero.As a result,many algorithms use a two-layer encoding approach to optimize binary variable Mask and real variable Dec separately.Nevertheless,existing optimizers often focus on locating non-zero variable posi-tions to optimize the binary variables Mask.However,approxi-mating the sparse distribution of real Pareto optimal solutions does not necessarily mean that the objective function is optimized.In data mining,it is common to mine frequent itemsets appear-ing together in a dataset to reveal the correlation between data.Inspired by this,we propose a novel two-layer encoding learning swarm optimizer based on frequent itemsets(TELSO)to address these SLMOPs.TELSO mined the frequent terms of multiple particles with better target values to find mask combinations that can obtain better objective values for fast convergence.Experi-mental results on five real-world problems and eight benchmark sets demonstrate that TELSO outperforms existing state-of-the-art sparse large-scale multi-objective evolutionary algorithms(SLMOEAs)in terms of performance and convergence speed.

Two-layer formation-containment fault-tolerant control of fixed-wing UAV swarm for dynamic target tracking

This paper tackles the formation-containment control problem of fixed-wing unmanned aerial vehicle(UAV)swarm with model uncertainties for dynamic target tracking in three-dimensional space in the faulty case of UAVs’actuator and sensor.The fixed-wing UAV swarm under consideration is organized as a“multi-leader-multi-follower”structure,in which only several leaders can obtain the dynamic target information while others only receive the neighbors’information through the communication network.To simultaneously realize the formation,containment,and dynamic target tracking,a two-layer control framework is adopted to decouple the problem into two subproblems:reference trajectory generation and trajectory tracking.In the upper layer,a distributed finite-time estimator(DFTE)is proposed to generate each UAV’s reference trajectory in accordance with the control objective.Subsequently,a distributed composite robust fault-tolerant trajectory tracking controller is developed in the lower layer,where a novel adaptive extended super-twisting(AESTW)algorithm with a finite-time extended state observer(FTESO)is involved in solving the robust trajectory tracking control problem under model uncertainties,actuator,and sensor faults.The proposed controller simultaneously guarantees rapidness and enhances the system’s robustness with fewer chattering effects.Finally,corresponding simulations are carried out to demonstrate the effectiveness and competitiveness of the proposed two-layer fault-tolerant cooperative control scheme.

A Two-Layer Fuzzy Control Strategy for the Participation of Energy Storage Battery Systems in Grid Frequency Regulation

To address the frequency fluctuation problem caused by the power dynamic imbalance between the power system and the loadwhen a large number of newenergy sources are connected to the grid,a two-layer fuzzy control strategy is proposed for the participation of the energy storage battery system in FM.Firstly,considering the coordination of FM units responding to automatic power generation control commands,a comprehensive allocation strategy of two signals under automatic power generation control commands is proposed to give full play to the advantages of two FM signals while enabling better coordination of two FM units responding to FM commands;secondly,based on the grid FM demand and battery FM capability,a double-layer fuzzy control strategy is proposed for FM units responding to automatic power generation control commands in a coordinated manner under dual-signal allocation mode to precisely allocate the power output depth of FM units,which can control the fluctuation of frequency deviation within a smaller range at a faster speed while maintaining the battery charge state;finally,the proposed Finally,the proposed control strategy is simulated and verified inMatlab/Simulink.The results show that the proposed control strategy can control the frequency deviation within a smaller range in a shorter time,better stabilize the fluctuation of the battery charge level,and improve the utilization of the FM unit.

Characteristic analysis of scattering field in two-layer media by Green's function

The problem of three-dimensional(3D) acoustic scattering in a complex medium has aroused considerable interest of researchers for many years. An ultrasonic scattered field calculating technique is proposed to study the scattering echo from strongly scattered materials in a two-layer medium in this work. Firstly, with the high frequency stationary phase method,the Green's function of two-layer fluid media is derived. And then based on the idea of integral equation discretization,the Green's function method is extended to two-layer fluid media to derive the scattering field expression of defects in a complex medium. With this method, the scattering field of 3D defect in a two-layer medium is calculated and the characteristics of received echoes are studied. The results show that this method is able to solve the scattering P wave field of 3D defect with arbitrary shape at any scattering intensity in two-layer media. Considering the circumstance of waterimmersion ultrasonic non-destructive test(NDT), the scattering sound field characteristics of different types of defects are analyzed by simulation, which will help to optimize the detection scheme and corresponding imaging method in practice so as to improve the detection quality.

Vibration of a Two-Layer“Metal+PZT”Plate Contacting with Viscous Fluid

The present work investigates the mechanically forced vibration of the hydro-elasto-piezoelectric system consisting of a two-layer plate“elastic+PZT”,a compressible viscous fluid,and a rigid wall.It is assumed that the PZT(piezoelectric)layer of the plate is in contact with the fluid and time-harmonic linear forces act on the free surface of the elastic-metallic layer.This study is valuable because it considers for the first time the mechanical vibration of the metal+piezoelectric bilayer plate in contact with a fluid.It is also the first time that the influence of the volumetric concentration of the constituents on the vibration of the hydro-elasto-piezoelectric system is studied.Another value of the present work is the use of the exact equations and relations of elasto-electrodynamics for elastic and piezoelectric materials to describe the motion of the plate layers within the framework of the piecewise homogeneous body model and the use of the linearized Navier-Stokes equations to describe the flow of the compressible viscous fluid.The plane-strain state in the plate and the plane flow in the fluid take place.For the solution of the corresponding boundary-value problem,the Fourier transform is used with respect to the spatial coordinate on the axis along the laying direction of the plate.The analytical expressions of the Fourier transform of all the sought values of each component of the system are determined.The origins of the searched values are determined numerically,after which numerical results on the stress on the fluid and plate interface planes are presented and discussed.These results are obtained for the case where PZT-2 is chosen as the piezoelectric material,steel and aluminum as the elastic metal materials,and Glycerin as the fluid.Analysis of these results allows conclusions to be drawn about the character of the problem parameters on the frequency response of the interfacial stress.In particular,it was found that after a certain value of the vibration frequency,the presence of the metal layer in the two-layer plate led to an increase in the absolute values of the above interfacial stress.

Cooperative Caching Strategy Based on Two-Layer Caching Model for Remote Sensing Satellite Networks

In Information Centric Networking(ICN)where content is the object of exchange,in-network caching is a unique functional feature with the ability to handle data storage and distribution in remote sensing satellite networks.Setting up cache space at any node enables users to access data nearby,thus relieving the processing pressure on the servers.However,the existing caching strategies still suffer from the lack of global planning of cache contents and low utilization of cache resources due to the lack of fine-grained division of cache contents.To address the issues mentioned,a cooperative caching strategy(CSTL)for remote sensing satellite networks based on a two-layer caching model is proposed.The two-layer caching model is constructed by setting up separate cache spaces in the satellite network and the ground station.Probabilistic caching of popular contents in the region at the ground station to reduce the access delay of users.A content classification method based on hierarchical division is proposed in the satellite network,and differential probabilistic caching is employed for different levels of content.The cached content is also dynamically adjusted by analyzing the subsequent changes in the popularity of the cached content.In the two-layer caching model,ground stations and satellite networks collaboratively cache to achieve global planning of cache contents,rationalize the utilization of cache resources,and reduce the propagation delay of remote sensing data.Simulation results show that the CSTL strategy not only has a high cache hit ratio compared with other caching strategies but also effectively reduces user request delay and server load,which satisfies the timeliness requirement of remote sensing data transmission.

Penetration Depth of Torpedo Anchor in Two-Layered Cohesive Soil Bed by Free Fall

The penetration depth of torpedo anchor in two-layered soil bed was experimentally investigated. A total of 177 experimental data were obtained in laboratory by varying the undrained shear strength of the two-layered soil and the thickness of the top soil layer. The geometric parameters of the anchor and the soil properties(the liquid limit, plastic limit, specific gravity, undrained shear strength, density, and water content) were measured. Based on the energy analysis and present test data, an empirical formula to predict the penetration depth of torpedo anchor in two-layered soil bed was proposed. The proposed formula was extensively validated by laboratory and field data of previous researchers. The results were in good agreement with those obtained for two-layered and single-layered soil bed.Finally, a sensitivity analysis on the parameters in the formula was performed.

Validity ranges of interfacial wave theories in a two-layer fluid system

In the present paper, we endeavor to accomplish a diagram, which demarcates the validity ranges for interfacial wave theories in a two-layer system, to meet the needs of design in ocean engineering. On the basis of the available solutions of periodic and solitary waves, we propose a guideline as principle to identify the validity regions of the interfacial wave theories in terms of wave period T, wave height H, upper layer thickness dl, and lower layer thick-ness d2, instead of only one parameter-water depth d as in the water surface wave circumstance. The diagram proposed here happens to be Le Mehaute＇s plot for free surface waves if water depth ratio r= d1/d2 approaches to infinity and the upper layer water density p1 to zero. On the contrary, the diagram for water surface waves can be used for two-layer interfacial waves if gravity acceleration g in it is replaced by the reduced gravity defined in this study under the condition of σ=（P2 - Pl）/P2 → 1.0 and r 〉 1.0. In the end, several figures of the validity ranges for various interfacial wavetheories in the two-layer fluid are given and compared with the results for surface waves.

Diffraction of Water Waves by A Vertically Floating Cylinder in A Two-Layer Fluid

In this paper, the diffraction of water waves by a vertically floating cylinder in a two-layer fluid of a finite depth is studied. Analytical expressions for the hydrodynamic loads on the vertically floating cylinder are obtained by use of the method of eigenfunction expansions. The hydrodynamic loads on the vertically floating cylinder in a two-layer fluid inelude not only the surge, heave and pitch exciting forces due to the incident wave of the surface-wave mode, but also those due to the incident wave of the internal-wave mode. This is different from the case of a homogenous fluid. Some given examples show that, for a two-layer fluid system with a small density difference, the hydrodynamic loads for the surface-wave mode do not differ significantly from those due to surface waves in a single-layer fluid, but the hydrodynamic loads for the internal-wave mode are important over a wide range of frequencies. Moreover, also considered are the free surface and interface elevations generated by the diffraction wave due to the incident wave of the surface-wave and interhal-wave modes, and transfer of energy between modes.

A Coupled Variable Coefficient Modified KdV Equation Arising from a Two-Layer Fluid System

A quite general coupled variable coefficient modified KdV (VCmKdV) equation in a two-layer fluid systemis derived by means of the reductive perturbation method.Making use of the CK's direct method,some similarityreductions of the coupled VCmKdV equation are obtained and their corresponding group explanations are discussed.Some exact solutions of the coupled equations are also presented.

A set of Boussinesq-type equations for interfacial internal waves in two-layer stratified fluid

Many new forms of Boussinesq-type equations have been developed to extend the range of applicability of the classical Boussinesq equations to deeper water in the Study of the surface waves. One approach was used by Nwogu （1993. J. Wtrw. Port Coastal and Oc. Eng. 119, 618-638） to improve the linear dispersion characteristics of the classical Boussinesq equations by using the velocity at an arbitrary level as the velocity variable in derived equations and obtain a new form of Boussinesq-type equations, in which the dispersion property can be optimized by choosing the velocity variable at an adequate level. In this paper, a set of Boussinesq-type equations describing the motions of the interracial waves propagating alone the interface between two homogeneous incompressible and inviscid fluids of different densities with a free surface and a variable water depth were derived using a method similar to that used by Nwogu （1993. J. Wtrw. Port Coastal and Oc. Eng. 119, 618-638） for surface waves. The equations were expressed in terms of the displacements of free surface and density-interface, and the velocity vectors at arbitrary vertical locations in the upper layer and the lower layer （or depth-averaged velocity vector across each layer） of a two-layer fluid. As expected, the equations derived in the present work include as special cases those obtained by Nwogu （1993, J. Wtrw. Port Coastal and Oc. Eng. 119, 618-638） and Peregrine （1967, J. Fluid Mech. 27, 815-827） for surface waves when the density of the upper fluid is taken as zero.

Hydroelastic Response of A Circular Plate in Waves on A Two-Layer Fluid of Finite Depth

The hydroelastic response of a circular, very large floating structure(VLFS), idealized as a floating circular elastic thin plate, is investigated for the case of time-harmonic incident waves of the surface and interfacial wave modes, of a given wave frequency, on a two-layer fluid of finite and constant depth. In linear potential-flow theory, with the aid of angular eigenfunction expansions, the diffraction potentials can be expressed by the Bessel functions. A system of simultaneous equations is derived by matching the velocity and the pressure between the open-water and the platecovered regions, while incorporating the edge conditions of the plate. Then the complex nested series are simplified by utilizing the orthogonality of the vertical eigenfunctions in the open-water region. Numerical computations are presented to investigate the effects of different physical quantities, such as the thickness of the plate, Young’s modulus, the ratios of the densities and of the layer depths, on the dispersion relations of the flexural-gravity waves for the two-layer fluid. Rapid convergence of the method is observed, but is slower at higher wave frequency. At high frequency, it is found that there is some energy transferred from the interfacial mode to the surface mode.

Second-order random interfacial wave solutions for two-layer fluid with a free surface

A previous study （Song. 2004. Geophys Res Lett, 31 （15）：L15302） of the second-order solutions for random interracial waves is extended in a constant depth, two-layer fluid system with a rigid lid is extended into a more general case of two-layer fluid with a top free surface. The rigid boundary condition on the upper surface is replaced by the kinematical and dynamical boundary conditions of a free surface, and the equations describing the random displacements of free surface, density-interface and the associated velocity potentials in the two-layer fluid are solved to the second order using the same expansion technology as that of Song （2004. Geophys Res Lett, 31 （15）：L15302）. The results show that the interface and the surface will oscillate synchronously, and the wave fields to the first-order both at the free surface and at the density-interface are made up of a linear superposition of many waves with different amplitudes, wave numbers and frequencies. The second-order solutions describe the second-order wave-wave interactions of the surface wave components, the interface wave components and among the surface and the interface wave components. The extended solutions also include special cases obtained by Thorpe for progressive interracial waves （Thorpe. 1968a.Trans R Soc London, 263A：563～614） and standing interracial waves （Thorpe. 1968b. J Fluid Mech, 32：489-528） for the two-layer fluid with a top free surface. Moreover, the solutions reduce to those derived for random surface waves by Sharma and Dean （1979.Ocean Engineering Rep 20） if the density of the upper layer is much smaller than that of the lower layer.

RAYLEIGH-MARANGONI-BENARD INSTABILITY IN TWO-LAYER FLUID SYSTEM

Rayleigh-Marangoni-Bénard instability in a system of two-layer fluids is studied nu- merically.The convective instabilities in the system of Silicon Oil(10cSt)and Fluorinert(FC70)liquids have been analyzed.The critical parameters at onset of convection are presented in a large range of two-layer depth ratios from 0.2 to 5.0.Numerical results show that the instability of the two-layer system depends strongly on its depth ratio.When the depth ratio increases,the instability mode changes from mechanical coupling to thermal coupling.Between these two typical coupling modes, a time-dependent oscillation is detected.Nevertheless,traveling wave states are found in the case of oscillatory instability.The oscillation mode results from the competition between Rayleigh instability and Marangoni effect.

Green Functions with Pulsating Sources in A Two-Layer Fluid of Finite Depth

The derivation of Green function in a two-layer fluid model has been treated in different ways. In a two-layer fluid with the upper layer having a free surface, there exist two modes of waves propagating due to the free surface and the interface. This paper is concerned with the derivation of Green functions in the three dimensional case of a stationary source oscillating. The source point is located either in the upper or lower part of a two-layer fluid of finite depth. The derivation is carried out by the method of singularities. This method has an advantage in that it involves representing the potential as a sum of singularities or multipoles placed within any structures being present. Furthermore, experience shows that the systems of equations resulted from using a singularity method possess excellent convergence characteristics and only a few equations are needed to obtain accurate numerical results. Validation is done by showing that the derived two-layer Green function can be reduced to that of a single layer of finite depth or that the upper Green function coincides with that of the lower, for each case. The effect of the density on the internal waves is demonstrated. Also, it is shown how the surface and internal wave amplitudes are compared for both the wave modes. The fluid in this case is considered to be inviscid and incompressible and the flow is irrotational.

Asymptotic solution of a weak nonlinear model for the mid-latitude stationary wind field of a two-layer barotropic ocean

A weak nonlinear model of a two-layer barotropic ocean with Rayleigh dissipation is built.The analytic asymptotic solution is derived in the mid-latitude stationary wind field,and the physical meaning of the corresponding problem is discussed.

Effect of the Coefficient on the Performance of A Two-Layer Boussinesq- Type Model

The coefficients embodied in a Boussinesq-type model are very important since they are determined to optimize the linear and nonlinear properties.In most conventional Boussinesq-type models,these coefficients are assigned the specific values.As for the multi-layer Boussinesq-type models with the inclusion of the vertical velocity,however,the effect of the different values of these coefficients on linear and nonlinear performances has never been investigated yet.The present study focuses on a two-layer Boussinesq-type model with the highest spatial derivatives being 2 and theoretically and numerically examines the effect of the coefficient on model performance.Theoretical analysis show that different values for(0.13≤α≤0.25)do not have great effects on the high accuracy of the linear shoaling,linear phase celerity and even third-order nonlinearity for water depth range of 0<kh≤10(k is wave number and h is water depth).The corresponding errors using different values are restricted within 0.1%,0.1%and 1%for the linear shoaling amplitude,dispersion and nonlinear harmonics,respectively.Numerical tests including regular wave shoaling over mildly varying slope from deep to shallow water,regular wave propagation over submerged bar,bichromatic wave group and focusing wave propagation over deep water are conducted.The comparison between numerical results using different values of,experimental data and analytical solutions confirm the theoretical analysis.The flexibility and consistency of the two-layer Boussinesq-type model is therefore demonstrated theoretically and numerically.

Crustal thickness beneath the Tanlu fault zone and its tectonic significance based on two-layer H-κstacking

Tanlu fault zone(TLFZ)is the largest active fault zone in eastern China.It is characterized by complex tectonic evolution and multiple faults and marks the boundary between the North and South China blocks.An indepth understanding of the distinct crustal structures of both parts of the TLFZ will provide valuable insights into the lithospheric and crustal thinning in eastern China,extensive magmatism since the Mesozoic,and formation mechanisms of metallogenic belts along the Yangtze River.In this study,a two-layer H-κstacking approach was adopted to estimate the thicknesses of the sediment and crystalline crust as well as the corresponding vP/vS ratios based on high-quality teleseismic P-wave receiver functions recorded by permanent and temporary stations in and around the TLFZ.The geological units in the study region were delineated,especially the crustal structures beneath extensive sedimentary basins on both sides of the TLFZ.The following conclusions can be drawn:(1)The crustal thickness in and around the TLFZ greatly varies depending on the segment.In the northern segment,the crust is relatively thin beneath the eastern part of the Songliao Basin,a broad uplift of the Moho can be observed,and the Moho descends from south to north.The crust below the central and southern segments becomes thinner from west to east.The thickness of the crust is less than 30 km toward the eastern side of the boundary between the Jiangsu and Anhui provinces,that is,significantly thinner than in other areas.In terms of the vP/vS ratios,high anomalies were detected in the central-southern segments of the TLFZ,indicating the upwelling of deep mantle magma via deep faults.(2)Positive isostatic gravity anomalies were observed in the eastern part of the northern segment of the TLFZ and in the eastern part of the Suwan segment.The crustal thickness is smaller than that obtained from the Airy model of isostasy.This suggests that the lower crust in this area may have experienced intensive transformation processes,which may be related to crustal thinning(caused by crustal extension)and the strong uplift of the mantle in eastern China.The isostatic gravity anomalies between the eastern and western parts of the TLFZ indicate that the fault zone plays a dominant role in controlling the development of the deep crustal structure.(3)Significant crustal thinning was observed beneath the eastern part of the boundary between the Jiangsu and Anhui provinces in the southern segment of the TLFZ,suggesting that this area is prone to lithospheric thinning of the North China Craton.Due to the subduction,compression,and retreat of the Paleo-Pacific Plate during the Yanshanian Period as well as the dehydration of subducting oceanic crust(within subduction zones),the asthenosphere and oceanic crust in eastern China partially melted,resulting in mantle enrichment.The basic magma from the mantle is accumulated at the base of the crust,leading to magmatic underplating.In areas with weak topography toward the east of the TLFZ,magma rises to the upper crust and surface,resulting in the enrichment of multiple metal deposits in this area.

Influence of the earth rotation on the interfacial wave solutions and wave-induced tangential stress in a two-layer fluid system

Interfacial waves and wave-induced tangential stress are studied for geostrophic small amplitude waves of two-layer fluid with a top free surface and a fiat bottom. The solutions were deduced from the general form of linear fluid dynamic equations of two-layer fluid under the f-plane approximation, and wave-induced tangential stress were estimated based on the solutions obtained. As expected, the solutions derived from the present work include as special cases those obtained by Sun et al. （2004. Science in China, Ser. D, 47（12）： 1147-1154） for geostrophic small amplitude surface wave solutions and wave-induced tangential stress if the density of the upper layer is much smaller than that of the lower layer. The results show that the interface and the surface will oscillate synchronously, and the influence of the earth＇s rotation both on the surface wave solutions and the interfacial wave solutions should be considered.