Theoretical study on dynamic effective electroelastic properties of random piezoelectric composites with aligned inhomogeneities

The closed-form solutions of the dynamic problem of heterogeneous piezoelectric materials are formulated by introducing polarizations into a reference medium and using the generalized reciprocity theorem.These solutions can be reduced to the ones of an elastodynamic problem.Based on the effective medium method,these closedform solutions can be used to establish the self-consistent equations about the frequencydependent effective parameters,which can be numerically solved by iteration.Theoretical predictions are compared with the experimental results,and good agreement can be found.Furthermore,the analyses on the effects of microstructure and wavelength on the effective properties,resonance frequencies,and attenuation are also presented,which may provide some guidance for the microstructure design and analysis of piezoelectric composites.

Effects of time-delayed vibration absorber on bandwidth of beam for low broadband vibration suppression

The effects of time-delayed vibration absorber(TDVA) on the dynamic characteristics of a flexible beam are investigated. First, the vibration suppression effect of a single TDVA on a continuous beam is studied. The first optimization criterion is given,and the results show that the introduction of time-delayed feedback control(TDFC) is beneficial to improving the vibration suppression at the anti-resonance band. When a single TDVA is used, the anti-resonance is located at a specific frequency by the optimum design of TDFC parameters. Then, in order to obtain low-frequency and broad bands for vibration suppression, multiple TDVAs are uniformly distributed on a continuous beam,and the relationship between the dynamic responses and the TDFC parameters is investigated. The obtained relationship shows that the TDVA has a significant regulatory effect on the vibration behavior of the continuous beam. The effects of the number of TDVAs and the nonlinearity on the bandgap variation are discussed. As the multiple TDVAs are applied, according to the different requirements on the location and bandwidth of the effective vibration suppression band, the optimization criteria for the TDFC parameters are given, which provides guidance for the applications of TDVAs in practical projects such as bridge and aerospace.

Paradoxical roles of inhibitory autapse and excitatory synapse in formation of counterintuitive anticipated synchronization

Different from the common delayed synchronization(DS)in which response appears after stimulation,anticipated synchronization(AS)in unidirectionally coupled neurons denotes a counterintuitive phenomenon in which response of the receiver neuron appears before stimulation of the sender neuron,showing an interesting function of brain to anticipate the future.The dynamical mechanism for the AS remains unclear due to complex dynamics of inhibitory and excitatory modulations.In this article,the paradoxical roles of excitatory synapse and inhibitory autapse in the formation of AS are acquired.Firstly,in addition to the common roles such that inhibitory modulation delays and excitatory modulation advances spike,paradoxical roles of excitatory stimulation to delay spike via type-II phase response and of inhibitory autapse to advance spike are obtained in suitable parameter regions,extending the dynamics and functions of the excitatory and inhibitory modulations.Secondly,AS is related to the paradoxical roles of the excitatory and inhibitory modulations,presenting deep understandings to the AS.Inhibitory autapse induces spike of the receiver neuron advanced to appear before that of the sender neuron at first,and then excitatory synapse plays a delay role to prevent the spike further advanced,resulting in the AS as the advance and delay effects realize a dynamic balance.Lastly,inhibitory autapse with strong advance,middle advance,and weak advance and delay effects induce phase drift(spike of the receiver neuron advances continuously),AS,and DS,respectively,presenting comprehensive relationships between AS and other behaviors.The results present potential measures to modulate AS related to brain function.

Investigations on High-Speed Flash Boiling Atomization of Fuel Based on Numerical Simulations

Flash boiling atomization(FBA)is a promising approach for enhancing spray atomization,which can generate a fine and more evenly distributed spray by increasing the fuel injection temperature or reducing the ambient pressure.However,when the outlet speed of the nozzle exceeds 400 m/s,investigating high-speed flash boiling atomization(HFBA)becomes quite challenging.This difficulty arises fromthe involvement ofmany complex physical processes and the requirement for a very fine mesh in numerical simulations.In this study,an HFBA model for gasoline direct injection(GDI)is established.This model incorporates primary and secondary atomization,as well as vaporization and boilingmodels,to describe the development process of the flash boiling spray.Compared to lowspeed FBA,these physical processes significantly impact HFBA.In this model,the Eulerian description is utilized for modeling the gas,and the Lagrangian description is applied to model the droplets,which effectively captures the movement of the droplets and avoids excessive mesh in the Eulerian coordinates.Under various conditions,numerical solutions of the Sauter mean diameter(SMD)for GDI show good agreement with experimental data,validating the proposed model’s performance.Simulations based on this HFBA model investigate the influences of fuel injection temperature and ambient pressure on the atomization process.Numerical analyses of the velocity field,temperature field,vapor mass fraction distribution,particle size distribution,and spray penetration length under different superheat degrees reveal that high injection temperature or low ambient pressure significantly affects the formation of small and dispersed droplet distribution.This effect is conducive to the refinement of spray particles and enhances atomization.

Frictional contact analysis of a rigid solid with periodic surface sliding on the thermoelectric material

Understanding and characterizing rough contact and wavy surfaces are essential for developing effective strategies to mitigate wear,optimize lubrication,and enhance the overall performance and durability of mechanical systems.The sliding friction contact problem between a thermoelectric(TE)half-plane and a rigid solid with a periodic wavy surface is the focus of this investigation.To simplify the problem,we utilize mixed boundary conditions,leading to a set of singular integral equations(SIEs)with the Hilbert kernels.The analytical solutions for the energy flux and electric current density are obtained by the variable transform method in the context of the electric and temperature field.The contact problem for the elastic field is transformed into the second-kind SIE and solved by the Jacobi polynomials.Notably,the smoothness of the wavy contact surface ensures that there are no singularities in the surface contact stress,and ensures that it remains free at the contact edge.Based on the plane strain theory of elasticity,the analysis primarily examines the correlation between the applied load and the effective contact area.The distribution of the normal stress on the surface with or without TE loads is discussed in detail for various friction coefficients.Furthermore,the obtained results indicate that the in-plane stress decreases behind the trailing edge,while it increases ahead of the trailing edge when subjected to TE loads.

Finite element simulation of elastoplastic fieldnear crack tips and results for a central crackedplate of le-lhp material under tension

The elastoplastic field near crack tips is investigated through finite element simulation.A refined mesh model near the crack tip is proposed. In the mesh refining area, element size continuously varies from the nanometer scale to themicrometer scale and the millimeter scale. Graphics of the plastic zone, the crack tip blunting, and the deformed crack tip elements are given in the paper.Based on the curves of stress and plastic strain, closely near the crack tip, the stresssingularity index and the stress intensity factor,as well as the plastic strain singularity index and the plastic strain intensity factor are determined.Thestress and plastic strainsingular index vary with the load, while the dimensions of the stress and the plastic strain intensity factorsdependon the stress and the plastic strain singularity index, respectively. The singular field near the elastoplastic crack tip is characterized by the stress singularity index and the stress intensity factor, or alternativelythe plastic strain singularity index and the plastic strain intensityfactor.At the end of the paper, following Irwin’s concept of fracture mechanics,σδKσδKcriterion andεδQεδQcriterion are proposed.Besides, crack tip angle criterion is also presented.

AXISYMMETRIC BENDING OF TWO-DIRECTIONAL FUNCTIONALLY GRADED CIRCULAR AND ANNULAR PLATES

Assuming the material properties varying with an exponential law both in the thick- ness and radial directions, axisymmetric bending of two-directional functionally graded circular and annular plates is studied using the semi-analytical numerical method in this paper. The deflections and stresses of the plates are presented. Numerical results show the well accuracy and convergence of the method. Compared with the finite element method, the semi-analytical nu- merical method is with great advantage in the computational efficiency. Moreover, study on ax- isymmetric bending of two-directional functionally graded annular plate shows that such plates have better performance than those made of isotropic homogeneous materials or one-directional functionally graded materials. Two-directional functionally graded material is a potential alternative to the one-directional functionally graded material. And the integrated design of materials and structures can really be achieved in two-directional functionally graded materials.

Preparation and properties of short natural fiber reinforced poly(lactic acid) composites

The natural fiber/poly(lactic acid) (PLA) composites were prepared with ramie and jute short fiber as reinforcement and PLA as matrix. The mechanical and thermal properties of the composites were investigated. The results show that the properties of the composites are better than those of plain PLA. When the content of the fiber is 30%, the composites can get the best mechanical properties. The dynamic mechanical analysis results show that the storage moduli of the PLA/ramie and PLA/jute composites increase with respect to the plain PLA. The Vicat softening temperature of the composites is greatly higher than that of PLA. The results of thermogravimetric analysis show that adding fiber to the PLA matrix can improve the degradation temperature of PLA.

Deformation mode and energy absorption of polycrystal-inspired square-cell lattice structures

Lattice structures are widely used in many engineering fields due to their excellent mechanical properties such as high specific strength and high specific energy absorption(SEA)capacity.In this paper,square-cell lattice structures with different lattice orientations are investigated in terms of the deformation modes and the energy absorption(EA)performance.Finite element(FE)simulations of in-plane compression are carried out,and the theoretical models from the energy balance principle are developed for calculating the EA of these lattice structures.Satisfactory agreement is achieved between the FE simulation results and the theoretical results.It indicates that the 30◦oriented lattice has the largest EA capacity.Furthermore,inspired by the polycrystal microstructure of metals,novel structures of bi-crystal lattices and quad-crystal lattices are developed through combining multiple singly oriented lattices together.The results of FE simulations of compression indicate that the EA performances of symmetric lattice bi-crystals and quad-crystals are better than those of the identical lattice polycrystal counterparts.This work confirms the feasibility of designing superior energy absorbers with architected meso-structures from the inspiration of metallurgical concepts and microstructures.

FORMULATION AND EVALUATION OF AN ANALYTICAL STUDY FOR CYLINDRICAL HELICAL SPRINGS

The free vibration analysis of cylindrical helical springs is carried out by means of an analytical study. In the governing equations of the motion of the springs, all displacement functions are defined at the centroid axis and also the effects of the rotational inertia, axial and shear deformations are included in the proposed model. Explicit analytical expressions which give the vibrating mode shapes are derived by rigorous application of the symbolic computing package MATHEMATICA and a process of searching is used to determine the exact natural frequencies. Numerical examples are provided for fixed-fixed boundary conditions. The free vibrational pa- rameters are chosen as the number of coils （n = 4- 14）, the helix pitch angle （a = 5 - 30°） and as the ratio of the diameters of the cylinder and the wire （D/d = 4 - 18） in a wide range. Validation of the proposed model has been achieved through comparison with a finite element model using two-node standard beam elements and the results available in published literature, which in these cases indicates a very good correlation.

Band gap analysis of periodic structures based on cell experimental frequency response functions(FRFs)

An approach is proposed to estimate the transfer function of the periodic structure, which is known as an absorber due to its repetitive cells leading to the band gap phenomenon. The band gap is a frequency range in which vibration will be inhibited. A transfer function is usually performed to gain band gap. Previous scholars regard estimation of the transfer function as a forward problem assuming known cell mass and stiffness matrices. However, the estimation of band gap for irregular or complicated cells is hardly accurate because it is difficult to model the cell exactly. Therefore, we treat the estimation as an inverse problem by employing modal identification and curve fitting. A transfer matrix is then established by parameters identitled through modal analysis. Both simulations and experiments have been performed. Some interesting conclusions about the relationship between modal parameters and band gap have been achieved.

Suppression of oscillatory congestion via trunk link bandwidth and control gain in star network

The time delay-induced instability in an Internet congestion control model is investigated. The star topology is considered, and the link bandwidth ratio and the control gain are selected as the tunable parameters for congestion suppression. The stability switch boundary is obtained by the eigenvalue analysis for the linearized system around the equilibrium. To investigate the oscillatory congestion when the equilibrium becomes unstable, the center manifold reduction and the normal form theory are used to study the periodic oscillation induced by the delay. The theoretical analysis and numerical simulation show that the ratio between bandwidths of the trunk link and the regular link,rather than these bandwidths themselves, is crucial for the stability of the congestion control system. The present results demonstrate that it is not always effective to increase the link bandwidth ratio for stabilizing the system, and for some certain delays, adjusting the control gain is more efficient.

Stability and Hopf bifurcation of a delayed ratio-dependent predator-prey system

Since the ratio-dependent theory reflects the fact that predators must share and compete for food, it is suitable for describing the relationship between predators and their preys and has recently become a very important theory put forward by biologists. In order to investigate the dynamical relationship between predators and their preys, a so-called Michaelis-Menten ratio-dependent predator-prey model is studied in this paper with gestation time delays of predators and preys taken into consideration. The stability of the positive equilibrium is investigated by the Nyquist criteria, and the existence of the local Hopf bifurcation is analyzed by employing the theory of Hopf bifurcation. By means of the center manifold and the normal form theories, explicit formulae are derived to determine the stability, direction and other properties of bifurcating periodic solutions. The above theoretical results are validated by numerical simulations with the help of dynamical software WinPP. The results show that if both the gestation delays are small enough, their sizes will keep stable in the long run, but if the gestation delays of predators are big enough, their sizes will periodically fluc-tuate in the long term. In order to reveal the effects of time delays on the ratio-dependent predator-prey model, a ratiodependent predator-prey model without time delays is considered. By Hurwitz criteria, the local stability of positive equilibrium of this model is investigated. The conditions under which the positive equilibrium is locally asymptotically stable are obtained. By comparing the results with those of the model with time delays, it shows that the dynamical behaviors of ratio-dependent predator-prey model with time delays are more complicated. Under the same conditions, namely, with the same parameters, the stability of positive equilibrium of ratio-dependent predator-prey model would change due to the introduction of gestation time delays for predators and preys. Moreover, with the variation of time delays, the positive equilibrium of the ratio-dependent predator-prey model subjects to Hopf bifurcation.

Dynamic quasi-continuum model for plate-type nano-materials and analysis of fundamental frequency

A dynamic quasi-continuum model is presented to analyze free vibration of plate-type cubic crystal nano-materials.According to the Hamilton principle,fundamental governing equations in terms of displacement components and angles of rotations are given.As an application of the model,the cylindrical bending deformation of the structure fixed at two ends is analyzed,and a theoretical formula evaluating the fundamental frequency is obtained by using Galerkin's method.Meanwhile,the solution for the classical continuous plate model is also derived,and the size-dependent elastic modulus and Poisson's ratio are taken in computation.The frequencies corresponding to different atomic layers are numerically presented for the plate-type NaC l nano-materials.Furthermore,a molecular dynamics(MD)simulation is conducted with the code LAMMPS.The comparison shows that the present quasi-continuum model is valid,and it may be used as an alternative model,which reflects scale effects in analyzing dynamic behaviors of such plate-type nano-materials.

3D analysis of functionally graded material plates with complex shapes and various holes

In this paper, the basic formulae for the semi-analytical graded FEM on FGM members are derived. Since FGM parameters vary along three space coordinates, the parameters can be integrated in mechanical equations. Therefore with the parameters of a given FGM plate, problems of FGM plate under various conditions can be solved. The approach uses 1D discretization to obtain 3D solutions, which is proven to be an effective numerical method for the mechanical analyses of FGM structures. Examples of FGM plates with complex shapes and various holes are presented.

A novel design scheme for acoustic cloaking of complex shape based on region partitioning and multi-origin coordinate transformation

Acoustic cloaking is an important application of acoustic metamaterials.This article proposes a novel design scheme for acoustic cloaking based on the region partitioning and multi-origin coordinate transformation.The cloaked region is partitioned into multiple narrow strips.For each strip,a local coordinate system is established with the local origin located at the strip center,and a coordinate transformation in the local coordinate system is conducted to squeeze the material along the strip length direction to form the cloaked region.To facilitate the implementation of the acoustic cloak,the multilayer effective medium is used to approximate the non-uniform anisotropic material parameters.The effectiveness of the proposed coordinate transformation method is verified by comparing the results from our method with those in the literature.Firstly,the results of a circular acoustic cloak in the literature are reproduced by using our finite element(FE)simulations for validation.Then,a comparison is made between the traditional coordinate transformation scheme and our new scheme for simulating an elliptical acoustic cloak.The results indicate that the proposed multi-origin coordinate transformation method has a better cloaking effect on the incident wave along the ellipse minor axis direction than the traditional method.This means that for the same object,an appropriate transformation scheme can be selected for different incident wave directions to achieve the optimal control effect.The validated scheme is further used to design an arch-shaped cloak composed of an upper semicircular area and a lower rectangular area,by combining the traditional single-centered coordinate transformation method for the semicircular area and the proposed multi-origin method for the rectangular area.The results show that the designed cloak can effectively control the wave propagation with significantly reduced acoustic pressure level.This work provides a flexible acoustic cloak design method applicable for arbitrary shapes and different wave incident directions,enriching the theory of acoustic cloaking based on coordinate transformation.

Dynamics of cantilever plates and its hybrid vibration control

Applying Lagrange-Germain＇s theory of elas- tic thin plates and Hamiltonian formulation, the dynamics of cantilever plates and the problem of its vibration control are studied, and a general solution is finally given. Based on Hamiltonian and Lagrangian density function, we can obtain the flexural wave equation of the plate and the relationship between the transverse and the longitudinal eigenvalues. Based on eigenfunction expansion, dispersion equations of propagation mode of cantilever plates are deduced. By satisfying the boundary conditions of cantilever plates, the natural frequencies of the cantilever plate structure can be given. Then, analytic solution of the problem in plate structure is obtained. An hybrid wave/mode control approach, which is based on both independent modal space control and wave control methods, is described and adopted to analyze the active vibration control of cantilever plates. The low-order （controlled by modal control） and the high-order （controlled by wave control） frequency response of plates are both improved. The control spillover is avoided and the robustness of the system is also improved. Finally, simulation results are analyzed and discussed.

Modeling of micropipette aspiration and optical tweezers stretching of erythrocytes with or without Malaria parasite

The erythrocytes play an important role in the human body. The healthy erythrocytes can undergo extremely large deformation while passing through small capillaries. Their infection by Malaria Plasmodium falcipurum （P.f.） will lead to capillary blockage and blood flow obstruction. Many experimental and computational methods have been applied to study the increase in stickiness and decrease in deformability of the Malaria （P.f.） infected erythrocytes. The novelty of this paper lies in the establishment of an multi-component model for investigating mechanical properties of Malaria （P.f.） infected erythrocytes, especially of their enclosed parasites. Finite element method was applied to simulate the erythrocytes＇ deformation in micropipette aspiration and optical tweezers stretching using the computational software ABAQUS. The comparisons between simulations and experiments were able to quantitatively conclude the effects of stiffness and stickiness of the parasitophorous vacuole membrane on the cells＇ deformation, which could not be obtained from experiments directly.

Negative self-feedback induced enhancement and transition of spiking activity for class-3 excitability

Post-inhibitory rebound(PIR)spike,which has been widely observed in diverse nervous systems with different physiological functions and simulated in theoretical models with class-2 excitability,presents a counterintuitive nonlinear phenomenon in that the inhibitory effect can facilitate neural firing behavior.In this study,a PIR spike induced by inhibitory stimulation from the resting state corresponding to class-3 excitability that is not related to bifurcation is simulated in the Morris–Lecar neuron.Additionally,the inhibitory self-feedback mediated by an autapse with time delay can evoke tonic/repetitive spiking from phasic/transient spiking.The dynamical mechanism for the PIR spike and the tonic/repetitive spiking is acquired with the phase plane analysis and the shape of the quasi-separatrix curve.The result extends the counterintuitive phenomenon induced by inhibition to class-3 excitability,which presents a potential function of inhibitory autapse and class-3 neuron in many neuronal systems such as the auditory system.

Partial wetting of the soft elastic graded substrate due to elastocapillary deformation

Surface tension plays a central role in the mechanical behavior of soft materials such as gels.Elastocapillary deformation of elastic graded substrates is ubiquitous in soft materials.In this work,the effect of a partially wetting sessile liquid droplet on the elastocapillary deformation of a soft elastic graded substrate is studied.The modulus is assumed to have an exponential form along the thickness direction.By applying the Fourier transformation,a mixed boundary-value problem is reduced into a dual integral equation.The numerical results show that the surface displacement is strongly affected by the inhomogeneity of the material.The study of the wetting properties of gel substrates is essential for both understanding the wetting phenomena of gels and developing gels for applications as soft actuators and sensors that can be used in wearable electronics and soft robotics.