Modeling and analysis of an inextensible beam with inertial and geometric nonlinearities

The present study focuses on an inextensible beam and its relevant inertia nonlinearity,which are essentially distinct from the commonly treated extensible beam that is dominated by the geometric nonlinearity.Explicitly,by considering a weakly constrained or free end(in the longitudinal direction),the inextensibility assumption and inertial nonlinearity(with and without an initial curvature)are introduced.For a straight beam,a multi-scale analysis of hardening/softening dynamics reveals the effects of the end stiffness/mass.Extending the straight scenario,a refined inextensible curved beam model is further proposed,accounting for both its inertial nonlinearity and geometric nonlinearity induced by the initial curvature.The numerical results for the frequency responses are also presented to illustrate the dynamic effects of the initial curvature and axial constraint,i.e.,the end mass and end stiffness.

Superior Mechanical Behavior and Flame Retardancy FRP via a Distribution Controllable 1D/2D Hybrid Nanoclay Synergistic Toughening Strategy

The incorporation of commercial flame retardants into fiber-reinforced polymer(FRP)composites has been proposed as a potential solution to improve the latter’s poor flame resistance.However,this approach often poses a challenge,as it can adversely affect the mechanical properties of the FRP.Thus,balancing the need for improved flame resistance with the preservation of mechanical integrity remains a complex issue in FRP research.Addressing this critical concern,this study introduces a novel additive system featuring a combination of one-dimensional(1D)hollow tubular structured halloysite nanotubes(HNTs)and two-dimensional(2D)polygonal flake-shaped nano kaolinite(NKN).By employing a 1D/2D hybrid kaolinite nanoclay system,this research aims to simultaneously improve the flame retardancy and mechanical properties.This innovative approach offers several advantages.During combustion and pyrolysis processes,the 1D/2D hybrid kaolinite nanoclay system proves effective in reducing heat release and volatile leaching.Furthermore,the system facilitates the formation of reinforcing skeletons through a crosslinking mechanism during pyrolysis,resulting in the development of a compact char layer.This char layer acts as a protective barrier,enhancing the material’s resistance to heat and flames.In terms of mechanical properties,the multilayered polygonal flake-shaped 2D NKN plays a crucial role by impeding the formation of cracks that typically arise from vulnerable areas,such as adhesive phase particles.Simultaneously,the 1D HNT bridges these cracks within the matrix,ensuring the structural integrity of the composite material.In an optimal scenario,the homogeneously distributed 1D/2D hybrid kaolinite nanoclays exhibit remarkable results,with a 51.0%improvement in mode II fracture toughness(GIIC),indicating increased resistance to crack propagation.In addition,there is a 34.5%reduction in total heat release,signifying improved flame retardancy.This study represents a significant step forward in the field of composite materials.The innovative use of hybrid low-dimensional nanomaterials offers a promising avenue for the development of multifunctional composites.By carefully designing and incorporating these nanoclays,researchers can potentially create a new generation of FRP composites that excel in both flame resistance and mechanical strength.

Flow and sound fields of scaled high-speed trains with different coach numbers running in long tunnel

Segregated incompressible large eddy simulation and acoustic perturbation equations were used to obtain the flow field and sound field of 1:25 scale trains with three,six and eight coaches in a long tunnel,and the aerodynamic results were verified by wind tunnel test with the same scale two-coach train model.Time-averaged drag coefficients of the head coach of three trains are similar,but at the tail coach of the multi-group trains it is much larger than that of the three-coach train.The eight-coach train presents the largest increment from the head coach to the tail coach in the standard deviation(STD)of aerodynamic force coefficients:0.0110 for drag coefficient(Cd),0.0198 for lift coefficient(Cl)and 0.0371 for side coef-ficient(Cs).Total sound pressure level at the bottom of multi-group trains presents a significant streamwise increase,which is different from the three-coach train.Tunnel walls affect the acoustic distribution at the bottom,only after the coach number reaches a certain value,and the streamwise increase in the sound pressure fluctuation of multi-group trains is strengthened by coach number.Fourier transform of the turbulent and sound pressures presents that coach number has little influence on the peak frequencies,but increases the sound pressure level values at the tail bogie cavities.Furthermore,different from the turbulent pressure,the first two sound pressure proper orthogonal decomposition(POD)modes in the bogie cavities contain 90%of the total energy,and the spatial distributions indicate that the acoustic distributions in the head and tail bogies are not related to coach number.

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.

Characterization of residual stresses and microstructural features in an Inconel 718 forged compressor disc

Residual stress plays an important part in fabricating commercial aero engine Inconel 718 components for their fatigue properties, reliability and durability. Due to the limitation of Chinese neutron diffraction instrument and lack of test practice and specifications, there is little systematic research on the residual stress of forged compressor disc. X-ray diffraction and neutron diffraction methods were used to measure the residual stress of Inconel 718 forged discs at the surface and in the interior, respectively. Scanning electron microscope and transmission electron microscope were used to characterize the microstructural features. The residual stress state at the disc is in near-surface compression, balanced by tension within the disc core. However, the surface residual stress of disc depends more on the rough machining than on the forging process. Also, the dislocation densities increase with decreasing distance to the surfaces of disc, and the residual stress accelerates dislocation generation and dynamic recrystallization.

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.

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.

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.

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.

Suppression of thermal postbuckling and nonlinear panel flutter motions of variable stiffness composite laminates using piezoelectric actuators

Variable stiffness composite laminates(VSCLs)are promising in aerospace engineering due to their designable material properties through changing fiber angles and stacking sequences.Aiming to control the thermal postbuckling and nonlinear panel flutter motions of VSCLs,a full-order numerical model is developed based on the linear quadratic regulator(LQR)algorithm in control theory,the classical laminate plate theory(CLPT)considering von Kármán geometrical nonlinearity,and the first-order Piston theory.The critical buckling temperature and the critical aerodynamic pressure of VSCLs are parametrically investigated.The location and shape of piezoelectric actuators for optimal control of the dynamic responses of VSCLs are determined through comparing the norms of feedback control gain(NFCG).Numerical simulations show that the temperature field has a great effect on aeroelastic tailoring of VSCLs;the curvilinear fiber path of VSCLs can significantly affect the optimal location and shape of piezoelectric actuator for flutter suppression;the unstable panel flutter and the thermal postbuckling deflection can be suppressed effectively through optimal design of piezoelectric patches.

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.

Effective electromechanical properties of cellular piezoelectret:A review

Due to the large quasi-piezoelectric d33 coefficient in the film thickness direction, cellular piezoelectret has emerged as a new kind of compliant electromechanical transducer materials. The macroscopic piezoelectric effect of cellular piezoelectret is closely related to the void microstructures as well as the material constants of host polymer. Complex void microstmctures are usually encountered in the optimum design of cellular piezoelectret polymer film with ad- vanced piezoelectric properties. Analysis of the effective electromechanical properties is generally needed. This article presents an overview of the recent progress on theoretical models and numerical simulation for the effective electromechanical properties of cellular piezoelectret. Emphasis is placed on our own works of cellular piezoelectret published in past several years.

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.

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.

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.

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.