Porous panels with fixed ends lose stability by divergence

The aeroelastic stability of one-dimensional porous panels with a Darcy boundary condition on its surface is examined theoretically. Analytical and numerical analyses demonstrate that a porous panel in a uniform, single-sided, incompressible flow becomes aeroelastically unstable via divergence. This primary route of instability is identical to the well-known mechanism for non-porous panels. However, the divergence speed of a porous panel is always greater than the non-porous limit and increases with a dimensionless porosity parameter formed by the aeroelastic system. Various chordwise porosity distributions along the panel are also investigated, where the uniformly-porous panel is shown to be the most stable configuration. The generality and robustness of the primary divergence instability for porous panels is established analytically using a simple but general flutter analysis approach based on the Routh–Hurwitz stability criterion.     

轻质金属点阵夹层板热屈曲临界温度分析

本文针对均匀温度场下四边简支和四边固支金属点阵夹层板的临界热屈曲温度进行了求解和参数影响分析。将点阵夹芯等效为均匀连续体,并且将夹层板的剪切刚度近似为点阵夹芯的抗剪切刚度,忽略夹芯的抗弯刚度且认为夹层板主要由面板来提供抗弯刚度。对于无法获得解析解的四边固支条件,通过对未知变量进行双傅里叶展开的方法求解了Ressiner夹层板模型的临界屈曲温度,理论分析结果与有限元计算结果吻合良好。进一步分析了不同边界条件、点阵胞元构型、点阵材料相对密度、面板厚度等对临界屈曲温度的影响规律。     

铝面板厚度对Nomex蜂窝夹层结构冲击后弯曲性能影响的试验研究

通过低速冲击试验和四点弯曲试验,研究了铝面板厚度对Nomex蜂窝夹层结构抗冲击能力和剩余强度的影响。结果表明:在冲击荷载作用下,面板发生变形的区域大小随面板厚度增加而变大,当面板厚度大于0.5mm时,变形区域直径趋于稳定;无论试件是否受到过冲击,在弯曲载荷作用下,0.2mm厚面板发生芯格内屈曲失稳,而其他厚度面板均发生格间失稳;对无冲击损伤的结构,0.2mm厚面板弯曲强度显著低于其他厚度面板;对含冲击损伤的结构,0.2mm厚面板的剩余强度百分比最高。     

Static instability analysis for travelling membranes and plates interacting with axially moving ideal fluid

The out-of-plane instability of a moving plate, travelling between two rollers with constant velocity, is studied, taking into account the mutual interaction between the buckled plate and the surrounding, axially flowing ideal fluid. Transverse displacement of the buckled plate (assumed cylindrical) is described by an integro-differential equation that includes the centrifugal force, the aerodynamic reaction of the external medium, the vertical projection of membrane tension, and the bending force. The aerodynamic reaction is found analytically as a functional of the displacement. To find the critical divergence velocity of the moving plate and its corresponding buckling mode, an eigenvalue problem and variational principle are derived. Plate divergence, both within a vacuum and when submerged in an external medium, is investigated with the application of analytical and numerical techniques.     

Application of the extended Kantorovich method to the bending of clamped cylindrical panels

Applicability and performance of the extended Kantorovich method (EKM) to obtain highly accurate approximate closed form solution for bending analysis of a cylindrical panel is studied. Fully clamped panel subjected to both uniform and non-uniform loadings is considered. Based on the Love–Kirchhoff first approximation for thin shallow cylindrical panels, the governing equations of the problem in terms of three displacement components include a system of two second order and one forth order partial differential equations. The governing PDE system is converted to a double set of ODE systems by assuming separable functions for displacements together with utilization of the extended Kantorovich method. The resulted ODE systems are solved iteratively. In each iteration, exact closed form solutions are presented for both ODE systems. Rapid convergence and high accuracy of the method is shown for various examples. Both displacement and stress predictions show close agreement with other analytical and finite element analysis.     

Instability of a viscoelastic liquid jet with axisymmetric and asymmetric disturbances

The temporal instability behavior of a viscoelastic liquid jet in the wind-induced regime with axisymmetric and asymmetric disturbances moving in an inviscid gaseous environment is investigated theoretically. The corresponding dispersion relation between the wave growth rate and the wavenumber is derived. The linear instability analysis shows that viscoelastic liquid jets are more unstable than their Newtonian counterparts, and less unstable than their inviscid counterparts, for both axisymmetric and asymmetric disturbances, respectively. The instability behavior of viscoelastic jets is influenced by the interaction of liquid viscosity and elasticity, in which the viscosity tends to dampen the instability, whereas the elasticity results in an enhancement of instability. Relatively, the effect of the ratio of deformation retardation to stress relaxation time on the instability of viscoelastic jets is weak. It is found that the liquid Weber number is a key measure that controls the viscoelastic jet instability behavior. At small Weber number, the axisymmetric disturbance dominates the instability of viscoelastic jets, i.e., the growth rate of an axisymmetric disturbance exceeds that of asymmetric disturbances. When the Weber number increases, both the growth rate and the instability range of disturbances increase drastically. The asymptotic analysis shows that at large Weber number, more asymmetric disturbance modes become unstable, and the growth rate of each asymmetric disturbance mode approaches that of the axisymmetric disturbance. Therefore, the asymmetric disturbances are more dangerous than that of axisymmetric disturbances for a viscoelastic jet at large Weber numbers. Similar to the liquid Weber number, the ratio of gas to liquid density is another key measure that affects the viscoelastic jet instability behavior substantially.     

Modeling and simulation of the viscoelastic fluid mold filling process by level set method

A model for unifying a viscoelastic fluid and a Newtonian fluid is established, in which the governing equations for the viscoelastic fluid and the Newtonian fluid are successfully united into a system of generalized Navier–Stokes equations. A level set method is set up to solve the model for capturing the moving interface in the mold filling process. The physical governing equations are solved by the finite volume method on a non-staggered grid and the interpolation technique on the collocated grid is used for the pressure-velocity and the stress-velocity decoupling problems. The level set and its reinitialization equation are solved by the finite difference method, in which the spatial derivatives are discretized by the 5th-order Weighted Essentially Non-Oscillatory (WENO) scheme, and the temporal derivatives are discretized by the 3rd-order Total Variation Diminishing Runge–Kutta (TVD-R–K) scheme. The validity of the method is verified by some benchmark problems. Then a simulation of viscoelastic fluid mold filling process is pursued with the method. The moving interface and all the information of the physical quantities during the injection process are captured. The die swelling phenomenon is found in the simulation. The influences of elasticity and viscosity on the physical quantities such as stresses etc. in the mold filling process are analyzed. Numerical results show that elastic characteristics such as the stretch and die swelling etc. reinforce accordingly as Weissenberg number increases. Pressures increase continuously in the mold filling process and the pressure maintains the maximum value at the inlet. Injection velocity is proportional to injection pressure. A higher viscosity leads to a higher pressure distribution, that is, the pressure decreases as Reynolds number increases.     

Chaotic Analysis of Nonlinear Viscoelastic Panel Flutter in Supersonic Flow

In this paper chaotic behavior of nonlinear viscoelastic panels in asupersonic flow is investigated. The governing equations, based on vonKàarmàn's large deflection theory of isotropic flat plates, areconsidered with viscoelastic structural damping of Kelvin's modelincluded. Quasi-steady aerodynamic panel loadings are determined usingpiston theory. The effect of constant axial loading in the panel middlesurface and static pressure differential have also been included in thegoverning equation. The panel nonlinear partial differential equation istransformed into a set of nonlinear ordinary differential equationsthrough a Galerkin approach. The resulting system of equations is solvedthrough the fourth and fifth-order Runge–Kutta–Fehlberg (RKF-45)integration method. Static (divergence) and Hopf (flutter) bifurcationboundaries are presented for various levels of viscoelastic structuraldamping. Despite the deterministic nature of the system of equations,the dynamic panel response can become random-like. Chaotic analysis isperformed using several conventional criteria. Results are indicative ofthe important influence of structural damping on the domain of chaoticregion.     

Metallic sandwich panels subjected to multiple intense shocks

The mechanical response and fracture of metal sandwich panels subjected to multiple impulsive pressure loads (shocks) were investigated for panels with honeycomb and folded plate core constructions. The structural performance of panels with specific core configurations under multiple impulsive pressure loads is quantified by the maximum transverse deflection of the face sheets and the core crushing strain at mid-span of the panels. A limited set of simulations was carried out to find the optimum core density of a square honeycomb core sandwich panels under two shocks. The panels with a relative core density of 4%–5% are shown to have minimum face sheet deflection for the loading conditions considered here. This was consistent with the findings related to the sandwich panel response subjected to a single intense shock. Comparison of these results showed that optimized sandwich panels outperform solid plates under shock loading. An empirical method for prediction of the deflection and fracture of sandwich panels under two consecutive shocks – based on finding an effective peak over-pressure – was provided. Moreover, a limited number of simulations related to response and fracture of sandwich panels under multiple shocks with different material properties were performed to highlight the role of metal strength and ductility. In this set of simulations, square honeycomb sandwich panels made of four steels representing a relatively wide range of strength, strain hardening and ductility values were studied. For panels clamped at their edge, the observed failure mechanisms are core failure, top face failure and tearing at or close to the clamped edge. Failure diagrams for sandwich panels were constructed which reveal the fracture and failure mechanisms under various shock intensities for panels subjected to up to three consecutive shocks. The results complement previous studies on the behavior and fracture of these panels under high intensity dynamic loading and further highlights the potential of these panels for development of threat-resistant structural systems.     

Dynamic behaviour of an axially moving plate undergoing small cylindrical deformation submerged in axially flowing ideal fluid

The out-of-plane dynamic response of a moving plate, travelling between two rollers at a constant velocity, is studied, taking into account the mutual interaction between the vibrating plate and the surrounding, axially flowing ideal fluid. Transverse displacement of the plate (assumed cylindrical) is described by an integro-differential equation that includes a local inertia term, Coriolis and centrifugal forces, the aerodynamic reaction of the external medium, the vertical projection of membrane tension, the bending resistance, and external perturbation forces. In the two-dimensional model thus set up, the aerodynamic reaction is found analytically as a functional of the cylindrical displacement, using the techniques of complex analysis. The resulting integro-differential problem is discretized in space with the Fourier-Galerkin method, and integrated in time with the diagonalization method. Examples are computed with physical parameters corresponding to air and some paper materials. The effects of the surrounding fluid on the critical velocity and first natural frequency are investigated, for stationary air, for an air mass moving with the plate, and for some arbitrary axial fluid velocities. The obtained results are applicable for both an ideal membrane and a plate with nonzero bending rigidity.     

Stability Analysis of Maxwell Viscoelastic Pipes Conveying Fluid with Both Ends Simply Supported

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线性变厚度粘弹性矩形板在随从力作用下的动力稳定性

利用粘弹性微分型本构关系和薄板理论,对线性变厚度粘弹性矩形薄板建立了在切向均布随从力作用下的运动微分方程,采用微分求积法研究了在随从力作用下线性变厚度粘弹性矩形薄板的稳定性问题,具体对对边简支对边固支和三边简支一边固支条件下体变为弹性、畸变服从Kelvin-Voigt模型的变厚度粘弹性矩形板在随从力下的广义特征值问题进行了求解,分析了薄板的长宽比、厚度比及材料的无量纲延滞时间的变化对随从力作用下矩形薄板的失稳形式及相应的临界荷载的影响.     

孔板空调风口送风射流的数值模拟

介绍Ｎ点风口模型用于数值模拟室内空气流动时描述孔板类送风口的入流边界条件．然后采用该风口模型对不同的孔板风口出流条件算例进行数值计算，并就轴心速度衰减、射流扩展角以及断面流速分布等射流特性与实验数据进行了对比．比较结果表明，Ｎ点风口模型用于描述数值模拟室内空气流动的孔板类风口入流边界条件，可以获得工程上足够满意的结果．     

Dynamical analysis of axially moving plate by finite difference method

The complex natural frequencies for linear free vibrations and bifurcation and chaos for forced nonlinear vibration of axially moving viscoelastic plate are investigated in this paper. The governing partial differential equation of out-of-plane motion of the plate is derived by Newton’s second law. The finite difference method in spatial field is applied to the differential equation to study the instability due to flutter and divergence. The finite difference method in both spatial and temporal field is used in the analysis of a nonlinear partial differential equation to detect bifurcations and chaos of a nonlinear forced vibration of the system. Numerical results show that, with the increasing axially moving speed, the increasing excitation amplitude, and the decreasing viscosity coefficient, the equilibrium loses its stability and bifurcates into periodic motion, and then the periodic motion becomes chaotic motion by period-doubling bifurcation.     

Light-Weight Design of CRH Wind Deflector Panels based on Woven Textile Sandwich Composites

The woven textile sandwich composite(WTSC) is a promising lightweight composite.In bending,two competing core shearing failure modes reduce the strength;deflection induced by the core shearing deformation reduces the flexural rigidity.To replace a solid composite laminate,the span of WTSC panel must be greater than a critical value,which was deduced on the condition that the load capacity and flexural rigidity of the WTSC panel are equal to those of the composite laminate.Three WTSC panels were tested in bending,so that the failure modes were observed,and the critical spans were determined.Using the alternative design method,the WTSC based wind deflector with reduced weight has been fabricated and mounted on the CRH(China Railway High-speed).     

Mathematical modelling of the axially moving panels subjected to thermomechanical actions

The paper is devoted to a stability and out-of-plane deformation analysis of an axially moving elastic web modelled as a panel (a plate undergoing cylindrical deformation). The panel is under homogeneous pure mechanical in-plane tension and thermal strains corresponding to the thermal tension and bending. In accordance with the static approach of stability analysis the problem of out-of-plane thermomechanical divergence (buckling) is reduced to an eigenvalue problem which is analytically solved. This problem corresponds to the case of in-plane thermomechanical tension and zero thermal bending. The general case of deformations induced by combined thermomechanical bending and tension is reduced to nonhomogeneous boundary-value problem and analyzed with the help of Fourier series.     

On two-dimensional linear waves in Blasius boundary layer over viscoelastic layers

This work concerns the direct numerical simulation of small-amplitude two-dimensional ribbon-excited waves in Blasius boundary layer over viscoelastic compliant layers of finite length. A vorticity-streamfunction formulation is used, which assures divergence-free solutions for the evolving flow fields. Waves in the compliant panels are governed by the viscoelastic Navier's equations. The study shows that Tollmien–Schlichting (TS) waves and compliance-induced flow instability (CIFI) waves that are predicted by linear stability theory frequently coexist on viscoelastic layers of finite length. In general, the behaviour of the waves is consistent with the predictions of linear stability theory. The edges of the compliant panels, where abrupt changes in wall property occur, are an important source of waves when they are subjected to periodic excitation by the flow. The numerical results indicate that the non-parallel effect of boundary-layer growth is destabilizing on the TS instability. It is further demonstrated that viscoelastic layers with suitable properties are able to reduce the amplification of the TS waves, and that high levels of material damping are effective in controlling the propagating CIFI.     

On the static and dynamic stability of thin beam conveying fluid

In this paper, numerical investigation of the statical and dynamical stability of aligned and misaligned viscoelastic cantilevered beam is performed with a terminal nozzle in the presence of gravity in two cases: (1) effect of fluid velocity on the flutter boundary of beam conveying fluid and (2) effect of gravity on the buckling boundary of beam conveying fluid. The beam is assumed to have a large width-to-thickness ratio, so the out-of-plane bending rigidity is far higher than the in-plane bending and torsional rigidities. Gravity vector is considered in the vertical direction. Thus, deflection of the beam because of the gravity effect couples the in-plane bending and torsional equations. The beam is modeled by Euler–Bernoulli beam theory, with the flow-induced inertia, Coriolis and centrifugal forces along the beam considered as a distributed load along the beam. Furthermore, the end nozzle is regarded as a lumped mass and modeled as a follower axial force. The extended Hamilton’s principle and the Galerkin method are utilized to derive the bending–torsional equations of motion. The coupled equations of motion are solved as eigenvalue problems. Also, several cases are examined to study the impact of gravity, beam inclination angle, mass ratio, nozzle aspect ratio, bending-to-bending rigidity ratio and bending-to-torsional rigidity ratio on flutter and buckling margin of the system.

     

Experimental investigation on flow modes of electrospinning

Electrospinning experiments are performed byusing a set of experimental apparatus,a stroboscopic systemis adopted for capturing instantaneous images of the conejet configuration.The cone and the jet of aqueous solutionsof polyethylene oxide(PEO) are formed from an orifice of acapillary tube under the electric field.The viscoelastic constitutive relationship of the PEO solution is measured anddiscussed.The phenomena owing to the jet instability aredescribed,five flow modes and corresponding structures areobtained with variations of the fluid flow rate Q,the electricpotential U and the distance h from the orifice of the capillary tube to the collector.The flow modes of the cone-jetconfiguration involves the steady bending mode,the rotating bending mode,the swinging rotating mode,the blurringbending mode and the branching mode.Regimes in the Q-Uplane of the flow modes are also obtained.These results mayprovide the fundamentals to predict the operating conditionsexpected in practical applications.     

Estimates for Divergence Velocities of Axially Moving Orthotropic Thin Plates

Some models for axially moving orthotropic thin plates are investigated analytically via methods of complex analysis to derive estimates for critical plate velocities. The linearized Kirchhoff plate theory is used, and the energy forms of steady-state models are considered with homogeneous and inhomogeneous tension profiles in the cross direction of the plate. With the help of the energy forms, some limits for the divergence velocity of the plate are found analytically. In numerical examples, the derived lower limits for the divergence velocity are analyzed for plates with small flexural rigidity.