黏弹夹芯板的有限元建模及实验研究

从有限元分析和数值模拟及实验验证的角度研究了黏弹夹芯板的频率依赖振动特性。夹芯板中间层为黏弹性材料,其刚度和阻尼的频率依赖性行为直接影响系统的模态频率和阻尼,并导致振动模式求解的复杂化。采用三阶七参数Biot模型描述黏弹性材料频率相关的黏弹性行为。开发了三层四节点28自由度的夹芯板单元,基于经典板理论和哈密顿原理建立了黏弹夹芯板的有限元动力学方程。通过引入辅助耗散坐标,将Biot模型和黏弹夹芯板的有限元动力学模型结合起来,并将其转化为常规二阶线性系统形式,极大简化了求解非线性振动特性的过程。对一边固定、另三边自由的黏弹夹芯板进行了前三阶固有频率和损耗因子的预测,并与实验结果对比。数值模拟结果和实验结果吻合良好,说明所提有限元方法是正确有效的。     

Some Results of the Finite Deflection Analysis of Clamped Skew Sandwich Plates

The suitability of Galerkin's method for the solution of the problem of the finite deflection analysis of clamped skew sandwich plates is studied. The five coupled nonlinear governing differential equations for sandwich plates are transformed into nonlinear algebraic equations by using Galerkin's method of error minimization. These equations are then solved using an iterative algorithm suggested by Brown. Comparisons of the results of the present analysis with available solutions show good agreement. Numerical results are presented for skew sandwich plates for a wide range of values of the core modulus for different skew angles and aspect ratios. Simplicity in formulation and computation is the advantage of the method as compared with other methods of nonlinear analysis. Computing time and memory requirements in a digital computer are relatively very small, which makes the method attractive.     

BENDING RESPONSES OF AN EXPONENTIALLY GRADED SIMPLY-SUPPORTED ELASTIC/VISCOELASTIC/ELASTIC SANDWICH PLATE

The bending response for exponentially graded composite (EGC) sandwich plates is investigated.The three-layer elastic/viscoelastic/elastic sandwich plate is studied by using the sinusoidal shear deformation plate theory as well as other familiar theories.Four types of sandwich plates are considered taking into account the symmetry of the plate and the thickness of each layer.The effective moduli and Illyushin’s approximation methods are used to solve the equations governing the bending of simply-supported EGC fiber-reinforced viscoelastic sandwich plates.Then numerical results for deflections and stresses are presented and the effects due to time parameter,aspect ratio,side-to-thickness ratio and constitutive parameter are investigated.     

Finite Deflection of Skew Sandwich Plates on Elastic Foundations by the Galerkin Method

ABSTRACT

Application of the Galerkin method to various fluid and structural mechanics problems that are governed by a single linear or nonlinear differential equation is well known [1-5]. Recently, the method has been extended to finite element formulations [6-10], In this paper the suitability of the Galerkin method for solution of large deflection problems of plates is studied. The method is first applied to investigate large deflection behavior of clamped isotropic plates on elastic foundations. After validity of the method is established, it is then extended to analyze problems of large deflection of clamped skew sandwich plates, both with and without elastic foundations. The plates are considered to be subjected to uniformly distributed loads. The governing differential equations for the sandwich plate in terms of displacements in Cartesian coordinates are first established and then transformed into skew coordinates. The nonlinear differential equations of the plates are then transformed into nonlinear algebraic equations, using the Galerkin method. These equations are solved using a Newton-Raphson iterative procedure. The parameters considered herein for large deflection behavior of skew sandwich plates are the aspect ratio of the plate, Poisson's ratio, skew angle, shearing stiffnesses of the core, and foundation moduli. Numerical results are presented for skew sandwich plates for various skew angles and aspect ratios. Simplicity and quick convergence are the advantages of the method, in comparison with other much more laborious numerical methods that require extensive computer facilities.     

Point-wise impulse (blast) response of a composite sandwich plate including core compressibility effects

This work analyzes the nonlinear impulse response of a composite sandwich plate exposed to a sudden point-wise transverse loading on the top face sheet. The nonlinearity arising from the core compressibility in the thickness direction is modeled and incorporated into the constitutive relations explicitly. As such, one can have a deep insight regarding the stress, strain and displacement profiles into the sandwich plate. The sandwich plate is assumed to be perfectly bonded at the face sheet/core interfaces. The equations of motion are formulated using Hamilton’s principle. The simply supported case is used to illustrate the procedure for solving the nonlinear equations. Numerical results are presented to demonstrate the response in terms of the transverse deformation and stresses in the composite sandwich plate. The effects of the variation of the geometrical parameters of the structure on the blast impulse response are also studied. Some conclusions are suggested regarding the associated optimal design of sandwich plates.     

Flutter of a viscoelastic plate in a supersonic gas flow

The flutter of a viscoelastic plate in a supersonic gas flow is studied. A technique and algorithm for numerical solution of nonlinear integro-differential equations with weakly singular kernels are elaborated. The critical flutter speed of viscoelastic plates is determined     

黏弹性板的大挠度蠕变屈曲

研究了具有初始小挠度受轴向压载黏弹性板的蠕变屈曲问题，在建立控制方程时，利用了von Karman非线性应变-位移关系，并考虑了初始挠度，用标准线性固体模型描述材料的黏弹性特性，在求解非线性积分方程时，利用梯形公式计算记忆积分式，将非线性积分方程化为非线性代数方程进行数值求解，得到了结构的蠕变变形过程，又将问题退化到小挠度情况进行研究，得到了挠度随时间扩展的解析解，分析了瞬时失稳临界载荷、持久临界载荷的物理意义，讨论了考虑几何非线性对黏弹性板蠕变屈曲的影响。     

Analysis and active control of nonlinear vibration of composite lattice sandwich plates

This paper is devoted to investigate the nonlinear vibration characteristics and active control of composite lattice sandwich plates using piezoelectric actuator and sensor. Three types of the sandwich plates with pyramidal, tetrahedral and Kagome cores are considered. In the structural modeling, the von Kármán large deflection theory is applied to establish the strain–displacement relations. The nonlinear equations of motion of the structures are derived by Hamilton’s principle with the assumed mode method. The nonlinear free and forced vibration responses of the lattice sandwich plates are calculated. The velocity feedback control (VFC) and H_∞ control methods are applied to design the controller. The nonlinear vibration responses of the sandwich plates with pyramidal, tetrahedral and Kagome cores are compared. The influences of the ply angle of the laminated face sheets, the thicknesses of the lattice core and face sheets and the excitation amplitude on the nonlinear vibration behaviors of the sandwich plates are investigated. The correctness of the H_∞ control algorithm is verified by comparing with the experiment results reported in the literature. The controlled nonlinear vibration response of the sandwich plate is computed and compared with that of the uncontrolled structural system. Numerical results indicate that the VFC and H_∞ control methods can effectively suppress the large amplitude vibration of the composite lattice sandwich plates.

     

Nonlinear damped vibrations of simply-supported sandwich plates in a rapidly changing temperature field

The paper studies the effects of a rapidly changed temperature on the free vibrations of simply supported sandwich plates. It has been taken into account that the properties of the facings and of the core of the sandwich plate change with the temperature. The effects of geometrical nonlinearities on the behaviour of the plate have also been included. The damping is considered by modelling the viscoelastic core as a Voigt-Kelvin solid. A Runge-Kutta method is employed to solve the governing equations and obtain the numerical results. It was found that the rapid change of temperature strongly affects the amplitude and frequency of the vibrations.     

Nonlinear vibration of viscoelastic sandwich plates under narrow-band random excitations

The effect of the narrow-band random excitation on the non-linear response of sandwich plates with an incompressible viscoelastic core is investigated. To model the core, both the transverse shear strains and rotations are assumed to be moderate and the displacement field in the thickness direction is assumed to be linear for the in-plane components and quadratic for the out-of-plane components. In connection to the moderate shear strains considered for the core, a non-linear single-integral viscoelastic model is also used for constitutive modeling of the core. The fifth-order perturbation method is used together with the Galerkin method to transform the nine partial differential equations to a single ordinary integro-differential equation. Converting the lower-order viscoelastic integral term to the differential form, the fifth-order method of multiple scale is applied together with the method of reconstitution to obtain the stochastic phase-amplitude equations. The Fokker–Planck–Kolmogorov equation corresponding to these equations is then solved by the finite difference method, to determine the probability density of the response. The variation of root mean square and marginal probability density of the response amplitude with excitation deterministic frequency and magnitudes are investigated and the bimodal distribution is recognized in narrow ranges of excitation frequency and magnitude.     

Dynamic Problems in the Theory of Sandwich Shells of Revolution with a Discrete Core under Nonstationary Loads

The equations of motion of sandwich shells of revolution with a discrete core are analyzed within the framework of the geometrically nonlinear theory of shells and plates. An efficient numerical algorithm is constructed to investigate nonstationary wave processes in elastic structures that are discrete-inhomogeneous across the thickness. Numerical examples are given     

A double-superposition global–local theory for vibration and dynamic buckling analyses of viscoelastic composite/sandwich plates: a complex modulus approach

A higher-order global–local theory is proposed based on the double-superposition concept for free vibration and dynamic buckling analyses of viscoelastic composite/sandwich plates subjected to thermomechanical loads. In contrast to all theories proposed so far for analysis of the viscoelastic plates, the continuity conditions of the transverse shear and normal stresses at the layer interfaces and the nonzero traction conditions at the top and bottom surfaces of the sandwich plates are satisfied. Another novelty is that these conditions may be satisfied for viscoelastic plates with temperature-dependent material properties and nonlinear behaviors subjected to thermomechanical loads. Furthermore, transverse flexibility is also taken into account. Some dynamic buckling/wrinkling analyses of the viscoelastic plates are performed in the present paper, for the first time. Comparisons made between results of the paper and results reported by well-known references confirm the accuracy and the efficiency of the proposed theory and the relevant solution algorithm.     

EFFECT OF DAMAGE ON NONLINEAR DYNAMIC PROPERTIES OF VISCOELASTIC RECTANGULAR PLATES

IntroductionRecently,compositestructureshavereceivedwideapplicationsinmodernindustriesincludingastronavigation ,aviation ,petroleumandchemicalindustry ,etc.However,thiskindofmaterialsgenerallyhavethepropertiesofviscoelasticitywiththeapparentcreepphenomenonandrelaxationbehaviors.Moreover,variousdamagewillemergeinthestructuresundertheactionofloading ,temperatureandenvironment.Damagemakesthemechanicalbehaviorsdeteriorategraduallybeforethefailure .Damageeffectswillsoftenthestiffnessofthestructure…     

黏弹性环形板的临界载荷及动力稳定性

利用线性黏弹性力学的Boltzmann叠加原理,在考察位移单值性条件的基础上,给出黏弹性环形板非线性动力学分析的初边值问题。通过Galerkin方法和引进新的状态变量,将其化归为四维非线性非自治常微分方程组,从而得到黏弹性环形板的四种临界载荷,同时考察了几何缺陷对黏弹性薄板临界载荷的影响。根据Floquet理论,得出黏弹性形板在周期激励下的线性动力稳定性判据。综合使用非线性动力学中的数值分析方法,研究了参数对黏弹性环形板非线性动力稳定性的影响。     

Aeroelastic dynamics stability of rotating sandwich annular plate with viscoelastic core layer

A dynamic model for a rotating sandwich annular plate with a viscoelastic core layer is developed. All fundamental equations and boundary conditions are established based on Hamilton’s principle, and the rotation effect and viscoelastic properties of the sandwich structure are taken into account. The aerodynamics force acting on the plate is described by a rotating damping model, and the constitutive behavior of the viscoelastic core layer is formulated by the frequency-dependent complex modulus. The effects of geometrical and material parameters on frequencies and damping of forward and backward traveling waves and the dynamic stability for the rotating sandwich plate are numerically analyzed by means of Galerkin’s method. The results show that the critical and flutter speeds of the rotating plate can be increased at some certain parameters of the viscoelastic core layer.     

Development of an analytical framework for viscoelastic corrugated-core sandwich plates and validation against FEM

In this study, an analytical procedure for the bending problem of a viscoelastic sandwich plate with a corrugated core is presented. Reissner–Mindlin plate theory and N-termed Prony series are employed to define the elastic and time-dependent contributions of the governing equations, respectively. Three different corrugation patterns, i.e., rectangular, trapezoidal, and triangular, are examined. Moreover, the structure is analyzed under both simply support and clamp boundary conditions. The calibrated material parameters of polymethyl methacrylate (PMMA) for the Generalized Maxwell rheological model are employed to show the viscoelastic response of the structure. A 3D finite element simulation of the problem is also conducted to confirm the accuracy of the analytical formulation. The two well-known creep and stress relaxation phenomena of the viscoelastic materials are examined for the mentioned corrugation cores and both boundary conditions analytically and numerically. The time-dependent dimensionless deflection and resultant von Mises stress distributions are provided. Besides, the variation of the results with various rise-times and applied load are studied in detail. The von Mises stress contours of the upper surface of the structure at the end of the creep test are also presented. The finite element method outcomes verify the analytical results with excellent compatibility. The proposed analytical procedure can be used as an efficient tool to study the effects of various parameters such as material, geometrical constants, and corrugation pattern on bending of viscoelastic sandwich plates with corrugated core problems for design and optimization, which involves a high number of simulations.

     

Nonlinear flutter of viscoelastic rectangular plates and cylindrical panels of a composite with a concentrated masses

The problem of flutter of viscoelastic rectangular plates and cylindrical panels with concentrated masses is studied in a geometrically nonlinear formulation. In the equation of motion of the plate and panel, the effect of concentrated masses is accounted for using the δ-Dirac function. The problem is reduced to a system of nonlinear ordinary integrodifferential equations by using the Bubnov-Galerkin method. The resulting system with a weakly singular Koltunov-Rzhanitsyn kernel is solved by employing a numerical method based on quadrature formulas. The behavior of viscoelastic rectangular plates and cylindrical panels is studied and the critical flow velocities are determined for real composite materials over wide ranges of physicomechanical and geometrical parameters.     

粘弹性夹芯层合旋转圆板的气动弹性动力稳定性分析

基于哈密尔顿原理,考虑作用于圆板上的空气动力载荷以及粘弹性复模量本构模型,本文建立了含有粘弹性夹芯层的旋转圆板的空气动力学模型,并给出了相应的稳定性的控制方程及边界条件。运用Galerkin方法,文中数值求解并给出了夹芯层合旋转圆板的动力学基本特征,以及结构几何参数、材料参数对于其前、后行波振动频率、阻尼和动力稳定性的影响。结果表明：通过优化合理选取粘弹性夹芯层合旋转圆板的几何参数和材料参数,可提高旋转圆板的临界转速和颤振速度,从而增强其稳定性。     

Dynamical behaviors of nonlinear viscoelastic thick plates with damage

Based on the deformation hypothesis of Timoshenko's plates and the Boltzmann's superposition principles for linear viscoelastic materials, the nonlinear equations governing the dynamical behavior of Timoshenko's viscoelastic thick plates with damage are presented. The Galerkin method is applied to simplify the set of equations. The numerical methods in nonlinear dynamics are used to solve the simplified systems. It could be seen that there are plenty of dynamical properties for dynamical systems formed by this kind of viscoelastic thick plate with damage under a transverse harmonic load. The influences of load, geometry and material parameters on the dynamical behavior of the nonlinear system are investigated in detail. At the same time, the effect of damage on the dynamical behavior of plate is also discussed.     

四边简支正交各向异性蜂窝型夹层板固有频率计算

该文以四边简支的方形蜂窝矩形夹层板为例,在经典夹层板理论的基础上,运用离散结构形式的运动控制方程和线性微分算子的可交换性,给出了一种把具有蜂窝型夹心的夹层板的包含三个广义位移的控制方程组化为,仅包含一个广义位移函数的单一方程的简单方法,并给出了四边简支蜂窝型夹层板的固有频率的精确解。研究结果对蜂窝夹层板的结构设计和工程应用具有指导意义。