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.     

Stability of sandwich plates by mixed,higher-order analytical formulation

A unified mixed, higher-order analytical formulation has been presented in this paper to predict general buckling as well as wrinkling of a general multi-layer, multi-core sandwich plate having any arbitrary sequence of stiff layers and cores. Assumptions of thin stiff layers and anti-plane core, which are usually made in the analysis of sandwiches, have been eliminated in the present formulation. Displacements as well as the transverse stress continuities have been enforced in the formulation by incorporating them as the degrees-of-freedom. The modal transverse stresses have been obtained directly as eigen vectors and thus their separate calculations have been advantageously avoided. Two sets of mixed models have been proposed on the basis of individual layer as well as equivalent single layer (ESL) theories by selectively incorporating non-linear components of Green’s strain tensor. Solutions from the models have been shown to be in excellent agreement with the available three-dimensional elasticity solutions as well as with the available experimental results. It has been demonstrated that the ESL theories cannot accurately evaluate the overall buckling as well as the wrinkling loads of sandwiches. Limitations of the typical simplifying assumptions have also been highlighted.     

Thermoplastic strain of circular sandwich plates on an elastic base

We consider thermomechanical bending of an elastoplastic circular (solid or annular) light-filler sandwich plate resting on an elastic base. The hypotheses of broken normal are used to describe the kinematics of the plate stack nonsymmetric along the thickness. The base reaction is described by the Winkler model. We obtain the system of equilibrium equations and its exact solution in terms of displacements. We also present numerical results for a sandwich annular metal-polymer plate.     

Non-linear vibrations of sandwich viscoelastic shells

This paper deals with the non-linear vibration of sandwich viscoelastic shell structures. Coupling a harmonic balance method with the Galerkin's procedure, one obtains an amplitude equation depending on two complex coefficients. The latter are determined by solving a classical eigenvalue problem and two linear ones. This permits to get the non-linear frequency and the non-linear loss factor as functions of the displacement amplitude. To validate our approach, these relationships are illustrated in the case of a circular sandwich ring.     

Dynamic analysis of viscoelastic sandwich bems

Dynamic analysis of sandwich beams is performed. The external layers are modeled as beams on the basis of the Timoshenko model, and the internal layer possesses the characteristics of Winkler's viscoelastic one-directional base. The free vibrations are described by a homogeneous system of conjugate partial differential equations. After separation of variables in the system of differential equations, the boundary problem is solved and four complex sequences—a frequency sequence and a sequence of free-vibration modes—are obtained. The orthogonality of the complex modes of the free vibration is demonstrated. The free-vibration problem is solved under arbitrary initial conditions. The results of computations conducted for different sandwich beams with different parameters are presented. Pedagogical University, Bydgoszcz, Poland. Published in Prikladnaya Mekhanika, Vol. 36, No. 5, pp. 122–130, May, 2000.     

Postbuckling behavior of rectangular moderately thick plates and sandwich plates

ＰＯＳＴＢＵＣＫＬＩＮＧＢＥＨＡＶｉＯＲＯＦＲＥＣＴＡＮＧＵＬＡＲＭＯＤＥＲＡＴＥＬＹＴＨＩＣＫＰＬＡＴＥＳＡＮＤＳＡＮＤＷＩＣＨＰＬＡＴＥＳＣｈｅｎｇＺｈｅｎ－ｑｉａｎｇ（成振强）ＷａｎｇＸｉｕ－ｘｉ（王秀喜）ＨｕａｎｇＭａｏ－ｇｕａｎｇ（黄茂光）...     

Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: an analytical approach

This paper presents an analytical investigation on the buckling analysis of symmetric sandwich plates with functionally graded material (FGM) face sheets resting on an elastic foundation based on the first-order shear deformation plate theory (FSDT) and subjected to mechanical, thermal and thermo-mechanical loads. The material properties of FGM face sheets are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. An analytical approach is used to reduce the governing equations of stability and then solved using an analytical solution which is named as power series Frobenius method for symmetric sandwich plates with six different boundary conditions. A detailed numerical study is carried out to examine the influence of the plate aspect ratio, side-to-thickness ratio, loading type, sandwich plate type, volume fraction index, elastic foundation coefficients and boundary conditions on the buckling response of FGM sandwich plates. This has not been done before and serves to fill the gap of knowledge in this area.     

Nonlinear bending of circular sandwich plates

In this paper, fundamental equations and boundary conditions of nonlinear axisymmetrical bending theory for the circular sandwich plates with a soft core are derived by means of the method of calculus of variations. Especially in the case of very thin faces, the preceding fundamental epuations and boundary conditions simplity considerably. For example, a circular sandwich plate with edge clamped but free to siip under the action of uniform lateral load is considered. A more accurate solution of this problem has been obtained by means of the modified iteration method.Notation r, ,z system of cylindrical coordinates - a radius of plate boundary - t thickness of the face - h thickness of the core - h ₀ distance from middle of thickness of lower face to middle of thickness of upper face - E Young's modulus of the face - Poisson's ratio of the face - G ₂ shear modulus of the core - D _f flexural rigidity of the face - D flexural rigidity of the plate - C shear rigidity of the plate - q uniform lateral load - u _i ,v _i ,w _{i(i=1, 2, 3)} radial, tangential and normal displacement of upper face, core and lower face, respectively - u radial displacement of the middle plane of the plate - w deflection of the middle plane of the plate - rotation of connecting line of corresponding points in middle planes of two faces - _1i , _i , _zi , _ri , _zi , _{rzi (i=1,2,3)} strains at a point of upper face, core and lower face - _ri , _i , _zi , _ri , _zi , _rzi(i=1,2,3) stresses at a point of upper face, core and lower face - _r , ₀ radial and tangential stress of the middle plane of the plate, respectively - U _i(i =1, 2, 3) strain energy of upper face, core and lower face, respectively - V work done by the external force - U total potential energy of the plate - M _r radial moment of the plate - Q _r shearing force of the plate - m radial moment of the face - stress function - dimensionless radial coordinate - k dimensionless characteristic parameter - W dimensionless deflection - W ₀ dimensionless center deflection - S _r ,S ₀ dimensionless radial and tangential stress, respectively - S _r (0),S ₀ (0) dimensionless radial and tangential stress at center, respectively - S ₀(1) dimensionless tangential stress at edge - P dimensionless uniform lateral load - A ₂,A ₃,B ₂,B ₃,a ₁,.....,a ₂, ₁, ₂,l _1,1,...l _{1 1,3},m ₁,...,m ₃₃,n ₀,₂,...n ₂₂,₆,R ₁,,...R ₃₃ auxiliary quantity - L differential operator     

Nonlinear analysis of skewed sandwich plates

Nonlinear static and dynamic behaviours of freely supported Rhombic sandwich plates have been studied following Banerjee's hypothesis. Numerical results for 0° skew angle are compared with other known results. Results for other skew angles are believed to be new.

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Sommario Si studia, seguendo l'ipotesi di Banerjee, il comportamento nonlineare statico e dinamico di piastre rombiche semplicemente appoggiate. Si presentano risultati numerici relativi a piastre rombiche e rettangolari: questi ultimi vengono paragonati a risultati già noti, mentre i primi si ritengono nuovi.

     

蜂窝夹层板结构等效模型比较分析

在对蜂窝夹层板结构进行有限元分析时,要对其进行等效处理,采取等效方法的合理性将直接影响到计算结果的准确性.分别采用Reissner理论、Hoff理论、三明治夹芯板理论三种不同的等效方法建立有限元模型,然后进行了静力分析和模态分析,并将每种等效方法的计算结果与实体单元建立的蜂窝夹层板模型计算结果进行了比较.与Reissn...     

A reduction model for eigensolutions of damped viscoelastic sandwich structures

The aim of this paper is to develop a reduction method to determine the modal characteristics of viscoelastic sandwich structures. The method is based on the high order Newton algorithm and reduction techniques. Numerical tests have been performed in the case of sandwich beams and cylindrical shells. The comparison of the results obtained by the reduction method with those given by direct simulation shows both a good agreement and a significant reduction in computational cost.     

Development and validation of a viscoelastic finite element model of an L2/L3 motion segment

The prediction of the time dependent response of the spine to dynamic loading conditions is essential in understanding the injury mechanisms leading to occupationally related low back disorders (OLBD). Many previous finite element (FE) models of the lumbar spine have over-simplified the geometry and the material properties of their elements, yielding results limited generalizability. This study reports on the development and validation of a nonlinear viscoelastic FE model that can quantify the mechanical responses of the L2/L3 motion segment to time varying external loads. This model was developed by consideration of the intrinsic material properties of its individual constituents. A piecewise parameter identification method was adopted due to the inherent complexity in determining the role and contribution of each element to the overall behavior of the motion segment. The results of simulation of four loading conditions (quasistatic, constant loading rate, creep and cyclic relaxation) showed a satisfactory agreement with experimental observations in the literature. The detailed estimates of the state of stress/strain of this validated FE model can be used to test the role of epidemiological risk factors such as prolonged awkward posture, speed of lift (strain rate effect) and complex repetitive loading in OLBD.     

The probability stability of viscoelastic plates

The almost sure stability of homogeneous viscoelastic plates subjected to a random wide-band stationary in-plane load is investigated. The viscoelastic behavior of the plate is described in terms of the Boltzmann superposition principle, the relaxation kemels of which are represented by the sums of exponents. On the assumption that the in-plane load is random wide-band stationary process, sufficient conditions for almost sure stability of viscoelastic plates are obtained by the applications of Lyapunov's direct method. Project supported by the National Natural Science Foundation of China (No. 59635140) and the National Postdoctoral Foundation.     

Verification and validation of impinging round jet simulations using an adaptive FEM

This paper illustrates the use of an adaptive finite element method as a means of achieving verification of codes and simulations of impinging round jets, that is obtaining numerical predictions with controlled accuracy. Validation of these grid‐independent solution is then performed by comparing predictions to measurements. We adopt the standard and accepted definitions of verification and validation (Technical Report AIAA‐G‐077‐1998, American Institute of Aeronautics and Astronautics, 1998; Verification and Validation in Computational Science and Engineering. Hermosa Publishers: Albuquerque, NM, 1998). Mesh adaptation is used to perform the systematic and rigorous grid refinement studies required for both verification and validation in CFD. This ensures that discrepancies observed between predictions and measurements are due to deficiencies in the mathematical model of the flow. Issues in verification and validation are discussed. The paper presents an example of code verification by the method of manufactured solution. Examples of successful and unsuccessful validation for laminar and turbulent impinging jets show that agreement with experiments is achieved only with a good mathematical model of the flow physics combined with accurate numerical solution of the differential equations. The paper emphasizes good CFD practice to systematically achieve verification so that validation studies are always performed on solid grounds. Copyright © 2004 John Wiley & Sons, Ltd.     

Convolutional variational principles and stability of viscoelastic plates

Summary Convolutional variational principle for stability of viscoelastic plates has been formulated. General analysis of the behaviour of viscoelastic plates before buckling and during buckling is given. The relation of critical values to eigenvalues of the operators of the highest and least order with respect to time is shown.

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Übersicht Für die Stabilität von viskoelastischen Platten wird ein Faltungs-Variationsprinzip formuliert. Eine allgemeine Beschreibung des Verhaltens viskoelastischer Platten vor und während des Beulvorganges ist gegeben. Der Zusammenhang zwischen den kritischen Baulwerten und den Eigenwerten der Operatoren höchster und niedrigster Ordnung bezüglich der Zeit ist aufgezeigt.

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Dedicated to Professor Heinz Neuber in honour of his 70th birthday.     

The buckled states of annular sandwich plates

In this paper, the axisymmetric buckled states of an annular sandwich plate (Reissner- type sandwich plate) with the clamped inner edge which is subjected to a uniform radial compressive thrust at the clamped outer edge are studied. Firstly, the basic equation of the buckled problem is derived. Secondly, the critical loads for some parameters are obtained by using the shooting method. Finally, we discuss the existence of the buckled states in the vicinity of the critical loads and obtain the asymptotic expansions of the buckled states.     

Resonant effects of local loads on circular sandwich plates on an elastic foundation

The axisymmetric forced vibrations of a circular sandwich plate on an elastic foundation are studied. The plate is subjected to axisymmetric surface and mechanical loads with frequency equal to one of the natural frequencies of the plate. The foundation reaction is described by the Winkler model. To describe the kinematics of an asymmetric sandwich, the hypothesis of broken normal is used. The core is assumed to be light. The analytical solution of the problem is obtained and numerical results are analyzed