In this paper, the transient response of a viscoelastic annular plate which has timedependent properties is determined mathematically under dynamic transverse load. The equilibrium equations of the fg sandwich plate are given based on a trigonometric shear deformation plate theory. Nonlinear vibration analysis of viscoelastic plates with. Analysis of buckling of sandwich plates with viscoelastic. Kirchhoff theory for thin viscoelastic plate resting on winkler foundation, in which the effect of the lateral normal stress is considered. Pdf an improved model for bending of thin viscoelastic plate on. Journal of low frequency noise, dynamic stability of rotating. Viscoelastic response of a floating ice plate to a.
Sizedependent vibration of axially moving viscoelastic. The sandwich plate is assumed to consist of a fully elastic core sandwiched by elasticviscoelastic fgm layers. This study gives fundamentals and some improvements of the classical plate theory proposed by kirchhoff. Thermomechanical behavior of flexible viscoelastic plates and. Considering the viscoelastic behavior of polymer foams, a new plate theory based on the direct approach is introduced and applied to plates composed of functionally graded materials fgm. Viscoelastic response of a floating ice plate to a steadily. Viscoelastic interconversion formulas are derived which relate the creep test, constant loading rate test, and dynamic test when the creep compliance can be approximated by a power law in time and linear. Higher order nonlocal viscoelastic strain gradient theory for. The membrane forces involving the rotating inertial force in the laplace domain are solved. Application of thermoviscoelastic laminated plate theory to. The viscoelastic properties obey the standard linear solid model in shear and the bulk behavior in elastic. A triangular finite element using laplace transform for. The creep behavior of any laminate can be predicted from laminated plate theory once the unidirectional material is characterized. The proposed viscoelastic plate theory formulation is applied to several examples including two anisotropic elastic plates and two anisotropic viscoelastic plates.
After deriving the equation of motion, the analytical method was used to solve the problem and to present the complex frequency in closedform expression. This theory enables the trial and testing of different throughthickness transverse shearstrain distributions and, among them, strain distributions that do not involve the undesirable. Thestandardlinearsolid model with conventional derivatives and with fractional. Cylindrical viscoelastic dampers in wide frequency range. An apparatus and schematic representation of dynamic viscoelasticity during the sol gel transition are shown in figure 9 and 10, respectively. Viscoelastic analysis of laminated plate buckling aiaa journal. Koever j shel development company, houston, texas experimental verification of the theory of folding of stratified viscoelastic media geoiogical society of. Here we present a new theory of viscoelastic plates with changing. Nov 01, 2016 to predict the timedependent behaviors of viscoelastic laminated composites, a threenode multilayered plate element is developed based on the efficient higherorder plate theory ehopt, which was originally proposed by cho and parmerter. Pdf analysis of the viscoelastic behavior of plates made of. The inclusion of the frequency and temperaturedependent behaviour of the viscoelastic material can be made by using the socalled elasticviscoelastic correspondence principle christensen, 1982, according to which, for a given temperature, matrices. We start from timediscrete solutions to a model of threedimensional viscoelasticity considered in friedrich and kruzik siam j math anal 50. Pdf an improved model for bending of thin viscoelastic.
An improved model for bending of thin viscoelastic plate. Analysis of viscoelastic laminated composite plates. Without imposing restrictive assumptions on the boundary frictional damping, we establish an explicit and general decay rate result that allows a wider class of relaxation functions and generalizes previous results existing in the literature. Pdf thermal effects on the bending response of fiber. We consider plates made of polymer foams with highly nonhomogeneous structure through the. Propagation of time harmonic plane waves in an infinite thermoviscoelastic material with voids has been investigated within the context of different theories of thermoelasticity. Theory of folding of stratified viscoelastic media and its. Based on kelvins model, the viscoelastic structural properties of micro plate are taken into consideration.
Buckling of fiberreinforced viscoelastic composite plates. The convolution theorem of laplace transformation is applied to circumvent the complexity of dealing with linear viscoelastic materials. Based on mindlin plate theory, the finite element model is developed by applying hamiltons variational principle without any integral transformation. In this paper we consider a viscoelastic plate equation with a nonlinear weakly dissipative feedback localized on a part of the boundary.
A general nonlinear viscoelastic plate theory and its. Transient response of a laminated sandwich plate with. Dynamic response determination of viscoelastic annular plates. Improved viscoelastic analysis of laminated composite and. The general form of complex potentials in approximations and the boundary conditions. The elasticviscoelastic correspondence principle for. Firstly, a higher order plate theory for modelling disperse solutions in elastic and viscoelastic fibrereinforced composites is proposed in order to investigate the radiation and attenuation of. Utilizing the first order shear deformation theory fsdt, hamiltons principle, method of energy, the motion equations are determined where the influences of size are captured by higher order nonlocal strain gradient approach.
Efficient higherorder zigzag theory for viscoelastic. The basic mechanical models of viscoelasticity, the maxwell and kelvin models, are introduced in section 10. The rheometer with a parallel plate or cone and plate test. Application of thermoviscoelastic laminated plate theory. Exiting studies dealing with viscoelastic plates e. Viscoelastic response is often used as a probe in polymer science, since it is sensitive to thematerials chemistry andmicrostructure. Pdf behavior of a viscoelastic composite plates under transient load.
To verify the calculation method proposed in this study, a threelayered plate 40 mm in length and 20 mm in width fig. Abstract subduction of tectonic plates into earths mantle occurs when. Wyss weitzlab group meeng tutorial 10x1035 0 5 10 strain 0 2 4 6 8 10 12 time s. Jan 11, 2021 the viscoelastic layers are considered as kelvinvoigt viscoelastic model. The partial differential equations system is deduced according to the dynamic version of the principle of virtual displacements and is based on a theory that accounts for the exponential distribution of transverse shear deformation. Elastic foundation analysis of uniformly loaded functionally. Analytical solutions for functionally graded sandwich. The equations of motion are extracted using hamiltons. Methodology and theory of viscoelastic dampers performance test. Inplane displacement fields are constructed by superimposing a cubic varying displacement field on a linear zigzag varying field.
Analytical solution for a viscoelastic plate on a pasternak. Effect of the viscoelastic foundations on the free vibration. Pdf a viscoelastic plate theory for the fast modelling of. Sinusoidal shear deformation theory ssdt is utilized due to its accuracy of polynomial functions than other plate theories. An improved model for bending of thin viscoelastic plate on.
Galerkin procedure has been implemented to derive the timedependent. The standard linear solid models with conventional derivatives and with fractionalorder derivatives are used as viscoelastic models. Viscoelastic properties of hydrogels, adhesives and biopolymers tianhong terri chen phd. Jan 01, 1989 the resulting viscoelastic effects are shown, and comparison between the results obtained within the classical laminated plate theory and the firstorder shear deformation theory is discussed. This paper presents a twovariable refined plate theory for free vibration of functionally graded material fgm plates lying on viscoelastic winklerpasternak foundations. Pdf analysis of the viscoelastic behavior of plates made. Fonseca abstract we apply a quasistatic nonlinear model for nonsimple viscoelastic materials at a.
Here we present a new theory of viscoelastic plates with changing properties in the thickness direction based on the direct approach in the plate theory and extended by the effective properties concept. Plate cone and plate concentric cylinders torsion rectangular very. On the basis of the general theory for floating ice plates, as presented in ref. A viscoelastic plate theory for the fast modelling of lamb. Dynamic response determination of viscoelastic annular. The behavior of viscoelastic material modeled using zener threeelement model. Vibration analysis of viscoelastic orthotropic nanoplates. Pan 9 analyzed the dynamic response problem of isotropic viscoelastic plates by extending, for this case, mindlins sheardeformation plate theory. Modelling of viscoelastic behaviour of plates springerlink. Material properties are graded according to a powerlaw variation from the interfaces to the faces of the plate.
The axisymmetric conditions are considered in the problem. Validity of thinplate theory in dynamic viscoelasticity. Then we reduce the obtained results to the problem of thin elastic plate resting on elastic foundation, and a different elastic flexural rigidity. The role of viscoelasticity in subducting plates agu publications. Analytical solutions for functionally graded sandwich plates. Viscoelastic response is often used as a probe in polymer science, since it is sensitive to. Research article analysis of the viscoelastic sphere impact against. The theory of orthotropic viscoelastic shear deformable composite flat panels and their dynamic stability international journal of solids and structures, vol. This phenomenon which was treated previously by using an approximate plate theory, l, 21, is analyzed here by using an exact theory for the deformation of a continuum under prestress 3, 4, 5, 61. The corresponding technique is based on the separation of plate into elastic panels between the ribs in. In this case, the constitutive equations for the stress resultants follows as. Generalized wiechert model is adopted to simulate the viscoelasticity of the structure mindlinreissner plate theory is utilized in finite element. Introduction viscoelastic effects in unidirectional composites e. Constitutive equations are derived considering linear viscoelastic behavior that is modeled by the kelvinvoigt linear viscoelastic theory 12.
Considering the viscoelastic behavior of polymer foams a new plate theory based on the direct approach is introduced and applied to plates composed of functionally graded materials fgm. The sandwich plate was rectangular and made of two composite laminates as skins and a viscoelastic core. For simplicity, let us consider a throughthethickness symmetric structure of the plate under consideration and an isotropic material behavior. The kirchhoff plate theory is employed to describe the mechanical property of each gradient layer with elastic modulus defined as the arbitrary function through the thickness direction. Viscoelastic theory is used to describe the response of a floating ice sheet to a moving vehicle. The basic equations for internal forces and stress distribution are derived based on the general viscoelastic theory under small deformation. Jun 01, 2015 an efficient higherorder plate theory for viscoelastic materials is developed to predict the timedependent mechanical behaviors of composite laminates. Static and dynamic analysis of a viscoelastic plate by the finite. Feb 01, 20 the vibration analysis of the viscoelastic orthotropic nanoplates was investigated based on the nonlocal plate theory and kelvinvoigt model. Elastic analysis of soilfoundation 1995 a beam resting. The study is based on a unified sheardeformable plate theory. Basics in rheology theory ta instruments rheometers and dmas instrumentation test methodologies rheological applications in biopolymer and biomedical materials hydrogels and creams. Analysis of the viscoelastic sphere impact against a.
Pdf buckling of fiberreinforced viscoelastic composite. The equations of motion developed by iesan 1 have been extended to incorporate the lordshulman theory lst and greenlindsay theory glt of thermoelasticity. The nonuniform distribution of temperature across the depth of the plate is accounted for by assuming that ice satisfies the postulates of thermorheologically simple solids. Lamb waves, plate theory, viscoelasticity, fibre composite. Mechanics of viscoelastic plates made of fgms archive ouverte hal. The modified couple stress theory mcst is employed because of its capability to interpret the size effect. Viscoelastic analysis of laminated plate buckling aiaa. Librescu and chandiramani 10 presented a paper that deals with the dynamic stability analysis of transversely isotropic viscoelastic plates subjected to inplane biaxial edgeload systems. This paper studies the quasistatic stability analysis of fiberreinforced viscoelastic composite plates subjected to inplane edge load systems. We adopt a twoparameter memory function to describe the behaviour of the. Solving the problem of linear viscoelasticity for piecewise. Sonoda et al 9,10 studied the circular and rectangular plate on linear viscoelastic foundation. Koever j shel development company, houston, texas experimental verification of the theory of folding of stratified viscoelastic media geoiogical society of america bulletin, v. Xian, 710048, bfaculty of printing and packaging engineering, xian university of technology, china.
Plane waves in thermoviscoelastic material with voids under. Theory of folding of stratified viscoelastic media and its implications in tectonics and orogenesis a. The formulation was based on the first order shear deformation theory and the rayleighritz method was used for approximating and determining the displacement field. Hygrothermal forced vibration of a viscoelastic laminated. Using rheology to characterize flow and viscoelastic.
The present work aims to examine the vibrations by a higherorder shear deformation theory including a new function of warping. An approximate method for solving the problem of linear viscoelasticity for thin anisotropic plates subject to transverse bending is proposed. On the basis of the thermoviscoelastic constitutive equation and classical kirchhoff thin plate theory, the motion differential equation of. Nonlinear transient vibration of viscoelastic plates. We can build up a theory of linear viscoelasticity by considering simple linear elements such as the elastic linear spring and the viscous linear dash pot2.
Thestandardlinearsolid model with conventional derivatives. Dynamic response of viscoelastic rectangle kirchhoff plate. The standard linear solid model is applied to simulate the viscoelasticity of. The twodimensional constitutive equations of a viscoelastic plate were formulated in the general form in 15. Dynamic characteristics and stability of axially moving viscoelastic plate with piezoelectric layer yan wanga, xiaoshan caoa, tao jingb and jimei wub aschool of civil engineering and architecture, xian university of technology, china. The theory developed further with the emergence of synthetic. We adopt a twoparameter memory function to describe the behaviour of the ice, subjected to a steadily moving line or point load. The method of small parameter is used to reduce the problem to a sequence of boundary problems of applied theory of bending of plates solved using complex potentials. Khanna, vibration of viscoelastic rectangular plate with linearly thickness variations in both directions j. The behaviour of viscoelastic plates can be described by several engineering theories, based on different assumptions and theoretical conceptions.
Thermal effects on the bending response of fiberreinforced viscoelastic composite plates using a sinusoidal shear deformation theory. There are many methods of measurements for viscoelastic liquid and gelation. Guided waves in functionally graded viscoelastic plates. Dec 01, 2020 the viscoelastic medium around the cnc is assumed applying the model of viscopasternak.
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