Viscoelastic response is often used as a probe in polymer science, since it is sensitive to thematerials chemistry andmicrostructure. Analysis of buckling of sandwich plates with viscoelastic. This paper studies the spatial behavior of steadystate solutions in bending problems of linear viscoelastic plates described by the reissnermindlin theory. Accordingly, the poissons ratio in this study is treated as constant value. The analysis focuses on evaluating two displacement theories of sandwich plates for various geometric and material properties and boundary conditions. The elasticviscoelastic correspondence principle for. May 17, 2012 the theory of orthotropic viscoelastic shear deformable composite flat panels and their dynamic stability international journal of solids and structures, vol. Leonov the university ofakron, department of polymer engineering, akron, ohio 443250301, usa abstract the present series of three consecutive papers develops a general theory for linear. An approximate nonlinear plate theory was developed under the kirchoff assumptions. The integral expressions resulting from fourier and hankel transforms of the governing equations are evaluated by two procedures. In the present paper, by taking advantage of the kirchhoff thin plate theory, it is easy to derive the partial differential equation governing the vibration of viscoelastic circular thin plates. This study gives fundamentals and some improvements of the classical plate theory proposed by kirchhoff. Numerous applications of linear viscoelasticity to characterization and analyses of viscoelastic.
On the bending of viscoelastic plates made of polymer foams. Nov 15, 2011 this paper analytically and numerically investigates the nonlinear vibration in parametric and internal resonances of inplane accelerating viscoelastic plates subjected to plane stresses. Mase 4 directly offered the fundamental equations for bending of viscoelastic plate by replacing the flexural rigidity of elastic plate with the rigidity of viscoelastic plate. Validity of thin plate theory in dynamic viscoelasticity m. An approach for dynamic characterisation of passive viscoelasticity and estimation of anthropometric inertia parameters of paraplegics knee joint. Theory of folding of stratified viscoelastic media and its.
The inplane translating speed is characterized as a simple harmonic variation about the constant mean axial speed. Viscoelasticity from theory to biological applications. Pister 6, robertson 7 and hewitt and mazumdar 8 applied the elasticityviscoelasticity correspondence pri. Considering the viscoelastic behavior of polymer foams, a new plate theory based on the direct approach is introduced and applied to plates composed of. The analysis of plates and shell structures can be performed applying theories deduced by various approaches. Balance of forces in a rod that buckles under an axial compression f and is laterally restrained by viscous dashpots. Pdf an improved model for bending of thin viscoelastic plate on. There are many methods of measurements for viscoelastic liquid and gelation.
Analysis of the viscoelastic behavior of plates made of functionally. Using the galaerkin method and the multiplier method, we establish the existence of solutions and prove an explicit and general decay rate result. In the present research, vibration and instability of axially moving viscoelastic micro plate is investigated. In the present paper, by taking advantage of the kirchhoff thinplate theory, it is easy to derive the partial differential equation governing the vibration of viscoelastic circular thin plates. The rheometer with a parallel plate or cone and plate test. A viscoelastic plate theory for the fast modelling of lamb.
Elastic foundation analysis of uniformly loaded functionally. We start from solutions to a model of threedimensional viscoelasticity where the viscosity stress tensor complies with the principle of timecontinuous frameindifference. Transient response of a laminated sandwich plate with viscoelastic core subjected to air blast. For nonhomogeneity of the plate material it is assumed that the density of the plate material varies parabolically along the xdirection. Sizedependent vibration of axially moving viscoelastic micro. On spatial behavior of harmonic vibrations in viscoelastic. In this paper we consider a viscoelastic plate equation with a nonlinear weakly dissipative feedback localized on a part of the boundary.
The spectral analysis technique has been applied to the solution of the wave equations. The analysis of the free vibration of rectangular sandwich plates with viscoelastic cores is purposed. A rectangular viscoelastic plate for which one of the sides is subjected to a displacement which varies harmonically in time and the remainder boundary is clamped is considered. Radovskii 5 discussed the problem of treating highway and airport pavement as thin viscoelastic plate. 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. Top plate area a bottom plate velocity 0 velocity v 0 force f shear stress, pascals viscosity, pa. The strain, y, is measured in radians, and the shear modulus, g, is given by g y x. First, it uses a simple and computationally efficient approximation based on thin plate theory e. As will be detailed in the next chapter, numerical. Pdf buckling of fiberreinforced viscoelastic composite.
This paper analytically and numerically investigates the nonlinear vibration in parametric and internal resonances of inplane accelerating viscoelastic plates subjected to plane stresses. This paper studies the quasistatic stability analysis of fiberreinforced viscoelastic composite plates subjected to inplane edge load systems. Comments on the phenomenological theory of linear viscoelasticity, 74 h. Viscoelastic characterization of an epdm rubber and finite. Sinusoidal shear deformation theory ssdt is utilized due to its accuracy of polynomi. Approximate interrelations among the linear viscoelastic functions 80 a. Transient ultrasonic waves in a viscoelastic plate. The higherorder shear deformation plate theories are summarized in table 1. Engineering viscoelasticity david roylance department of materials science and engineering.
Validity of thinplate theory in dynamic viscoelasticity. Refs 2, 3 present most practical representations of viscoelastic behavior. Application of thermoviscoelastic laminated plate theory. The sandwich plate was rectangular and made of two composite laminates as skins and a viscoelastic core. Pdf an improved model for bending of thin viscoelastic plate resting on winkler. Get article pdf viscoelastic properties of bamboo were measured over a. An improved model for bending of thin viscoelastic plate on. Pdf free vibration behavior of viscoelastic annular plates using. Material properties are graded according to a powerlaw variation from the interfaces to the faces of the plate. The first theory was developed for the vibratory bending of unsymmetrical sandwich plates by rao and nakra1. Vibrationanalysisofnonhomogenousorthotropic viscoelastic. Viscoelastic analysis of laminated plate buckling aiaa.
Existence and a general decay results for a viscoelastic. The microfailure event has been represented as a point source and ray theory has been applied to develop the physical model of wave propagation. In this work a model is proposed of the propagation in a viscoelastic plate of waves due to a damage event. Generalized wiechert model is adopted to simulate the viscoelasticity of the structure mindlinreissner plate theory is utilized in finite element formulation employing the consistent mass matrix. Analysis of the viscoelastic sphere impact against a. Pdf random vibration analysis of viscoelastic circular. Aboudi did the postbuckling analysis of viscoelastic laminated plates using higherorder theory. Elastic materials strain when stretched and immediately return to their original state once the stress is removed. The study is based on a unified sheardeformable plate theory. For viscoelastic materials, basic elastic and viscous. Characterization of pressure sensitive adhesives by rheology. Viscoelastic functionally graded materials, asme j. Sandwich plates are one of the important components in construction of engineering and especially aerospace structures. May 17, 2012 viscoelastic analysis of an exponentially graded sandwich plate 29 march 2012 journal of mechanical science and technology, vol.
Relations from nonlinear constitutive equations, 76 4. An apparatus and schematic representation of dynamic viscoelasticity during the sol gel transition are shown in figure 9 and 10, respectively. Sizedependent vibration of axially moving viscoelastic. The standard linear solid models with conventional derivatives and with fractionalorder derivatives are used as viscoelastic models. The reissner mindlin8 theory is simply obtained from the linear relationship. Validity of thinplate theory in dynamic viscoelasticity m. Mechanics of viscoelastic plates made of fgms archive ouverte hal. Mecitoglu faculty of aeronautics and astronautics, istanbul technical university, turkey abstract this paper is focused on the theoretical and experimental study of the dynamic. Viscoelastic response is often used as a probe in polymer science, since it is sensitive to. Freed nasa glenn research center, polymers branch, ms 493, 21 0000 brookdark road, brook park, ohio 445, usa a. 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. Pohle adelphi university, garden city, new york received 17 october 1963 resonance damping for a vibrating plate is investigated both according to the exact equations of dynamical. By takaya kobayashi, masami sato and yasuko mihara. Viscous materials, like water, resist shear flow and strain linearly with time when a stress is applied.
On the basis of the general theory for floating ice plates, as presented in ref. The book presents the formulation of the boundary value problem and demonstrates the separation of variables condition. Calculation of spectra from experimental functions, 81 1. Such data can be treated using timetemperature superposition tts theory, overcoming the difficulty of extrapolating limited laboratory tests at shorter times to longer term, real world. Pohle adelphi university, garden city, new york received 17 october 1963 resonance damping for a vibrating plate is investigated both according to. An introduction, second edition discusses the integral form of stress strain constitutive relations. The different possibilities of the formulation of plate theories are discussed in 27, 31 among others. Based on experience with homogeneous beam and plate theory, and experience of others, such as yu and yan and dowell, in sandwich constructions, it was felt. Pdf behavior of a viscoelastic composite plates under. Free vibration of sandwich plates with viscoelastic cores. In this paper, we consider a viscoelastic plate equation with a logarithmic nonlinearity. Get article pdf viscoelastic properties of bamboo were measured over a range of frequency. In this paper, buckling analysis of sandwich plates was investigated experimentally and analytically using layerwise theory. A general nonlinear viscoelastic plate theory and its.
Viscoelasticity is the property of materials that exhibit both viscous and elastic characteristics when undergoing deformation. Transient response of a laminated sandwich plate with. Parametric and internal resonances of inplane accelerating. This result extends and improves many results in the literature such as gorka 19, hiramatsu et al. Viscoelastic analysis of an exponentially graded sandwich plate 29 march 2012 journal of mechanical science and technology, vol. Hyer department of mechanical engineering and mechanics, old dominion university, norfolk, virginia 23508, u. The nearfield response of a thick viscoelastic plate at epicenter, off. Biot 300 central park west, new york, new york 10024 and f. Here we present a new theory of viscoelastic plates with changing properties in the thickness direction. W e s tart from solutions to a model of threedimensional. The sandwich plate is assumed to consist of a fully elastic core sandwiched by elasticviscoelastic fgm layers.
The text describes the mathematical framework to predict material behavior. The solution is based on the approximate theory of thin plates using the kirchhoff and the rayleigh corrections. In this section, the method by means of rheometer is introduced. Anderson department of aerospace engineering, university of michigan and r.
The sandwich plate is assumed to consist of a fully elastic core sandwiched by elastic viscoelastic fgm layers. Application of thermoviscoelastic laminated plate theory to predict warpage of printed circuit boards. The free vibration analysis of rectangular viscoelastic plates with simply supported boundary. In the present research, vibration and instability of axially moving viscoelastic microplate is investigated. Application of thermoviscoelastic laminated plate theory to predict warpage of printed circuit boards 305 the youngs modulus. This progress makes possible to perform more complex and at the same time, accurate simulations 1012. Viscoelastic analysis of laminated plate buckling aiaa journal. First, it uses a simple and computationally efficient approximation based on thinplate theory e. The theory of orthotropic viscoelastic shear deformable composite flat panels and their dynamic stability international journal of solids and structures, vol. The different possibilities of the formulation of plate theories are discussed in 27,31 among others. Application of thermoviscoelastic laminated plate theory to. Lamb waves, plate theory, viscoelasticity, fibre composite, structural health monitoring. A thin rectangular viscoelastic orthotropic plate under.
Most of such works utilized the models similar to those for bending of elastic plate. The equilibrium equations of the fg sandwich plate are given based on a trigonometric shear deformation plate theory. 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. Acoustic emission wave propagation in a viscoelastic plate. Roland polymer physics section naval research laboratory washington, dc isbn 9780199571574. The lovekirchho plate theory is a particular case of such an enriched kinematics.