A dynamical model for multilayered plates with independent shear deformations

Author:
Scott W. Hansen

Journal:
Quart. Appl. Math. **55** (1997), 601-621

MSC:
Primary 73K10; Secondary 35Q72, 73C02

DOI:
https://doi.org/10.1090/qam/1486538

MathSciNet review:
MR1486538

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Abstract | References | Similar Articles | Additional Information

Abstract: In this paper a dynamic model for an -layered plate is developed based upon the assumptions of Reissner-Mindlin plate theory. Each plate layer is assumed to be transversely isotropic, transversely homogeneous and of a uniform thickness; however, no symmetry in the material properties or thicknesses of each plate is assumed. The layers are assumed to be perfectly bonded so that no slip occurs along the interface. No additional *a priori* kinematic restrictions are imposed upon the motion of the plates. The equations of motion are derived by the principle of virtual work. Existence and uniqueness results are obtained. In the case where the layers are symmetric we show that all solutions decouple into a bending solution (with antisymmetric displacements about the mid-plane) and an in-plane solution (with symmetric displacements).

**[1]**R. A. DiTaranto,*Theory of vibratory bending for elastic and viscoelastic layered finite-length beams*, J. Appl. Mech.**32**, 881-886 (1965)**[2]**S. W. Hansen,*A model for a two-layered plate with interfacial slip*, Internat. Ser. Numer. Math.**118**: ``Estimation and Control of Distributed Parameter Systems: Nonlinear Phenomena", eds: W. Desch, F. Kappel, K. Kunisch, Birkhäuser-Verlag, Basel, 1994 MR**1313515****[3]**R. Heuer,*Static and dynamic analysis of transversely isotropic, moderately thick sandwich beams by analogy*, Acta Mechanica**91**, 1-9 (1992)**[4]**E. M. Kerwin,*Damping of flexural waves by constrained visco-elastic layer*, J. Acoustical Soc. America**31**, 952-962 (1959)**[5]**J. E. Lagnese,*Boundary Stabilization of Thin Plates*in*SIAM Studies in Applied Mathematics*, SIAM, Philadelphia, 1989 MR**1061153****[6]**J. E. Lagnese and J.-L. Lions,*Modelling Analysis and Control of Thin Plates*in*Recherches en Mathématiques Appliquées*, RMA**6**, Springer-Verlag, New York, 1989 MR**953313****[7]**J.-L. Lions and E. Magenes,*Probèmes aux Limites Non-Homogènes et Applications, Vol. I*, Dunod, Paris, 1968 MR**0247244****[8]**D. J. Mead,*A comparison of some equations for the flexural vibration of damped sandwich beams*, J. Sound Vib.**83**, 363-377 (1982)**[9]**R. D. Mindlin,*Influence of rotary inertia and shear on flexural motions of isotropic elastic plates*, J. Appl. Mech.**18**, 31-38 (1951)**[10]**E. Reissner,*The effect of transverse shear deformations on the bending of elastic plates*, J. Appl. Mech.**12**, A69-A77 (1945) MR**0012579****[11]**E. Reissner,*On the bending of elastic plates*, Quart. Appl. Math.**4**, 55-68 (1947) MR**0020440****[12]**E. Reissner,*Reflections on the theory of elastic plates*, Appl. Mech. Rev.**38**, 1453-1464 (1985)**[13]**F.-Y. Wang,*Two-dimensional theories deduced from three-dimensional theory for a transversely isotropic body-I. Plate problems*, Internat. J. Solids Structures**4**, 455-470 (1990)**[14]**M.-J. Yan and E. H. Dowell,*Governing equations for vibrating constrained-layer damping sandwich plates and beams*, J. Appl. Mech.**39**, 1041-1046 (1972)**[15]**Y.-Y. Yu,*Simple thickness-shear modes of vibration of infinite sandwich plates*, J. Appl. Mech.**26**, 679-681 (1959) MR**0109505**

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DOI:
https://doi.org/10.1090/qam/1486538

Article copyright:
© Copyright 1997
American Mathematical Society