10.24423/EngTrans.3085.20230718
The Dynamic Stability Problem of Composite Annular Plates with Auxetic Properties
This paper presents the effect of the auxeticity on the behaviour of a plate subjected to the loss of stability. The plate structure is composed of three layers built of auxetic or conventional facings and a conventional core. The plate is loaded mechanically in the plane of facings with forces increasing in time. The main technique of the problem solution is based on the orthogonalisation and finite differences methods. Selected examples of plates were calculated with the use of the finite difference method. The obtained results allow observing the similarities and differences between plate models, whose structures are built of conventional layers or mixed layers: auxetic-foam-auxetic. Investigations complement the knowledge of the responses of the composite structures with auxetic properties. They show the possibility of using special plate structures whose materials are characterised by the negative value of Poisson’s ratio.
Copyright © The Author(s). This is an open-access article distributed under the terms of the Creative Commons Attribution-ShareAlike 4.0 International (CC BY-SA 4.0).
References
Chen Y.-R., Chen L.-W., Wang C.-C., Axisymmetric dynamic instability of rotating polar orthotropic sandwich annular plates with a constrained damping layer, Composite Structures, 73(3): 290–302, 2006, doi: 10.1016/j.compstruct.2005.01.039.
Wang H.-J., Chen L.=W., Axisymmetric dynamic stability of rotating sandwich circular plates, Journal Vibration and Acoustics, 126(3): 407–415, 2004, doi: 10.1115/1.1688765.
Alipour M.M., Shariyat M., Analytical zigzag formulation with 3D elasticity corrections for bending and stress analysis of circular/annular composite sandwich plates with auxetic cores, Composite Structures, 132: 175–197, 2015, doi: 10.1016/j.compstruct.2015.05.003.
Pham H.C., Pham M.P., Hoang T.T., Duong T.M., Nguyen D.D., Static bending analysis of auxetic plate by FEM and a new third-order shear deformation plate theory, VNU Journal of Science: Natural Sciences and Technology, 36(1), 2020, doi: 10.25073/2588-1140/vnunst.5000.
Shariyat M., Alipour M.M., Analytical bending and stress analysis of variable thickness FGM auxetic conical/cylindrical shells with general tractions, Latin American Journal of Solids and Structures, 14(5): 805–843, 2017, doi: 10.1590/1679-78253413.
Lim T.-C., Circular auxetic plates, Journal of Mechanics, 29(1): 121–133, 2013, doi: 10.1017/jmech.2012.113.
Lim T.-C., Buckling and vibration of circular auxetic plates, Journal of Engineering of Materials and Technology, 136(2): 021007, 2014, doi: 10.1115/1.4026617.
Faghfouri S., Rammerstorfer F.G., Buckling of stretched disks – with comparisons and extensions to auxetics, International Journal of Mechanical Sciences, 213: 106876, 2022, doi: 10.1016/j.ijmecsci.2021.106876.
Li C., Shen H.-S., Wang H., Nonlinear dynamic response of sandwich plates with functionally graded auxetic 3D lattice core, Nonlinear Dynamics, 100(4): 3235–3252, 2020, doi: 10.1007/s11071-020-05686-4.
Tran T.T., Pham Q.H., Nguyen-Thoi T., Tran T.-V., Dynamic analysis of sandwich auxetic honeycomb plates subjected to moving oscillator load on elastic foundation, Advances in Materials Science and Engineering, 2020: Article ID 6309130, 2020, doi: 10.1155/2020/6309130.
Behravan Rad A., Static analysis of non-uniform 2D functionally graded auxetic-porous circular plates interacting with the gradient elastic foundations involving friction force, Aerospace Science and Technology, 76: 315–339, 2018, doi: 10.1016/j.ast.2018.01.036.
Volmir A.S., The Nonlinear Dynamic of Plates and Shells [in Russian: Nelineinaya Dinamika Plastinok i Obolochek], Science, Moscow, 1972.
Pawlus D., Dynamic stability of three-layered annular plates with wavy forms of buckling, Acta Mechanica, 216(1): 123–138, 2011, doi: 10.1007/s00707-010-0352-3.
Pawlus D., Solution to the problem of axisymmetric and asymmetric dynamic instability of three-layered annular plates, Thin-Walled Structures, 49(5): 660–668, 2011, doi: 10.1016/j.tws.2010.09.013.
Pawlus D., Dynamic stability of three-layered annular plates with viscoelastic core [in Polish], Scientific Bulletin of the Technical University of Lodz, 1075; Technical University of Lodz, Lodz, 2010.
Volmir A.S., Stability of Deformed System [in Russian: Ustoichivost Deformiruemykh Sistem], Science, Moscow, 1967.
Wojciech S., Numerical solution of the problem of dynamic stability of annular plates [in Polish: Numeryczne rozwiązanie zagadnienia stateczności dynamicznej płyt pierścieniowych], Journal of Theoretical and Applied Mechanics, 17(2), 247–262, 1979.
ABAQUS/Standard. User’s Manual, Hibbit, Karlsson & Sorensen, Inc., Pawtucket, RI, USA, 1998.
Donescu S., Chiroiu V., Munteanu L., On the Young’s modulus of a auxetic composite structure, Mechanics Research Communications, 36(3): 294–301, 2009, doi: 10.1016/j.mechrescom.2008.10.006.
Pawlus D., Static stability of composite annular plates with auxetic properties, Materials, 15(10): 3579, 2022, doi: 10.3390/ma15103579. https://doi.org/10.3390/ma15103579
DOI: 10.24423/EngTrans.3085.20230718