Use of the higher-order plate theory of I. N. Vekua type in problems of dynamics of heterogeneous plane waveguides

Egorova, O. V.; Rabinskiy, L. N.; Zhavoronok, S. I.

doi:10.24423/aom.3074

Artykuł - szczegóły

Tytuł artykułu

Use of the higher-order plate theory of I. N. Vekua type in problems of dynamics of heterogeneous plane waveguides

Autorzy

Egorova O. V. , Rabinskiy L. N. , Zhavoronok S. I.

Treść / Zawartość

Pełne teksty:

Pobierz

Identyfikatory

DOI

10.24423/aom.3074

Warianty tytułu

Języki publikacji

Abstrakty

The dynamics of elastic plane waveguides is studied on the basis of the extended formulation of the plate theory of Nth order. The plate model is based on the Lagrangian formalism of analytical dynamics combined with the dimensional reduction approach and the biorthogonal expansion of the spatial distribution of the displacement. The boundary conditions shifted from the faces onto the base plane are interpreted as constraints for the variational formulation of two-dimensional plate models. The normal wave dispersion in plates is modelled, the convergence of the approximate solutions is studied using the known exact solution for a plane layer as a reference. The proposed plate theory is used to analyse the normal wave dispersion in power graded waveguides of both symmetric and asymmetric structures, the locking phase frequencies for various power indices are computed.

Słowa kluczowe

thin-walled waveguides plates analytical dynamics Lagrangian formalism constraint equations normal waves phase frequencies convergence

Wydawca

Instytut Podstawowych Problemów Techniki PAN

Czasopismo

Archives of Mechanics

Rocznik

2020

Tom

Vol. 72, nr 1

Strony

3--25

Opis fizyczny

Bibliogr. 68 poz., rys.

Twórcy

autor

Egorova O. V.

olha.egorova@yandex.ru

Faculty of Applied Mechanics, Moscow Aviation Institute (National Research University), 125993, 4 Volokolamskoe Shosse, Moscow, Russian Federation

autor

Rabinskiy L. N.

Faculty of Applied Mechanics, Moscow Aviation Institute (National Research University), 125993, 4 Volokolamskoe Shosse, Moscow, Russian Federation

autor

Zhavoronok S. I.

Department of Mechanics of Smart and Composite Materials and Systems, Institute of Applied Mechanics of Russian Academy of Sciences, 125040, 7 Leningradskiy Ave., Moscow, Russian Federation

Bibliografia

1. M. Koizumi, The concept of FGM, Ceramic Transactions. Functionally Gradient Materials, 34, 3–10, 1993.
2. N. Noda, Thermal stresses in materials with temperature-dependent properties, Applied Mechanics Reviews, 44, 383–397, 1991.
3. G.N. Praveen, J.N. Reddy, Nonlinar transient thermoelastic analysis of functionally graded ceramic/metal plates, International Journal of Solids and Structures, 35, 33, 4457–4476, 1998.
4. G.M. Kulikov, S.V. Plotnikova, Three-dimensional solution of the free vibration problem for metal-ceramics shells using the Method of Sampling Surfaces, Mechanics of Composite Materials, 53, 1, 31–44, 2017.
5. S.S. Pendhari, M.P. Mahajan, T. Kant, Static analysis of functionally graded laminates according to power-law variation of elastic modulus under bidirectional bending, International Journal of Computational Methods, 14, 5, p. 1750055, 2017.
6. F.Z. Zaoui, A. Tounsi, D. Quinas, Free vibration of functionally graded plates resting on elastic foundations based on quasi-3D hybrid-type higher order shear deformation theory, Smart Structures and Systems, 20, 4, 509–524, 2017.
7. H. Altenbach, V.A. Eremeyev, Eigen-vibrations of Plates made of Functionally Graded Material, Computers, Materials, Continua, 9, 2, 153–177, 2009.
8. L. Lu, M. Chekroun, O. Abraham, V. Maupin, Mechanical properties estimation of functionally graded materials using surfece waves recorded with a laser interferometer, Independent Nondestructive Testing and Evaluation International, 44, 2, 169–177, 2011.
9. J. Yu, B. Wu, The inverse of maerial properties of functionally graded pipes using the dispersion of guided waves and an artificial neural network, Independent Nondestructive Testing and Evaluation International, 42, 5, 452–468, 2009.
10. M. Sale, P. Rizzo, A. Marzani, Semi-analytical formulation for the uided waves-based reconstruction of elastic moduli, Mechanical Systems and Signal Processing, 25, 6, 2241–2256, 2011.
11. R. Nedin, S. Nesterov, A. Vatulyan, On reconstruction of thermalphysic characteristics of functionally graded hollow cylinders, Applied Mathematical Modelling, 40, 4, 2711–2719, 2016.
12. Z.-Q. Chang, R.C. Batra, Three-dimensional thermoelastic deformations of a functionally graded elliptic plate, Composites: Part B. Engineering, 31, 97–106, 2000.
13. Z.-Q. Cheng, J.N. Reddy, Three-dimensional thermoelastic deformations of functionally graded rectengular plates, European Journal of Mechanics A/Solids, 20, 841–855, 2001.
14. J.N. Reddy, Z.-Q. Cheng, Three dimensional solutions of smart functionally graded plates, Journal of Applied Mechanics, 68, 234–241, 2001.
15. S. Brischetto, A closed-form 3D-shell solution for multilayered structures subjected to different load combinations, Aerospace Science and Technology, 70, 29–46, 2017.
16. S. Brischetto, A general exact elastic shell solution for bending analysis of functionally graded materials, Composite Structures, 175, 70–85, 2017.
17. S. Brischetto, Exact three-dimensional static analysis of single- and multi-layered plates and shells, Composites: Part B. Engineering, 119, 230–252, 2017.
18. C.C. Vel, R.C. Batra, Three-dimensional exact solution for the vibration of functionally graded rectangular plates, Journal of Sound and Vibration, 272, 703–730, 2004.
19. S. Brischetto, E. Carrera, Importance of igher order modes and refined theories in free vibration analysis of composite plates, Journal of Applied Mechanics, 77, 1, Article no. 011013 (14 pages), 2010.
20. R.C. Batra, S. Aimmanee, Vibrations of thick isotropic plates with higher-order shear and normal deformable plate theories, Computers & Structures, 83, 12–13, 934–955, 2005.
21. J.-H. Kang, A.W. Leissa, Three-dimensional vibration analysis of thick, complete conical shells, Journal of Applied Mechanics, 71, 6, 502–507, 2004.
22. H. Altenbach, On the determination of transverse shear stiffness of orthotropic plates, Zeitschrift für Angewandte Mathematik und Physik, 51, 629–649, 2000.
23. H. Altenbach, An alternative determination of transverse shear stiffness for sandwich and laminated plates, International Journal of Solids and Structures, 37, 25, 3503–3520, 2000.
24. I.N. Vekua, Shell Theories: General Methods of Construction, Pitman Advanced Publishing Program, Boston, 1985.
25. V.V. Zozulya, A higher order theory for shells, plates and rods, International Journal of Mechanical Sciences, 103, 40–54, 2015.
26. S.I. Zhavoronok, A Vekua-type linear theory of thick elastic shells, ZAMM – Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 94, 1–2, 164–184, 2014.
27. V.V. Zozulya, C. Chang, A high order theory for functionally graded axisymmetric cylindrical shells, International Journal of Mechanical Science, 60, 1, 12–22, 2012.
28. A. Gupta, M. Talha, An assessment of a non-polynomial based higher order shear and normal deformation theory for vibration response of gradient plates with initial geometric imperfections, Composites Part B: Engineering, 107, 1, 141–161, 2016.
29. A. Gupta, M. Talha, B.N. Singh, Vibration characteristics of functionally graded material plate with various boundary constraints using higher order shear deformation theory, Composites Part B: Engineering, 94, 1, 64–74, 2016.
30. S.A. Sheikholeslami, A.R. Saidi, Vibration analysis of functionally graded rectangular plates resting on elastic foundation using higher-order shear and normal deformable plate theory, Composite Structures, 106, 350–361, 2013.
31. M. Mehrkash, M. Azkari, H.R. Mirdamadi, Reliability assessment of different plate theories for elastic wave propagation analysis in functionally graded plates, Ultrasonics, 54, 1, 106–120, 2014.
32. A.L. Goldenveizer, J.D. Kaplunov, Dynamic boundary layers in problems of vibrations of shells, Mechanics of Solids, 23, 4, 146–155, 1988.
33. J.D. Kaplunov, L.Yu. Kossovich, E.V. Nolde, Dynamics of thin-walled elastic bodies, Academic Press, San Diego, London, Boston, New York, Sydney, Tokyo, Toronto, 1998.
34. X. Cao, J. Jin, Y. Ru, J. Shi, Asymptotic analytical solution for horizontal shear waves in a piezoelectric elliptic culinder shell, Acta Mechanica, 226, 10, 3387–3400, 2015.
35. D. Gordeziani, M. Avalishvili, G. Avalishvili, Hierarchical models for elastic shells in curvilinear coordinates, Computers & Mathematics with Applications, 51, 1789–1808, 2006.
36. C. Schwab, S. Wright, Boundary layers of hierarchical beam and plate models, Journal of Elasticity, 38, 1–40, 1995.
37. A. Idesman, Accurate finite-element modeling of wave propagation in composite and functionally graded materials, Composite Structures, 117, 298–308, 2014.
38. A.M.A. Neves, A.J.M. Ferreira, E. Carrera, M. Cinefra, C.M.C. Roque, R.M.N. Jorge, C.M.M. Soares, Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique, Composites Part B: Engineering, 44, 1, 657–674, 2013.
39. B.D. Annin, Y.M. Volchkov, Nonclassical models of the theory of plates and shells, Journal of Applied Mechanics and Technical Physics, 57, 5, 769–776, 2016.
40. R. Kienzler, P. Schneider, Consistent theories of isotropic and anisotropic plates, Journal of Theoretical and Applied Mechanics, 50, 3, 755–768, 2012.
41. X. Cao, F. Jin, I. Jeon, Calculation of propagation properties of Lamb waves in a functionally graded material (FGM) plate by power series technique, Independent Nondestructive Testing and Evaluation International, 44, 1, 84–92, 2011.
42. D. Zhou, F.T.K. Au, Y.K. Cheung, S.H. Lo, Three-dimensional vibration analysis of circular and annular plates via the Chebyshev–Ritz method, International Journal of Solids and Structures, 40, 3089–3105, 2003.
43. L. Elmaimouni, J.E. Lefebvre, V. Zhang, T. Gryba, Guided waves in radially graded cylinders: a polynomial approach, Independent Nondestructive Testing and Evaluation International, 38, 5, 344–353, 2005.
44. L. Elmaimouni, J.E. Lefebvre, F.E. Ratolojanahary, A. Raherison, T. Gryba, J. Carlier, Modal analysis and harmonic response of resonators: An extension of a mapped orthogonal functions technique, Wave Motion, 48, 1, 93–104, 2011.
45. J.G. Yu, C. Zhang, J.E. Lefebvre, Guided wave characteristics in functionally graded piezoelectric rings with rectangular cross-sections, Acta Mechanica, 226, 3, 597–609, 2015.
46. J. Yu, J.E. Lefebvre, L. Elmaimouni, Guided waves in multilayered plates: An improved orthogonal polynoial approach, Acta Mechanica Solida Sinica, 27, 5, 542–550, 2014.
47. M. Zheng, S. He, Y. Lu, B. Wu, State-vector formalism and the Legendre polynomial solution for modelling guided waves in anisotropic plates, Journal of Sound and Vibration, 412, 372–388, 2018.
48. G.M. Kulikov, S.V. Plotnikova, Strong sampling surfaces formulation for laminated composite plates, Composite Structures, 172, 73–82, 2017.
49. G.M. Kulikov, S.V. Plotnikova, Strong sampling surfaces formulation for layered shells, International Journal of Solids and Structures, 121, 75–85, 2017.
50. G.M. Kulikov, S.V. Plotnikova, Three-dimensional analysis of metal-ceramics shells by the method of sampling surfaces, Mechanics of Composite Materials, 51, 4, 455–464, 2015.
51. G.M. Kulikov, S.V. Plotnikova, Three-dimensional exact analysis of piezoelectric laminated plates via a sampling surfaces method, International Journal of Solids and Structures, 50, 11–12, 1916–1929, 2013.
52. G.M. Kulikov, E. Carrera, S.V. Plotnikova, Hybrid-mixed quadrilateral element for laminated plates composed of functionally graded materials, Advanced Materials and Technologies, 1, 14–55, 2017.
53. G.M. Kulikov, S.V. Plotnikova, Three-dimensional exact analysis of functionally graded laminated composite materials, Advanced Structured Materials, 45, 223–241, 2015.
54. Y.M. Volchkov, L.A. Dergileva, Reducing three-dimensional elasticity problems to two-dimensional problems by approximating stresses and displacements by Legendre polynomials, Journal of Applied Mechanics and Technical Physics, 48, 3, 450–459, 2007.
55. A.A. Amosov, S.I. Zhavoronok, An approximate high-order theory of thick anisotropic shells, International Journal for Computational Civil and Structural Engineering, 1, 5, 28–38, 2003.
56. S.I. Zhavoronok, A.N. Leontiev, K.A. Leontiev, Analysis of thick-walled rotation shells based on the Legendre polynomials, International Journal for Computational Civil and Structural Engineering, 6, 1–2, 105–111, 2010.
57. S.I. Zhavoronok, Variational formulations of Vekua-type shell theories and some their applications, Shell Structures: Theory and Applications, 3, 341–344, 2014.
58. S.I. Zhavoronok, On the variational formulation of the extended thick anisotropic shells theory of I.N. Vekua type, Procedia Enginering, 111, 888–895, 2015.
59. S.I. Zhavoronok, A general higher-order shell theory based on the analytical dynamics of constrained continuum systems, Shell Structures: Theory and Applications, 4, 189–192, 2017.
60. E.L. Kuznetsova, E.L. Kuznetsova, L.N. Rabinskiy, S.I. Zhavoronok, On the equations of the analytical dynamics of the quasi-3D plate theory of I.N. Vekua type and some their solutions, Journal of Vibroengineering, 20, 2, 1108–1117, 2018.
61. O.V. Egorova, A.S. Kurbatov, L.N. Rabinskiy, S.I. Zhavoronok, Modeling of the dynamics of plane functionally graded waveguides based on the different formulations of the plate theory of I.N. Vekua type, Mechanics of Advanced Materials and Structures, 2019, DOI: 10.1080/15376494.2019.1578008.
62. P.A. Zhilin, Mechanics of deformable directed surfaces, International Journal of Solids and Structures, 12, 635–648, 1976.
63. H. Altenbach, V. Eremeyev, On the linear theory of micropolar plates, ZAMM –Journal of Applied Mathematics and Mechanics/Zeitschrift für Angewandte Mathematik und Mechanik, 89, 4, 242–256, 2009.
64. W. Pietraszkiewicz, V. Konopinska, On unique kinematics for the branching shells, International Journal of Solids and Structures, 48, 2238–2244, 2011.
65. H. Matsunaga, Free vibration and stability of functionally graded plates according to a 2D higher-order deformation theory, Composite Structures, 82, 499–512, 2008.
66. S.I. Zhavoronok, On the use of extended plate theories of Vekua-Amosov type for vave dispersion problems, International Journal for Computational Civil and Structural Engineering, 14, 1, 36–48, 2018.
67. G.H. Golub, R. Underwood, Stationary value of the ratio of quadratic forms subject to linear constraints, 1969.
68. L.N. Rabinskiy, S.A. Sitnikov, Development of technologies for obtaining composite material based on silicone binder for its further use in space electric rocket engines, Periodico Tche Quimica, 15, Special Issue 1, 390–395.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).

Typ dokumentu

Bibliografia

Identyfikator YADDA

bwmeta1.element.baztech-91f10252-eb1a-4258-940d-099ba5ceffbf