Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
 Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936

Russian Russian English English About Journal | Issues | Guidelines | Editorial Board | Contact Us
 


IPMech RASWeb hosting is provided
by the Ishlinsky Institute for
Problems in Mechanics
of the Russian
Academy of Sciences
IssuesArchive of Issues2016-5pp.527-537

Archive of Issues

Total articles in the database: 10864
In Russian (. . ): 8009
In English (Mech. Solids): 2855

<< Previous article | Volume 51, Issue 5 / 2016 | Next article >>
N.F. Morozov, P.E. Tovstik, and T.P. Tovstik, "Generalized Timoshenko-Reissner Model for a Multilayer Plate," Mech. Solids. 51 (5), 527-537 (2016)
Year 2016 Volume 51 Number 5 Pages 527-537
DOI 10.3103/S0025654416050034
Title Generalized Timoshenko-Reissner Model for a Multilayer Plate
Author(s) N.F. Morozov (St.-Petersburg State University, Universitetskaya nab. 7-9, St. Petersburg, 199034 Russia; Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bol'shoy pr. 61, St. Petersburg, 199078 Russia, morozov@nm1016.spb.edu)
P.E. Tovstik (St.-Petersburg State University, Universitetskaya nab. 7-9, St. Petersburg, 199034 Russia; Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bol'shoy pr. 61, St. Petersburg, 199078 Russia, peter.tovstik@mail.ru)
T.P. Tovstik (Institute for Problems in Mechanical Engineering, Russian Academy of Sciences, Bol'shoy pr. 61, St. Petersburg, 199078 Russia, tovstik_t@mail.ru)
Abstract A multilayer plate with isotropic (or transversally isotropic) layers strongly differing in rigidity is considered. This plate is reduced to an equivalent homogeneous transversally isotropic Timoshenko-Reissner plate whose deflections and free transverse vibration frequencies are close to those of the multilayer plate. By comparison with the exact solution of test three-dimensional problems of elasticity, the error of the proposed method is estimated both for the static problem and for free vibrations. This comparison can readily be carried out for the hinged edges of the plate, and explicit approximate formulas are obtained for the vibration frequencies. The scope of the proposed model turned out to be rather wide (the Young moduli of soft and rigid layers can differ by a factor of 1000). In the case of boundary conditions other than hinged support, a closed-form solution cannot be constructed in general. For rigidly fixed edges, the asymptotic method proposed by V. V. Bolotin is generalized to the case of a Timoshenko-Reissner plate.
Keywords multilayer plate, generalized Timoshenko-Reissner model, asymptotic integration, deflection, low-frequency transverse vibrations, Bolotin method
References
1.  G. Kirchhoff, Vorlesungen über Mathematische Physik: Mechanik (Taubner, Leipzig, 1876).
2.  A. E. H. Love, A Treatise on the Mathematical Theory of Elasticity (Cambridge Univ. Press, Cambridge, 1927; ONTI HKGiP SSSR, Moscow-Leningrad, 1935).
3.  S. P. Timoshenko, "On the Correction for Shear of the Differential Equation for Transverse Vibrations of Prismatic Bars," Phil. Mag. 41 (6), 742-746 (1921).
4.  E. Reissner, "The Effect of Transverse Shear Deformation on the Bending of Elastic Plates," Trans. ASME. J. Appl. Mech. 12 (2), 69-77 (1945).
5.  P. E. Tovstik and T. P. Tovstik, "On the 2D Models of Plates and Shells Including Shear," ZAMM 87 (2), 160-171 (2007).
6.  L. A. Agalovyan, Asymptotic Theory of Anisotropic Plates and Shells (Nauka, Moscow, 1997) [in Russian].
7.  P. E. Tovstik, "On Asymptotic Character of Approximate Models of Beams, Plates, and Shells," Vestnik SPbGU, Ser. 1, No. 3, 49-51 (2007).
8.  P. E. Tovstik and T. P. Tovstik, "A Thin-Plate Bending Equation of Second-Order Accuracy," Dokl. Ross. Akad. Nauk 457 (6), 660-663 (2014) [Dokl. Phys. (Engl. Transl.) 59 (8), 389-392 (2014)].
9.  E. I. Grigolyuk and G. M. Kulikov, "Generalized Model of the Mechanics of Thin-Walled Structures Made of Composite Materials," Mekh. Komp. Mater., No. 4, 698-704 (1988) [Mech. Comp. Mater. (Engl. Transl.) 24 (4), 537-543 (1989)].
10.  V. A. Rodionova, B. F. Titaev, and K. F. Chernykh, Applied Theory of Anisotropic Plates and Shells (Izdat. SPbGU, St. Petersburg, 1996) [in Russian].
11.  N. F. Morozov and P. E. Tovstik, "Bending of a Two-Layer Beam with Non-Rigid Contact between the Layers," Prikl. Mat. Mekh. 75 (1), 112-121 (2011) [J. Appl. Math. Mech. (Engl. Transl.) 75 (1), 77-84 (2011)].
12.  R. Kienzler and P. Shneider, "Comparison of Various Linear Plate Theories in the Light of a Consistent Second-Order Approximation," Shell Structures. Theory and Applications 3, 109-112 (2014).
13.  V. V. Bolotin, B. P. Makarov, G. V. Mishenkov, and Yu. Yu. Shveiko, "Asymptotic Method for Studying the Spectrum of Natural Frequencies of Elastic Plates," in Strength Calculations, No. 6 (Mashgiz, Moscow, 1960), pp. 231-253 [in Russian].
Received 09 June 2016
Link to Fulltext
<< Previous article | Volume 51, Issue 5 / 2016 | Next article >>
Orphus SystemIf you find a misprint on a webpage, please help us correct it promptly - just highlight and press Ctrl+Enter

101 Vernadsky Avenue, Bldg 1, Room 246, 119526 Moscow, Russia (+7 495) 434-3538 mechsol@ipmnet.ru https://mtt.ipmnet.ru
Founders: Russian Academy of Sciences, Branch of Power Industry, Machine Building, Mechanics and Control Processes of RAS, Ishlinsky Institute for Problems in Mechanics RAS
© Mechanics of Solids
webmaster
Rambler's Top100