Geodesic
Exact solutions of the problem of flexural and cross-section-shear buckling modes and free oscillations of the rectangular orthotropic plate with loose edges
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 152 (2010) no. 1, pp. 181-198 Cet article a éte moissonné depuis la source Math-Net.Ru

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The article regards linearized problems about elastic stability of an orthotropic rectangular plate with loose edges under the influence of running forces of the invariable directions which cause in a plate either a single-sided and double-end compression, or pure shear. For stating the problem we use the known equations of the specified theory of plates of Timoshenko type considering the cross-section shears. On the basis of double trigonometrical base-load functions such analytical solutions of the specified problems are presented which fulfill all static boundary conditions. Depending on the structure of these solutions in order to conform to the equations of perturbed equilibrium of a plate the corresponding equations of Bubnov method are made, proceeding from which the bifurcation values of operating forces are defined and buckling modes corresponding to them are ultimately determined. On the basis of the stated method some analytical solutions are also discovered for the problem of small free oscillations of a plate with loose edges.
Keywords: linearized stability problem, rectangular plate, pure shear, flexural and cross-section-shear buckling modes, free oscillations, loose edges, trigonometrical base-load functions, analytical solutions, Bubnov method.
Mots-clés : double-end compression 
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     title = {Exact solutions of the problem of flexural and cross-section-shear buckling modes and free oscillations of the rectangular orthotropic plate with loose edges},
     journal = {U\v{c}\"enye zapiski Kazanskogo universiteta. Seri\^a Fiziko-matemati\v{c}eskie nauki},
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V. N. Paimushin; T. V. Polyakova. Exact solutions of the problem of flexural and cross-section-shear buckling modes and free oscillations of the rectangular orthotropic plate with loose edges. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, Tome 152 (2010) no. 1, pp. 181-198. http://geodesic.mathdoc.fr/item/UZKU_2010_152_1_a17/

[1] Paimushin V. N., “Tochnye i priblizhennye resheniya zadachi o ploskikh formakh svobodnykh kolebanii pryamougolnoi plastiny so svobodnymi krayami, osnovannye na trigonometricheskikh bazisnykh funktsiyakh”, Mekhanika kompozitnykh materialov, 41:4 (2005), 461–488

[2] Paimushin V. N., Polyakova T. V., “Tochnye analiticheskie resheniya zadachi o ploskikh formakh poteri ustoichivosti pryamougolnoi ortotropnoi plastiny s nezakreplennymi krayami v usloviyakh dvukhstoronnego nagruzheniya”, Mekhanika kompozitnykh materialov, 43:2 (2007), 149–170 | MR

[3] Paimushin V. N., Polyakova T. V., “Tochnye analiticheskie resheniya trekhmernoi zadachi o svobodnykh kolebaniyakh ortotropnogo pryamougolnogo parallelepipeda so svobodnymi granyami”, Mekhanika kompozitnykh materialov i konstruktsii, 12, no. 3, In-t prikl. mekhaniki RAN, M., 2006, 317–336

[4] Bolotin V. V., Nekonservativnye zadachi teorii uprugoi ustoichivosti, Gos. izd-vo fiz.-mat. lit., M., 1961, 340 pp. | MR

[5] Rikrads R. B., Teters G. A., Ustoichivost obolochek iz kompozitnykh materialov, Zinatne, Riga, 1974, 310 pp.

[6] Paimushin V. N., Khusainov V. R., “Uravneniya i klassifikatsiya svobodnykh i sobstvennykh kolebanii simmetrichnykh po tolschine trekhsloinykh plastin s transversalno-myagkim zapolnitelem”, Mekhanika kompozitnykh materialov i konstruktsii, 7, no. 3, In-t prikl. mekhaniki RAN, M., 2001, 310–317