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Erschienen in: Mechanics of Composite Materials 1/2011

01.03.2011

On the classes of problems for deformable one-layer and multilayer thin bodies solvable by the asymptotic method

verfasst von: L. A. Aghalovyan

Erschienen in: Mechanics of Composite Materials | Ausgabe 1/2011

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Abstract

A survey of studies by the author and his disciples on the solution of some classes of problems for deformable thin bodies (strip-beams, plates, and shells) is presented. Classical and nonclassical boundary-value problems of the statics and dynamics of anisotropic and layered bodies are considered. Free and forced vibrations of one-layer and multilayer thin bodies are investigated. The coupled problems of thermoelasticity are solved.

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15.
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17.
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18.
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19.
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22.
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23.
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24.
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25.
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26.
Zurück zum Zitat L. A. Aghalovyan and A. M. Poghosyan, “Forced vibrations of a two-layer orthotropic plate with Coulomb friction between the layers,” Izv. Nats. Akad. Nauk Resp. Armen., Mekhanika, 58, No. 3, 36–47 (2005). L. A. Aghalovyan and A. M. Poghosyan, “Forced vibrations of a two-layer orthotropic plate with Coulomb friction between the layers,” Izv. Nats. Akad. Nauk Resp. Armen., Mekhanika, 58, No. 3, 36–47 (2005).
27.
Zurück zum Zitat L. A. Aghalovyan and A. M. Poghosyan, “Forced vibrations of a three-layer orthotropic plate at an incomplete contact between the lower layers,” Izv. Nats. Akad. Nauk Resp.Armen., Mekhanika, 60, No. 3, 46–56 (2007). L. A. Aghalovyan and A. M. Poghosyan, “Forced vibrations of a three-layer orthotropic plate at an incomplete contact between the lower layers,” Izv. Nats. Akad. Nauk Resp.Armen., Mekhanika, 60, No. 3, 46–56 (2007).
28.
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29.
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30.
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31.
Zurück zum Zitat M. L. Aghalovyan, “On the character of forced vibrations of plates with the general anisotropy,” in: Trans. Int. Conf.: XVIII Sess. Int. School Models Mech. Contin. Medium [in Russian], Izd. Saratov. Univ., Saratov (2007), pp. 14–18. M. L. Aghalovyan, “On the character of forced vibrations of plates with the general anisotropy,” in: Trans. Int. Conf.: XVIII Sess. Int. School Models Mech. Contin. Medium [in Russian], Izd. Saratov. Univ., Saratov (2007), pp. 14–18.
32.
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33.
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34.
Zurück zum Zitat M. Z. Sargsyan, “On the forced vibrations of orthotropic plates freely lying on a rigid substrate with account of viscous friction,” in: Trans. Int. School-Conf. Young Sci. Mechanics [in Russian], Yerevan (2009), pp. 297–303. M. Z. Sargsyan, “On the forced vibrations of orthotropic plates freely lying on a rigid substrate with account of viscous friction,” in: Trans. Int. School-Conf. Young Sci. Mechanics [in Russian], Yerevan (2009), pp. 297–303.
35.
Zurück zum Zitat L. A. Aghalovyan and R. S. Ghevorkyan, “Asymptotic solution of the first boundary-value problem of elasticity theory on the forced vibrations of an isotropic strip,” Prikl. Matem. Mekh., 72, Iss. 4, 633–643 (2008). L. A. Aghalovyan and R. S. Ghevorkyan, “Asymptotic solution of the first boundary-value problem of elasticity theory on the forced vibrations of an isotropic strip,” Prikl. Matem. Mekh., 72, Iss. 4, 633–643 (2008).
36.
Zurück zum Zitat L. A. Aghalovyan and T. V. Zakaryan, “On the asymptotics of forced vibrations of an orthotropic strip,” Dokl. Nat. Akad. Nauk Resp. Armen., 107, No. 2, 173–178 (2007). L. A. Aghalovyan and T. V. Zakaryan, “On the asymptotics of forced vibrations of an orthotropic strip,” Dokl. Nat. Akad. Nauk Resp. Armen., 107, No. 2, 173–178 (2007).
37.
Zurück zum Zitat T. V. Zakaryan, “On the first dynamic boundary-value problem of elasticity theory for a two-layer orthotropic strip,” Izv. Nats. Akad. Nauk Resp. Armen. Mekhanika, 61, No. 3, 41–50 (2008). T. V. Zakaryan, “On the first dynamic boundary-value problem of elasticity theory for a two-layer orthotropic strip,” Izv. Nats. Akad. Nauk Resp. Armen. Mekhanika, 61, No. 3, 41–50 (2008).
38.
Zurück zum Zitat L. A. Aghalovyan and T. V. Zakaryan, “On the solution of the first dynamic three-dimensional boundary-value problem for an orthotropic rectangular plate,” Dokl. Nats. Akad. Nauk Armen., 109, No. 4, 304–309 (2009). L. A. Aghalovyan and T. V. Zakaryan, “On the solution of the first dynamic three-dimensional boundary-value problem for an orthotropic rectangular plate,” Dokl. Nats. Akad. Nauk Armen., 109, No. 4, 304–309 (2009).
39.
Zurück zum Zitat L. A. Aghalovyan and T. V. Zakaryan, “Asymptotic solution of the first dynamic boundary-value problem of elasticity theory for an orthotropic strip,” in Actual Problems of Mechanics of Continuum Medium [in Russian], Yerevan (2007), pp. 21–27. L. A. Aghalovyan and T. V. Zakaryan, “Asymptotic solution of the first dynamic boundary-value problem of elasticity theory for an orthotropic strip,” in Actual Problems of Mechanics of Continuum Medium [in Russian], Yerevan (2007), pp. 21–27.
40.
Zurück zum Zitat T. V. Zakaryan, “On the boundary layer in a three-dimensional problem on forced vibrations of orthotropic plates,” in: Trans. Int. School-Conf. Young Sci. Mechanics [in Russian], Yerevan (2009), pp. 214–218. T. V. Zakaryan, “On the boundary layer in a three-dimensional problem on forced vibrations of orthotropic plates,” in: Trans. Int. School-Conf. Young Sci. Mechanics [in Russian], Yerevan (2009), pp. 214–218.
41.
Zurück zum Zitat L. A. Aghalovyan and M. L. Aghalovyan, “Nonclassical boundary-value problems on the free and forced vibrations of anisotropic plates,” in Mechanics of Shells and Plates, Trans. XIX Int. Conf. Theor. Shells Plates [in Russian], Nizhnii Novgorod (1999), pp. 16–20. L. A. Aghalovyan and M. L. Aghalovyan, “Nonclassical boundary-value problems on the free and forced vibrations of anisotropic plates,” in Mechanics of Shells and Plates, Trans. XIX Int. Conf. Theor. Shells Plates [in Russian], Nizhnii Novgorod (1999), pp. 16–20.
42.
Zurück zum Zitat L. A. Aghalovyan and M. L. Aghalovyan, “To the determination of frequencies and modes of free vibrations of orthotropic strips,” Dokl. Nats. Akad. Nauk Resp. Armen., 103, No. 4, 296–301 (2003). L. A. Aghalovyan and M. L. Aghalovyan, “To the determination of frequencies and modes of free vibrations of orthotropic strips,” Dokl. Nats. Akad. Nauk Resp. Armen., 103, No. 4, 296–301 (2003).
43.
Zurück zum Zitat L. A. Aghalovyan and L. G. Ghulghazaryan, “On the frequencies of free vibrations and on the boundary layer of an orthotropic plate in mixed boundary-value problems,” Izv. Nats. Akad. Nauk Resp. Armen. Mekhanika, 54, No. 2, 32–41 (2001). L. A. Aghalovyan and L. G. Ghulghazaryan, “On the frequencies of free vibrations and on the boundary layer of an orthotropic plate in mixed boundary-value problems,” Izv. Nats. Akad. Nauk Resp. Armen. Mekhanika, 54, No. 2, 32–41 (2001).
44.
Zurück zum Zitat L. A. Aghalovyan and R. Zh. Oghanesyan, “Asymptotics of free vibrations of a three-layer orthotropic plate under mixed boundary-value conditions,” in: Trans. V Int. Conf. Probl. Dynam. Interact. Deform. Media [in Russian], Gitutyun, Yerevan (2005), pp. 14–22. L. A. Aghalovyan and R. Zh. Oghanesyan, “Asymptotics of free vibrations of a three-layer orthotropic plate under mixed boundary-value conditions,” in: Trans. V Int. Conf. Probl. Dynam. Interact. Deform. Media [in Russian], Gitutyun, Yerevan (2005), pp. 14–22.
45.
Zurück zum Zitat R. Zh. Oghanesyan, “On the solution of boundary layer in the problem on free vibrations of orthotropic plates,” Izv. Nats. Akad. Nauk Armen. Mekhanika, 57, No. 3, 32–37 (2004). R. Zh. Oghanesyan, “On the solution of boundary layer in the problem on free vibrations of orthotropic plates,” Izv. Nats. Akad. Nauk Armen. Mekhanika, 57, No. 3, 32–37 (2004).
46.
Zurück zum Zitat L. A. Aghalovyan and M. L. Aghalovyan, Asymptotics of Free Vibrations of Anisotropic Plates Fastened with an Absolutely Rigid Base, Modern Probl. Deform. Bodies. Mechanics., Yerevan, Vol. 1(2005), pp. 8–19. L. A. Aghalovyan and M. L. Aghalovyan, Asymptotics of Free Vibrations of Anisotropic Plates Fastened with an Absolutely Rigid Base, Modern Probl. Deform. Bodies. Mechanics., Yerevan, Vol. 1(2005), pp. 8–19.
47.
Zurück zum Zitat L. A. Aghalovyan and T. V. Zakaryan, “On the frequencies and modes of free vibrations of an orthotropic strip with free longitudinal edges,” Problems of Dynamic Interaction of Deformable Media [in Russian], Yerevan, (2008), pp. 36–42. L. A. Aghalovyan and T. V. Zakaryan, “On the frequencies and modes of free vibrations of an orthotropic strip with free longitudinal edges,” Problems of Dynamic Interaction of Deformable Media [in Russian], Yerevan, (2008), pp. 36–42.
48.
Zurück zum Zitat L. A. Aghalovyan and L. G. Ghulghazaryan, “Nonclassical boundary-value problems on forced vibrations of orthotropic shells,” Prikl. Mekh., 45, No. 8, 105–122 (2009). L. A. Aghalovyan and L. G. Ghulghazaryan, “Nonclassical boundary-value problems on forced vibrations of orthotropic shells,” Prikl. Mekh., 45, No. 8, 105–122 (2009).
49.
Zurück zum Zitat L. A. Aghalovyan, R. S. Gevorgyan, and L. G. Ghulghazaryan, “The asymptotic solution of 3D dynamic problems for orthotropic cylindrical and toroidal shells,” in: Proc. NAS RA. Mechanics, 63, No. 1, 6–22 (2010). L. A. Aghalovyan, R. S. Gevorgyan, and L. G. Ghulghazaryan, “The asymptotic solution of 3D dynamic problems for orthotropic cylindrical and toroidal shells,” in: Proc. NAS RA. Mechanics, 63, No. 1, 6–22 (2010).
50.
Zurück zum Zitat L. A. Aghalovyan and L. G. Ghulghazaryan, “Asymptotic solutions of non-classical boundary-value problems of the natural vibrations of orthotropic shells,” J. Appl. Math. Mech., 70, 102–115 (2006).CrossRef L. A. Aghalovyan and L. G. Ghulghazaryan, “Asymptotic solutions of non-classical boundary-value problems of the natural vibrations of orthotropic shells,” J. Appl. Math. Mech., 70, 102–115 (2006).CrossRef
51.
Zurück zum Zitat R. S. Ghevorkyan, “Asymptotic solutions of coupled dynamic problems of thermoelasticity for isotropic plates,” Prikl. Matem. Mekh., 72, Iss.1, 148–156 (2008). R. S. Ghevorkyan, “Asymptotic solutions of coupled dynamic problems of thermoelasticity for isotropic plates,” Prikl. Matem. Mekh., 72, Iss.1, 148–156 (2008).
Metadaten
Titel
On the classes of problems for deformable one-layer and multilayer thin bodies solvable by the asymptotic method
verfasst von
L. A. Aghalovyan
Publikationsdatum
01.03.2011
Verlag
Springer US
Erschienen in
Mechanics of Composite Materials / Ausgabe 1/2011
Print ISSN: 0191-5665
Elektronische ISSN: 1573-8922
DOI
https://doi.org/10.1007/s11029-011-9187-9

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