메뉴 건너뛰기




Volumn 91, Issue 9, 2011, Pages 699-710

On the spectrum and stiffness of an elastic body with surface stresses

Author keywords

Courant's maximum minimum principle.; Eigenfrequencies; Energy spaces of Sobolev's type; Rayleigh variational principle; Surface stresses

Indexed keywords


EID: 80051708270     PISSN: 00442267     EISSN: 15214001     Source Type: Journal    
DOI: 10.1002/zamm.201000214     Document Type: Article
Times cited : (53)

References (29)
  • 1
    • 80051766635 scopus 로고    scopus 로고
    • Sobolev Spaces, 2nd edition, Pure and Applied Mathematics, (Academic Press, Amsterdam).
    • R.A. Adams and J.J.F. Fournier, Sobolev Spaces, 2nd edition, Pure and Applied Mathematics, Vol. 140 (Academic Press, Amsterdam, 2003).
    • (2003) , vol.140
    • Adams, R.A.1    Fournier, J.J.F.2
  • 2
    • 77049092309 scopus 로고    scopus 로고
    • On the existence of solution in the linear elasticity with surface stresses
    • H. Altenbach, V.A. Eremeyev, and L.P. Lebedev, On the existence of solution in the linear elasticity with surface stresses, Z. Angew. Math. Mech. 90(7), 535-536 (2010).
    • (2010) Z. Angew. Math. Mech. , vol.7-90 , pp. 535-536
    • Altenbach, H.1    Eremeyev, V.A.2    Lebedev, L.P.3
  • 3
    • 73349099001 scopus 로고    scopus 로고
    • Linear theory of shells taking into account surface stresses
    • H. Altenbach, V.A. Eremeyev, and N.F. Morozov, Linear theory of shells taking into account surface stresses, Dokl. Phys. 54(12), 531-535 (2009).
    • (2009) Dokl. Phys. , vol.12-54 , pp. 531-535
    • Altenbach, H.1    Eremeyev, V.A.2    Morozov, N.F.3
  • 4
    • 80051737170 scopus 로고    scopus 로고
    • Mathematical Elasticity. Vol. I: Three-Dimensional Elasticity (North-HollAmsterdam, 1988).
    • P. Ciarlet, Mathematical Elasticity. Vol. I: Three-Dimensional Elasticity (North-HollAmsterdam, 1988).
    • Ciarlet, P.1
  • 5
    • 84950242370 scopus 로고    scopus 로고
    • Methods of Mathematical Physics. Vol. I (Wiley, Singapore, 1989).
    • R. Courant and D. Hilbert, Methods of Mathematical Physics. Vol. I (Wiley, Singapore, 1989).
    • Courant, R.1    Hilbert, D.2
  • 6
    • 67249160086 scopus 로고    scopus 로고
    • Theory of elasticity at the nanoscale, in: Advances in Applied Mechanics (Elsevier).
    • H.L. Duan, J. Wang, and B.L. Karihaloo, Theory of elasticity at the nanoscale, in: Advances in Applied Mechanics (Elsevier, 2008) pp. 1-68.
    • (2008) , pp. 1-68
    • Duan, H.L.1    Wang, J.2    Karihaloo, B.L.3
  • 7
    • 33646934932 scopus 로고    scopus 로고
    • Nanoporous materials can be made stiffer than non-porous counterparts by surface modification
    • H.L. Duan, J. Wang, B.L. Karihaloo, and Z.P. Huang, Nanoporous materials can be made stiffer than non-porous counterparts by surface modification, Acta Mater. 54, 2983-2990 (2006).
    • (2006) Acta Mater. , vol.54 , pp. 2983-2990
    • Duan, H.L.1    Wang, J.2    Karihaloo, B.L.3    Huang, Z.P.4
  • 8
    • 66149157755 scopus 로고    scopus 로고
    • The influence of surface tension on the effective stiffness of nanosize plates
    • V.A. Eremeyev, H. Altenbach, and N.F. Morozov, The influence of surface tension on the effective stiffness of nanosize plates, Dokl. Phys. 54(2), 98-100 (2009).
    • (2009) Dokl. Phys. , vol.2-54 , pp. 98-100
    • Eremeyev, V.A.1    Altenbach, H.2    Morozov, N.F.3
  • 9
    • 0000390501 scopus 로고
    • Existence theorems in elasticity, in: Handbuch der Physik, edited by S. Flügge (Springer, Berlin).
    • G. Fichera, Existence theorems in elasticity, in: Handbuch der Physik, edited by S. Flügge (Springer, Berlin, 1972) pp. 347-389.
    • (1972) , pp. 347-389
    • Fichera, G.1
  • 10
    • 0041305370 scopus 로고
    • Effect of surface stress on natural frequency of thin crystals
    • M.E. Gurtin, X. Markenscoff, and R.N. Thurston, Effect of surface stress on natural frequency of thin crystals, Appl. Phys. Lett. 29(9), 529-530 (1976).
    • (1976) Appl. Phys. Lett. , vol.9-29 , pp. 529-530
    • Gurtin, M.E.1    Markenscoff, X.2    Thurston, R.N.3
  • 11
    • 0016441185 scopus 로고
    • A continuum theory of elastic material surfaces
    • M.E. Gurtin and A.I. Murdoch, A continuum theory of elastic material surfaces, Arch. Ration. Mech. Anal. 57(4), 291-323 (1975).
    • (1975) Arch. Ration. Mech. Anal. , vol.4-57 , pp. 291-323
    • Gurtin, M.E.1    Murdoch, A.I.2
  • 12
    • 0041305377 scopus 로고
    • Surface stress and normal mode of vibration of thin crystals: GaAs
    • J. Lagowski, H.C. Gatos, and E.S. Sproles, Surface stress and normal mode of vibration of thin crystals: GaAs, Appl. Phys. Lett. 26(9), 493-495 (1975).
    • (1975) Appl. Phys. Lett. , vol.9-26 , pp. 493-495
    • Lagowski, J.1    Gatos, H.C.2    Sproles, E.S.3
  • 13
    • 84995480026 scopus 로고    scopus 로고
    • Tensor Analysis with Applications in Mechanics (World Scientific, New Jersey).
    • L.P. Lebedev, M.J. Cloud, and V.A. Eremeyev, Tensor Analysis with Applications in Mechanics (World Scientific, New Jersey, 2010).
    • (2010)
    • Lebedev, L.P.1    Cloud, M.J.2    Eremeyev, V.A.3
  • 14
    • 80051738136 scopus 로고    scopus 로고
    • Functional Analysis in Mechanics (Springer, New York, 2003).
    • L.P. Lebedev and I.I. Vorovich, Functional Analysis in Mechanics (Springer, New York, 2003).
    • Lebedev, L.P.1    Vorovich, I.I.2
  • 15
    • 0040190749 scopus 로고    scopus 로고
    • Functional Analysis. Applications in Mechanics and Inverse Problems, 2nd edition, Solid Mechanics and Its Applications, (Kluwer, New York).
    • L.P. Lebedev, I.I. Vorovich, and G.M.L. Gladwell, Functional Analysis. Applications in Mechanics and Inverse Problems, 2nd edition, Solid Mechanics and Its Applications, Vol. 100 (Kluwer, New York, 2002).
    • (2002) , vol.100
    • Lebedev, L.P.1    Vorovich, I.I.2    Gladwell, G.M.L.3
  • 16
    • 80051770803 scopus 로고    scopus 로고
    • A Treatise on the Mathematical Theory of Elasticity, 4th edition (Dover, New York, 1944).
    • A.E.H. Love, A Treatise on the Mathematical Theory of Elasticity, 4th edition (Dover, New York, 1944).
    • Love, A.E.H.1
  • 17
    • 80051743691 scopus 로고    scopus 로고
    • Theory of Elasticity (in Polish) (Państwowe Wydawnictwo Naukowe, Warsaw, 1970).
    • W. Nowacki, Theory of Elasticity (in Polish) (Państwowe Wydawnictwo Naukowe, Warsaw, 1970).
    • Nowacki, W.1
  • 18
    • 80051771601 scopus 로고    scopus 로고
    • Introduction to Mechanics of Surface Phenomena in Deformable Solids (in Russian) (Naukova Dumka, Kiev, 1985).
    • Y.S. Podstrigach and Y.Z. Povstenko, Introduction to Mechanics of Surface Phenomena in Deformable Solids (in Russian) (Naukova Dumka, Kiev, 1985).
    • Podstrigach, Y.S.1    Povstenko, Y.Z.2
  • 19
    • 0348081150 scopus 로고
    • Theoretical investigation of phenomena caused by heterogeneous surface tension in solids
    • Y.Z. Povstenko, Theoretical investigation of phenomena caused by heterogeneous surface tension in solids, J. Mech. Phys. Solids 41(9), 1499-1514 (1993).
    • (1993) J. Mech. Phys. Solids , vol.9-41 , pp. 1499-1514
    • Povstenko, Y.Z.1
  • 20
    • 0343625613 scopus 로고
    • Integral equation methods in plane-strain elasticity with boundary reinforcement, 1998).
    • P. Schiavone and C.Q. Ru, Integral equation methods in plane-strain elasticity with boundary reinforcement, Proc. R. Soc. Lond. A, Math. Phys. Eng. Sci. 454(1976), 2223-2242 (1998).
    • (1976) Proc. R. Soc. Lond. A, Math. Phys. Eng. Sci. , vol.454 , pp. 2223-2242
    • Schiavone, P.1    Ru, C.Q.2
  • 21
    • 71649084796 scopus 로고    scopus 로고
    • Solvability of boundary value problems in a theory of plane-strain elasticity with boundary reinforcement, 1331-1338 ().
    • P. Schiavone and C.Q. Ru, Solvability of boundary value problems in a theory of plane-strain elasticity with boundary reinforcement, Int. J. Eng. Sci. 47(11-12), 1331-1338 (2009).
    • (2009) Int. J. Eng. Sci. , vol.47 , pp. 11-12
    • Schiavone, P.1    Ru, C.Q.2
  • 22
    • 70349319345 scopus 로고    scopus 로고
    • Modeling of surface stress effects on bending behavior of nanowires: Incremental deformation theory
    • F. Song and G.L. Huang, Modeling of surface stress effects on bending behavior of nanowires: Incremental deformation theory, Phys. Lett. A 373(43), 3969-3973 (2009).
    • (2009) Phys. Lett. A , vol.43-373 , pp. 3969-3973
    • Song, F.1    Huang, G.L.2
  • 24
    • 80051717540 scopus 로고    scopus 로고
    • Vibration Problems in Engineering, 2nd edition (D. van Nostrand Company, New York, 1928);, Vibration Problems in Engineering, 5th edition (Wiley, New York, 1990).
    • S. Timoshenko, Vibration Problems in Engineering, 2nd edition (D. van Nostrand Company, New York, 1928); W. Weaver, S. Timoshenko, and D.H. Young, Vibration Problems in Engineering, 5th edition (Wiley, New York, 1990).
    • Timoshenko, S.1    Weaver, W.2    Timoshenko, S.3    Young, D.H.4
  • 25
    • 34250743139 scopus 로고    scopus 로고
    • Effects of surface elasticity and residual surface tension on the natural frequency of microbeams
    • G.F. Wang and X.Q. Feng, Effects of surface elasticity and residual surface tension on the natural frequency of microbeams, Appl. Phys. Lett. 90(23), 231904 (2007).
    • (2007) Appl. Phys. Lett. , vol.23-373 , pp. 231904
    • Wang, G.F.1    Feng, X.Q.2
  • 26
    • 78751643234 scopus 로고    scopus 로고
    • Effect of surface stresses on the vibration and buckling of piezoelectric nanowires
    • G.F. Wang and X.Q. Feng, Effect of surface stresses on the vibration and buckling of piezoelectric nanowires, Europhys. Lett. 91(5), 56007 (2010).
    • (2010) Europhys. Lett. , vol.5-91 , pp. 56007
    • Wang, G.F.1    Feng, X.Q.2
  • 27
    • 72949090381 scopus 로고    scopus 로고
    • The effects of surface tension on the elastic properties of nano structures
    • Z.Q. Wang, Y.P. Zhao, and Z.P. Huang, The effects of surface tension on the elastic properties of nano structures, Int. J. Eng. Sci. 48(2), 140-150 (2010).
    • (2010) Int. J. Eng. Sci. , vol.2-48 , pp. 140-150
    • Wang, Z.Q.1    Zhao, Y.P.2    Huang, Z.P.3
  • 28
    • 51349169425 scopus 로고    scopus 로고
    • The effects of surface and initial stresses on the bending stiffness of nanowires
    • H.X. Zhu, The effects of surface and initial stresses on the bending stiffness of nanowires, Nanotechnology 19(40), 405703 (2008).
    • (2008) Nanotechnology , vol.19-48 , pp. 405703
    • Zhu, H.X.1
  • 29
    • 70350430138 scopus 로고    scopus 로고
    • Effects of surface and initial stresses on the bending stiffness of trilayer plates and nanofilms
    • H.X. Zhu, J.X. Wang, and B.L. Karihaloo, Effects of surface and initial stresses on the bending stiffness of trilayer plates and nanofilms, J. Mech. Mater. Struct. 4(3), 589-604 (2009).
    • (2009) J. Mech. Mater. Struct. , vol.3-4 , pp. 589-604
    • Zhu, H.X.1    Wang, J.X.2    Karihaloo, B.L.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.