메뉴 건너뛰기




Volumn 331, Issue 4, 2003, Pages 303-317

Local problems for vibrating systems with concentrated masses: A review

Author keywords

Concentrated masses; High frequencies; Low frequencies; Spectral analysis

Indexed keywords

VIBRATION;

EID: 0038813791     PISSN: 16310721     EISSN: None     Source Type: Journal    
DOI: 10.1016/S1631-0721(03)00058-5     Document Type: Short Survey
Times cited : (52)

References (41)
  • 1
    • 0021650084 scopus 로고
    • Perturbation of eigenvalues in thermoelasticity and vibration of systems with concentrated masses
    • Trend in Applications of Pure Mathematics to Mechanics, Springer-Verlag, Berlin
    • E. Sanchez-Palencia, Perturbation of eigenvalues in thermoelasticity and vibration of systems with concentrated masses, in: Trend in Applications of Pure Mathematics to Mechanics, in: Lecture Notes in Phys., Vol. 195, Springer-Verlag, Berlin, 1984, pp. 346-368.
    • (1984) Lecture Notes in Phys. , vol.195 , pp. 346-368
    • Sanchez-Palencia, E.1
  • 3
    • 0001815368 scopus 로고
    • Homogenization problems in elasticity. Spectra of singularly perturbed operators
    • R.J. Knops, A.A. Lacey (Eds.), Cambridge University Press, New York
    • O.A. Oleinik, Homogenization problems in elasticity. Spectra of singularly perturbed operators, in: R.J. Knops, A.A. Lacey (Eds.), Non-Classical Continuum Mechanics, Cambridge University Press, New York, 1987, pp. 81-95.
    • (1987) Non-Classical Continuum Mechanics , pp. 81-95
    • Oleinik, O.A.1
  • 5
    • 0002592047 scopus 로고
    • Perturbation of the eigenvalues of a membrane with a concentrated mass
    • C. Leal, J. Sanchez-Hubert, Perturbation of the eigenvalues of a membrane with a concentrated mass, Quart. Appl. Math. XLVII (1) (1989) 93-103.
    • (1989) Quart. Appl. Math. , vol.47 , Issue.1 , pp. 93-103
    • Leal, C.1    Sanchez-Hubert, J.2
  • 6
    • 0000256360 scopus 로고
    • Perturbation des valeurs propres pour des systèmes avec masse concentrée
    • J. Sanchez-Hubert, Perturbation des valeurs propres pour des systèmes avec masse concentrée, C. R. Acad. Sci. Paris, Sér. II 309 (1989) 507-510.
    • (1989) C. R. Acad. Sci. Paris, Sér. II , vol.309 , pp. 507-510
    • Sanchez-Hubert, J.1
  • 10
    • 0000255676 scopus 로고
    • Interaction of concentrated masses in a harmonically oscillating spatial body with Neumann boundary conditions
    • S.A. Nazarov, Interaction of concentrated masses in a harmonically oscillating spatial body with Neumann boundary conditions, Math. Model Numer. Anal. 27 (6) (1993) 777-799.
    • (1993) Math. Model Numer. Anal. , vol.27 , Issue.6 , pp. 777-799
    • Nazarov, S.A.1
  • 11
    • 0002122474 scopus 로고
    • Spectral properties of oscillatory systems with adjoined masses
    • Yu.D. Golovaty, Spectral properties of oscillatory systems with adjoined masses, Trans. Moscow Math. Soc. 54 (1993) 23-59.
    • (1993) Trans. Moscow Math. Soc. , vol.54 , pp. 23-59
    • Golovaty, Yu.D.1
  • 12
    • 0001314471 scopus 로고
    • On vibrations of a body with many concentrated masses near the boundary
    • M. Lobo, E. Pérez, On vibrations of a body with many concentrated masses near the boundary, Math. Models Methods Appl. Sci. 3 (2) (1993) 249-273.
    • (1993) Math. Models Methods Appl. Sci. , vol.3 , Issue.2 , pp. 249-273
    • Lobo, M.1    Pérez, E.2
  • 13
    • 0002948808 scopus 로고
    • Vibrations of a body with many concentrated masses near the boundary: High frequency vibrations
    • E. Sanchez-Palencia (Ed.), Hermann, Paris
    • M. Lobo, E. Pérez, Vibrations of a body with many concentrated masses near the boundary: High frequency vibrations, in: E. Sanchez-Palencia (Ed.), Spectral Analysis of Complex Structures, Hermann, Paris, 1995, pp. 85-101.
    • (1995) Spectral Analysis of Complex Structures , pp. 85-101
    • Lobo, M.1    Pérez, E.2
  • 14
    • 0001363664 scopus 로고
    • Vibrations of a membrane with many concentrated masses near the boundary
    • M. Lobo, E. Pérez, Vibrations of a membrane with many concentrated masses near the boundary, Math. Models Methods Appl. Sci. 5 (5) (1995) 565-585.
    • (1995) Math. Models Methods Appl. Sci. , vol.5 , Issue.5 , pp. 565-585
    • Lobo, M.1    Pérez, E.2
  • 15
    • 0012357678 scopus 로고    scopus 로고
    • On the local vibrations for systems with many concentrated masses
    • M. Lobo, E. Pérez, On the local vibrations for systems with many concentrated masses, C. R. Acad. Sci. Paris, Sér. IIb 324 (1997) 323-329.
    • (1997) C. R. Acad. Sci. Paris, Sér. IIb , vol.324 , pp. 323-329
    • Lobo, M.1    Pérez, E.2
  • 16
    • 0033209552 scopus 로고    scopus 로고
    • On the eigenfunctions associated with the high frequencies in systems with a concentrated mass
    • D. Gómez, M. Lobo, E. Pérez, On the eigenfunctions associated with the high frequencies in systems with a concentrated mass, J. Math. Pures Appl. 78 (1999) 841-865.
    • (1999) J. Math. Pures Appl. , vol.78 , pp. 841-865
    • Gómez, D.1    Lobo, M.2    Pérez, E.3
  • 17
    • 33745461206 scopus 로고    scopus 로고
    • The skin effect in vibrating systems with many concentrated masses
    • M. Lobo, E. Pérez, The skin effect in vibrating systems with many concentrated masses, Math. Methods Appl. Sci. 24 (2001) 59-80.
    • (2001) Math. Methods Appl. Sci. , vol.24 , pp. 59-80
    • Lobo, M.1    Pérez, E.2
  • 18
    • 0037288604 scopus 로고    scopus 로고
    • On the whispering gallery modes on the interfaces of membranescomposed of two materials with very different densities
    • E. Pérez, On the whispering gallery modes on the interfaces of membranescomposed of two materials with very different densities, Math. Models Methods Appl. Sci. 13 (1) (2003) 75-98.
    • (2003) Math. Models Methods Appl. Sci. , vol.13 , Issue.1 , pp. 75-98
    • Pérez, E.1
  • 19
    • 17644432158 scopus 로고    scopus 로고
    • On eigenvibrations of a body with light concentrated masses on the surface
    • G.A. Chechkin, E. Pérez, E.I. Yablokova, On eigenvibrations of a body with light concentrated masses on the surface, Russian Math. Surveys 57 (6) (2002) 195-196.
    • (2002) Russian Math. Surveys , vol.57 , Issue.6 , pp. 195-196
    • Chechkin, G.A.1    Pérez, E.2    Yablokova, E.I.3
  • 20
    • 0037428003 scopus 로고    scopus 로고
    • On the vibrations of a plate with a concentrated mass and very small thickness
    • D. Gómez, M. Lobo, E. Pérez, On the vibrations of a plate with a concentrated mass and very small thickness, Math. Methods Appl. Sci. 26 (2003) 27-65.
    • (2003) Math. Methods Appl. Sci. , vol.26 , pp. 27-65
    • Gómez, D.1    Lobo, M.2    Pérez, E.3
  • 21
    • 85031176992 scopus 로고    scopus 로고
    • Vibrating systems with concentrated masses: On the local problem and the low frequencies
    • C. Constanda, A. Larguillier, M. Ahues (Eds.), Birkhäuser, to appear
    • E. Pérez, Vibrating systems with concentrated masses: on the local problem and the low frequencies, in: C. Constanda, A. Larguillier, M. Ahues (Eds.), Proceedings of the 7th International Conference on Integral Methods in Sciences and Engineering, Birkhäuser, 2003, to appear.
    • (2003) Proceedings of the 7th International Conference on Integral Methods in Sciences and Engineering
    • Pérez, E.1
  • 22
    • 0036856202 scopus 로고    scopus 로고
    • Asymptotics for the eigenelements of vibrating membranes with very heavy thing inclusions
    • Yu.D. Golovaty, D. Gómez, M. Lobo, E. Pérez, Asymptotics for the eigenelements of vibrating membranes with very heavy thing inclusions, C. R. Mécanique 330 (11) (2002) 777-782.
    • (2002) C. R. Mécanique , vol.330 , Issue.11 , pp. 777-782
    • Golovaty, Yu.D.1    Gómez, D.2    Lobo, M.3    Pérez, E.4
  • 23
    • 0347080223 scopus 로고    scopus 로고
    • Vibrations of a thick periodic junction with concentrated masses
    • T. Melnyk, Vibrations of a thick periodic junction with concentrated masses, Math. Models Methods Appl. Sci. 11 (6) (2001) 1001-1027.
    • (2001) Math. Models Methods Appl. Sci. , vol.11 , Issue.6 , pp. 1001-1027
    • Melnyk, T.1
  • 24
    • 3242796463 scopus 로고    scopus 로고
    • High frequency vibrations in a stiff problem
    • M. Lobo, E. Pérez, High frequency vibrations in a stiff problem, Math. Models Methods Appl. Sci. 7 (2) (1997) 291-311.
    • (1997) Math. Models Methods Appl. Sci. , vol.7 , Issue.2 , pp. 291-311
    • Lobo, M.1    Pérez, E.2
  • 25
    • 0011345213 scopus 로고
    • Asymptotic behavior of an elastic body with a surface having small stuck regions
    • M. Lobo, E. Pérez, Asymptotic behavior of an elastic body with a surface having small stuck regions, RAIRO Modél. Math. Anal. Numér. 22 (4) (1988) 609-624.
    • (1988) RAIRO Modél. Math. Anal. Numér. , vol.22 , Issue.4 , pp. 609-624
    • Lobo, M.1    Pérez, E.2
  • 26
    • 0005438842 scopus 로고
    • Homogénéisation de frontieres par epi-convergence en élasticité linéaire
    • A. Brillard, M. Lobo, E. Pérez, Homogénéisation de frontieres par epi-convergence en élasticité linéaire, RAIRO Modél. Math. Anal. Numér. 24 (1) (1990) 5-26.
    • (1990) RAIRO Modél. Math. Anal. Numér. , vol.24 , Issue.1 , pp. 5-26
    • Brillard, A.1    Lobo, M.2    Pérez, E.3
  • 27
    • 0001079911 scopus 로고
    • Boundary homogenization of certain elliptic problems for cylindrical bodies
    • M. Lobo, E. Pérez, Boundary homogenization of certain elliptic problems for cylindrical bodies, Bull. Sci. Math. Sér. IIb 116 (1992) 399-426.
    • (1992) Bull. Sci. Math. Sér. IIb , vol.116 , pp. 399-426
    • Lobo, M.1    Pérez, E.2
  • 28
    • 0002494698 scopus 로고
    • Un terme étrange venu d'ailleurs
    • H. Brezis, J.-L. Lions (Eds.), in: Res. Notes Math., Vol. 60 & 70, Pitman, London, 154-178
    • D. Cioranescu, F. Murat, Un terme étrange venu d'ailleurs, in: H. Brezis, J.-L. Lions (Eds.), Collège de France Séminar, Vol. II & III, in: Res. Notes Math., Vol. 60 & 70, Pitman, London, 1982, pp. 98-138, 154-178.
    • (1982) Collège de France Séminar , vol.2-3 , pp. 98-138
    • Cioranescu, D.1    Murat, F.2
  • 29
    • 0038470603 scopus 로고    scopus 로고
    • On homogenization of solutions of boundary value problems in domains, perforated along manifolds
    • M. Lobo, O.A. Oleinik, T.A. Shaposhnikova, E. Pérez, On homogenization of solutions of boundary value problems in domains, perforated along manifolds, Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 25 (1998) 611-629.
    • (1998) Ann. Scuola Norm. Sup. Pisa Cl. Sci. , vol.25 , Issue.4 , pp. 611-629
    • Lobo, M.1    Oleinik, O.A.2    Shaposhnikova, T.A.3    Pérez, E.4
  • 32
    • 0031539810 scopus 로고    scopus 로고
    • On spectral pollution in the finite element approximation of thin elastic "membrane" shells
    • J. Rappaz, J. Sanchez-Hubert, E. Sanchez-Palencia, D. Vassiliev, On spectral pollution in the finite element approximation of thin elastic "membrane" shells, Numer. Math. 75 (4) (1997) 473-500.
    • (1997) Numer. Math. , vol.75 , Issue.4 , pp. 473-500
    • Rappaz, J.1    Sanchez-Hubert, J.2    Sanchez-Palencia, E.3    Vassiliev, D.4
  • 35
    • 0001561763 scopus 로고
    • Regular degeneration and boundary layer for linear differential equations with small parameter
    • M.I. Visik, L.A. Lusternik, Regular degeneration and boundary layer for linear differential equations with small parameter, Trans. Amer. Math. Soc. Ser. 2 20 (1957) 239-364.
    • (1957) Trans. Amer. Math. Soc. Ser. 2 , vol.20 , pp. 239-364
    • Visik, M.I.1    Lusternik, L.A.2
  • 36
    • 0009041768 scopus 로고
    • Modes and quasimodes
    • V.I. Arnold, Modes and quasimodes, Funct. Anal. Appl. 6 (2) (1972) 94-101.
    • (1972) Funct. Anal. Appl. , vol.6 , Issue.2 , pp. 94-101
    • Arnold, V.I.1
  • 37
    • 0037793857 scopus 로고    scopus 로고
    • Semiclassical asymptotics of eigenfunctions
    • M.V. Fedoryuk (Ed.), Springer-Verlag, Heidelberg
    • V.F. Lazutkin, Semiclassical asymptotics of eigenfunctions, in: M.V. Fedoryuk (Ed.), Partial Differential Equations V, Springer-Verlag, Heidelberg, 1999, pp. 133-171.
    • (1999) Partial Differential Equations V , pp. 133-171
    • Lazutkin, V.F.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.