메뉴 건너뛰기




Volumn 70, Issue 12, 2007, Pages 1430-1450

Free vibration of generally supported rectangular Kirchhoff plates: State-space-based differential quadrature method

Author keywords

Differential quadrature; Internal line supports; Joint coupling matrices; Mixed boundaries; Natural frequency; State space

Indexed keywords

BOUNDARY CONDITIONS; NATURAL FREQUENCIES; PLATES (STRUCTURAL COMPONENTS); TRANSFER MATRIX METHOD; VIBRATIONS (MECHANICAL);

EID: 34250341228     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.1929     Document Type: Article
Times cited : (30)

References (41)
  • 1
    • 0002277941 scopus 로고
    • Plate vibration research, 1976-1980: Classical theory
    • Leissa AW. Plate vibration research, 1976-1980: classical theory. The Shock and Vibration Digest 1981; 13(9): 11-22.
    • (1981) The Shock and Vibration Digest , vol.13 , Issue.9 , pp. 11-22
    • Leissa, A.W.1
  • 2
    • 0002277941 scopus 로고
    • Plate vibration research, 1976-1980: Complicating effects
    • Leissa AW. Plate vibration research, 1976-1980: complicating effects. The Shock and Vibration Digest 1981; 13(10):19-36.
    • (1981) The Shock and Vibration Digest , vol.13 , Issue.10 , pp. 19-36
    • Leissa, A.W.1
  • 3
    • 0002669431 scopus 로고
    • Recent research in plate vibrations: 1981-1985. Part I: Classical theory
    • Leissa AW. Recent research in plate vibrations: 1981-1985. Part I: Classical theory. The Shock and Vibration Digest 1987; 19(2):11-18.
    • (1987) The Shock and Vibration Digest , vol.19 , Issue.2 , pp. 11-18
    • Leissa, A.W.1
  • 4
    • 0023315801 scopus 로고
    • Recent research in plate vibrations: 1981-1985. Part II: Complicating effects
    • Leissa AW. Recent research in plate vibrations: 1981-1985. Part II: Complicating effects. The Shock and Vibration Digest 1981; 19(3):10-24.
    • (1981) The Shock and Vibration Digest , vol.19 , Issue.3 , pp. 10-24
    • Leissa, A.W.1
  • 6
    • 85143418088 scopus 로고
    • Determination of natural frequencies of continuous plates hinged along two opposite edges
    • Veletsos AS, Newmark NM. Determination of natural frequencies of continuous plates hinged along two opposite edges. Journal of Applied Mechanics (ASME) 1956; 23(1):97-102.
    • (1956) Journal of Applied Mechanics (ASME) , vol.23 , Issue.1 , pp. 97-102
    • Veletsos, A.S.1    Newmark, N.M.2
  • 7
    • 0018518277 scopus 로고
    • Eigenfrequencies of continuous plates with arbitrary number of equal spans
    • Elishakoff I, Sternberg A. Eigenfrequencies of continuous plates with arbitrary number of equal spans. Journal of Applied Mechanics (ASME) 1979; 46(3):656-662.
    • (1979) Journal of Applied Mechanics (ASME) , vol.46 , Issue.3 , pp. 656-662
    • Elishakoff, I.1    Sternberg, A.2
  • 8
    • 0021757549 scopus 로고
    • The receptance method applied to the free vibration of continuous rectangular plates
    • Azimi S, Hamilton JF, Soedel W. The receptance method applied to the free vibration of continuous rectangular plates. Journal of Sound and Vibration 1984; 93(1):9-29.
    • (1984) Journal of Sound and Vibration , vol.93 , Issue.1 , pp. 9-29
    • Azimi, S.1    Hamilton, J.F.2    Soedel, W.3
  • 11
    • 0023647914 scopus 로고
    • The flexural vibration of line supported rectangular plate systems
    • Kim SC, Dickinson SM. The flexural vibration of line supported rectangular plate systems. Journal of Sound and Vibration 1987; 114(1):129-142.
    • (1987) Journal of Sound and Vibration , vol.114 , Issue.1 , pp. 129-142
    • Kim, S.C.1    Dickinson, S.M.2
  • 12
    • 0026419752 scopus 로고
    • Vibration analysis of multi-span plates having orthogonal straight edges
    • Liew KM, Lam KY. Vibration analysis of multi-span plates having orthogonal straight edges. Journal of Sound and Vibration 1991; 147(2):255-264.
    • (1991) Journal of Sound and Vibration , vol.147 , Issue.2 , pp. 255-264
    • Liew, K.M.1    Lam, K.Y.2
  • 13
    • 0000727982 scopus 로고    scopus 로고
    • Free vibration of line supported rectangular plates using a set of static beam functions
    • Zhou D, Cheung YK. Free vibration of line supported rectangular plates using a set of static beam functions. Journal of Sound and Vibration 1999; 223(2):231-245.
    • (1999) Journal of Sound and Vibration , vol.223 , Issue.2 , pp. 231-245
    • Zhou, D.1    Cheung, Y.K.2
  • 14
    • 0037145686 scopus 로고    scopus 로고
    • Discrete singular convolution and its application to the analysis of plates with internal supports. Part 1: Theory and algorithm
    • Wei GW, Zhao YB, Xiang Y. Discrete singular convolution and its application to the analysis of plates with internal supports. Part 1: Theory and algorithm. International Journal for Numerical Methods in Engineering 2002; 55(8):913-946.
    • (2002) International Journal for Numerical Methods in Engineering , vol.55 , Issue.8 , pp. 913-946
    • Wei, G.W.1    Zhao, Y.B.2    Xiang, Y.3
  • 15
    • 0037145689 scopus 로고    scopus 로고
    • Discrete singular convolution and its application to the analysis of plates with internal supports. Part 2: Applications
    • Xiang Y, Zhao YB, Wei GW. Discrete singular convolution and its application to the analysis of plates with internal supports. Part 2: Applications. International Journal for Numerical Methods in Engineering 2002; 55(8):947-971.
    • (2002) International Journal for Numerical Methods in Engineering , vol.55 , Issue.8 , pp. 947-971
    • Xiang, Y.1    Zhao, Y.B.2    Wei, G.W.3
  • 16
    • 29144447722 scopus 로고    scopus 로고
    • Accurate analytical type solutions for free vibration frequencies and mode shapes of multi-span bridge decks: The span-by-span approach
    • Gorman DJ, Garibaldi L. Accurate analytical type solutions for free vibration frequencies and mode shapes of multi-span bridge decks: the span-by-span approach. Journal of Sound and Vibration 2006; 290(1-2):321-336.
    • (2006) Journal of Sound and Vibration , vol.290 , Issue.1-2 , pp. 321-336
    • Gorman, D.J.1    Garibaldi, L.2
  • 17
    • 0021306982 scopus 로고
    • A review and catalogue of plate bending elements
    • Hrabok MM, Hrudley TM. A review and catalogue of plate bending elements. Computers and Structures 1984; 19(3):479-495.
    • (1984) Computers and Structures , vol.19 , Issue.3 , pp. 479-495
    • Hrabok, M.M.1    Hrudley, T.M.2
  • 18
    • 0014767317 scopus 로고
    • The effectiveness of excessive nodal continuities in the finite element analysis of thin rectangular and skew plates in bending
    • Smith IM, William D. The effectiveness of excessive nodal continuities in the finite element analysis of thin rectangular and skew plates in bending. International Journal for Numerical Methods in Engineering 1970; 2(2):253-257.
    • (1970) International Journal for Numerical Methods in Engineering , vol.2 , Issue.2 , pp. 253-257
    • Smith, I.M.1    William, D.2
  • 20
    • 34250360433 scopus 로고
    • Frequency analysis of certain single and continuous span bridges
    • Rockey KC, Bannister JL, Evans HR eds, Crosby Lockwood
    • Cheung MS, Cheung YK, Reddy DV. Frequency analysis of certain single and continuous span bridges. In Developments in Bridges Design and Construction, Rockey KC, Bannister JL, Evans HR (eds). Crosby Lockwood: 1971; 188-199.
    • (1971) Developments in Bridges Design and Construction , pp. 188-199
    • Cheung, M.S.1    Cheung, Y.K.2    Reddy, D.V.3
  • 21
    • 0027590434 scopus 로고
    • Finite strip-elements for the dynamic analysis of orthotropic plate structures
    • Golley BW, Petrolito J. Finite strip-elements for the dynamic analysis of orthotropic plate structures. Journal of Sound and Vibration 1993; 163(3):479-491.
    • (1993) Journal of Sound and Vibration , vol.163 , Issue.3 , pp. 479-491
    • Golley, B.W.1    Petrolito, J.2
  • 22
    • 85024283381 scopus 로고
    • Eigenvalue problems of rectangular plates with mixed edge conditions
    • Keer LM, Stahl B. Eigenvalue problems of rectangular plates with mixed edge conditions. Journal of Applied Mechanics (ASME) 1972; 39(2):513-520.
    • (1972) Journal of Applied Mechanics (ASME) , vol.39 , Issue.2 , pp. 513-520
    • Keer, L.M.1    Stahl, B.2
  • 23
    • 0019875520 scopus 로고
    • Application of a series-type method to vibration of orthotropic rectangular plates with mixed boundary conditions
    • Narita Y. Application of a series-type method to vibration of orthotropic rectangular plates with mixed boundary conditions. Journal of Sound and Vibration 1981; 77(3):345-355.
    • (1981) Journal of Sound and Vibration , vol.77 , Issue.3 , pp. 345-355
    • Narita, Y.1
  • 25
    • 0021757554 scopus 로고
    • Flexural free vibrations of rectangular plates with complex supported conditions
    • Fan SC, Cheung YK. Flexural free vibrations of rectangular plates with complex supported conditions. Journal of Sound and Vibration 1984; 93(1):81-94.
    • (1984) Journal of Sound and Vibration , vol.93 , Issue.1 , pp. 81-94
    • Fan, S.C.1    Cheung, Y.K.2
  • 26
    • 0021386374 scopus 로고
    • An exact analytical approach to the free vibration analysis of rectangular plates with mixed boundary conditions
    • Gorman DJ. An exact analytical approach to the free vibration analysis of rectangular plates with mixed boundary conditions. Journal of Sound and Vibration 1984; 93(2):235-247.
    • (1984) Journal of Sound and Vibration , vol.93 , Issue.2 , pp. 235-247
    • Gorman, D.J.1
  • 27
    • 0027628074 scopus 로고
    • Roles of domain decomposition method in plate vibrations: Treatment of mixed discontinuous periphery boundaries
    • Liew KM, Hung KC, Lim MK. Roles of domain decomposition method in plate vibrations: treatment of mixed discontinuous periphery boundaries. International Journal of Mechanical Science 1993; 35(7):615-632.
    • (1993) International Journal of Mechanical Science , vol.35 , Issue.7 , pp. 615-632
    • Liew, K.M.1    Hung, K.C.2    Lim, M.K.3
  • 29
    • 0028457971 scopus 로고
    • Analysis of vibrating rectangular plates with non-uniform boundary conditions by using the differential quadrature method
    • Laura PAA, Gutierrez RH. Analysis of vibrating rectangular plates with non-uniform boundary conditions by using the differential quadrature method. Journal of Sound and Vibration 1994; 173(5):702-706.
    • (1994) Journal of Sound and Vibration , vol.173 , Issue.5 , pp. 702-706
    • Laura, P.A.A.1    Gutierrez, R.H.2
  • 30
    • 0024014784 scopus 로고
    • Two new approximate methods for analyzing free vibration of structural components
    • Bert CW, Jang SK, Striz AG. Two new approximate methods for analyzing free vibration of structural components. AIAA Journal 1988; 26(5):612-618.
    • (1988) AIAA Journal , vol.26 , Issue.5 , pp. 612-618
    • Bert, C.W.1    Jang, S.K.2    Striz, A.G.3
  • 32
    • 0000800590 scopus 로고    scopus 로고
    • Analysis of vibrating thick rectangular plate with mixed boundary constraints using differential quadrature element method
    • Liu FL, Liew KM. Analysis of vibrating thick rectangular plate with mixed boundary constraints using differential quadrature element method. Journal of Sound and Vibration 1999; 225(5):915-934.
    • (1999) Journal of Sound and Vibration , vol.225 , Issue.5 , pp. 915-934
    • Liu, F.L.1    Liew, K.M.2
  • 33
    • 1542644014 scopus 로고    scopus 로고
    • Static and free vibration analyses of rectangular plates by the new version of the differential quadrature element method
    • Wang YL, Wang XW, Zhou Y. Static and free vibration analyses of rectangular plates by the new version of the differential quadrature element method. International Journal for Numerical Methods in Engineering 2004; 59(9):1207-1226.
    • (2004) International Journal for Numerical Methods in Engineering , vol.59 , Issue.9 , pp. 1207-1226
    • Wang, Y.L.1    Wang, X.W.2    Zhou, Y.3
  • 34
    • 0041517714 scopus 로고    scopus 로고
    • Elasticity solution for free vibration of laminated beams
    • Chen WQ, Lv CF, Bian ZG. Elasticity solution for free vibration of laminated beams. Composite Structures 2003; 62(1):75-82.
    • (2003) Composite Structures , vol.62 , Issue.1 , pp. 75-82
    • Chen, W.Q.1    Lv, C.F.2    Bian, Z.G.3
  • 35
    • 0347317892 scopus 로고    scopus 로고
    • Free vibration analysis of generally laminated beams via state-space-based differential quadrature
    • Chen WQ, Lv CF, Bian ZG. Free vibration analysis of generally laminated beams via state-space-based differential quadrature. Composite Structures 2004; 63(3-4):417-425.
    • (2004) Composite Structures , vol.63 , Issue.3-4 , pp. 417-425
    • Chen, W.Q.1    Lv, C.F.2    Bian, Z.G.3
  • 36
    • 0343660288 scopus 로고
    • Dynamic analysis of large space structures using transfer matrices and joint coupling matrices
    • Nagem RJ, Williams JH. Dynamic analysis of large space structures using transfer matrices and joint coupling matrices. Mechanics of Structures and Machines 1989; 17(3):349-371.
    • (1989) Mechanics of Structures and Machines , vol.17 , Issue.3 , pp. 349-371
    • Nagem, R.J.1    Williams, J.H.2
  • 37
    • 33746299849 scopus 로고    scopus 로고
    • Free vibration of long-span continuous rectangular Kirchhoff plates with internal rigid line supports
    • Lü CF, Lee YY, Lim CW, Chen WQ. Free vibration of long-span continuous rectangular Kirchhoff plates with internal rigid line supports. Journal of Sound and Vibration 2006; 297(1-2):351-364.
    • (2006) Journal of Sound and Vibration , vol.297 , Issue.1-2 , pp. 351-364
    • Lü, C.F.1    Lee, Y.Y.2    Lim, C.W.3    Chen, W.Q.4
  • 38
    • 11244327837 scopus 로고    scopus 로고
    • 3D free vibration analysis of cross-ply laminated plates with one pair of opposite edges simply supported
    • Chen WQ, Lü CF. 3D free vibration analysis of cross-ply laminated plates with one pair of opposite edges simply supported. Composite Structures 2005; 69(1-2):77-87.
    • (2005) Composite Structures , vol.69 , Issue.1-2 , pp. 77-87
    • Chen, W.Q.1    Lü, C.F.2
  • 39
    • 0026939625 scopus 로고
    • Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations
    • Shu C, Richards BE. Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations. International Journal for Numerical Methods in Fluids 1992; 15(7):791-798.
    • (1992) International Journal for Numerical Methods in Fluids , vol.15 , Issue.7 , pp. 791-798
    • Shu, C.1    Richards, B.E.2
  • 41
    • 0025749119 scopus 로고
    • Differential quadrature method in the buckling analysis of beams and composite plates
    • Sherbourne AN, Pandey MD. Differential quadrature method in the buckling analysis of beams and composite plates. Computers and Structures 1991; 40(4):903-913.
    • (1991) Computers and Structures , vol.40 , Issue.4 , pp. 903-913
    • Sherbourne, A.N.1    Pandey, M.D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.