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Volumn 25, Issue 2, 2007, Pages 201-217

Nonlinear dynamic response of MDOF systems by the method of harmonic differential quadrature (HDQ)

Author keywords

Harmonic differential quadrature; Nonlinear analysis; Structural dynamics

Indexed keywords

DEGREES OF FREEDOM (MECHANICS); DYNAMIC ANALYSIS; DYNAMIC RESPONSE; NONLINEAR ANALYSIS; NUMERICAL METHODS; PROBLEM SOLVING;

EID: 34147185193     PISSN: 12254568     EISSN: None     Source Type: Journal    
DOI: 10.12989/sem.2007.25.2.201     Document Type: Article
Times cited : (14)

References (48)
  • 2
    • 84985822198 scopus 로고
    • Stability and accuracy analysis of direct integration methods
    • Bathe, K.J. and Wilson, E.L. (1973), "Stability and accuracy analysis of direct integration methods", Earthq. Eng. Struct. Dyn., 1, 283-291.
    • (1973) Earthq. Eng. Struct. Dyn , vol.1 , pp. 283-291
    • Bathe, K.J.1    Wilson, E.L.2
  • 3
    • 0024014784 scopus 로고
    • Two new approximate methods for analyzing free vibration of structural components
    • Bert, C.W., Jang, S.K. and Striz, A.G. (1987), "Two new approximate methods for analyzing free vibration of structural components", AIAA J., 26(5), 612-618.
    • (1987) AIAA J , vol.26 , Issue.5 , pp. 612-618
    • Bert, C.W.1    Jang, S.K.2    Striz, A.G.3
  • 4
    • 0029724421 scopus 로고    scopus 로고
    • Differential quadrature method in computational mechanics: A review
    • Bert, C.W. and Malik, M. (1996), "Differential quadrature method in computational mechanics: A review", Appl. Mech. Rev., 49(1), 1-28.
    • (1996) Appl. Mech. Rev , vol.49 , Issue.1 , pp. 1-28
    • Bert, C.W.1    Malik, M.2
  • 5
    • 0024282103 scopus 로고
    • Comparative evaluation of six different numerical methods for nonlinear dynamic systems
    • Bert, C.W. and Stricklin, J.D. (1988), "Comparative evaluation of six different numerical methods for nonlinear dynamic systems", J. Sound Vib., 127(2), 221-229.
    • (1988) J. Sound Vib , vol.127 , Issue.2 , pp. 221-229
    • Bert, C.W.1    Stricklin, J.D.2
  • 7
    • 0345832022 scopus 로고    scopus 로고
    • Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns
    • Civalek, Ö. (2004), "Application of differential quadrature (DQ) and harmonic differential quadrature (HDQ) for buckling analysis of thin isotropic plates and elastic columns", Eng. Struct., An Int. J., 26(2), 171-186.
    • (2004) Eng. Struct., An Int. J , vol.26 , Issue.2 , pp. 171-186
    • Civalek, O.1
  • 9
    • 0348144661 scopus 로고    scopus 로고
    • Harmonic differential quadrature (HDQ) for axisymmetric bending analysis of thin isotropic circular plates
    • Civalek, Ö. and Ülker, M. (2004a), "Harmonic differential quadrature (HDQ) for axisymmetric bending analysis of thin isotropic circular plates", Struct. Eng. Mech., 17(1), 1-14.
    • (2004) Struct. Eng. Mech , vol.17 , Issue.1 , pp. 1-14
    • Civalek, O.1    Ülker, M.2
  • 10
    • 0042363514 scopus 로고    scopus 로고
    • Free vibration analysis of elastic beams using harmonic differential quadrature (HDQ)
    • Civalek, Ö. and Ülker, M. (2004b), "Free vibration analysis of elastic beams using harmonic differential quadrature (HDQ)", Math. and Comput. Appl., 9(2), 257-264.
    • (2004) Math. and Comput. Appl , vol.9 , Issue.2 , pp. 257-264
    • Civalek, O.1    Ülker, M.2
  • 11
    • 16244372890 scopus 로고    scopus 로고
    • Geometrically non-linear static and dynamic analysis of plates and shells resting on elastic foundation by the method of polynomial differential quadrature (PDQ)
    • PhD. Thesis, Firat University, in Turkish, Elazig
    • Civalek, Ö. (2004b), "Geometrically non-linear static and dynamic analysis of plates and shells resting on elastic foundation by the method of polynomial differential quadrature (PDQ)", PhD. Thesis, Firat University, (in Turkish), Elazig.
    • (2004)
    • Civalek, O.1
  • 12
    • 18744365641 scopus 로고    scopus 로고
    • Linear and nonlinear dynamic response of multi-degree-of freedom-systems by the method of harmonic differential quadrature (HDQ)
    • PhD. Thesis, Dokuz Eylül University, İzmir
    • Civalek, Ö. (2003), "Linear and nonlinear dynamic response of multi-degree-of freedom-systems by the method of harmonic differential quadrature (HDQ)", PhD. Thesis, Dokuz Eylül University, İzmir.
    • (2003)
    • Civalek, O.1
  • 14
    • 0002148282 scopus 로고    scopus 로고
    • Generalized differential quadrature method for buckling analysis
    • Du, H., Liew, K.M. and Lim, M.K. (1996), "Generalized differential quadrature method for buckling analysis", J. Eng. Mech., ASCE, 22(2), 95-100.
    • (1996) J. Eng. Mech., ASCE , vol.22 , Issue.2 , pp. 95-100
    • Du, H.1    Liew, K.M.2    Lim, M.K.3
  • 15
    • 0024887285 scopus 로고
    • A survey of direct time-integration methods in computational structural dynamics-I, explicit methods
    • Dokainish, M.A. and Subbaraj, K. (1989), "A survey of direct time-integration methods in computational structural dynamics-I, explicit methods", Comput. Struct., 32(6), 1371-1386.
    • (1989) Comput. Struct , vol.32 , Issue.6 , pp. 1371-1386
    • Dokainish, M.A.1    Subbaraj, K.2
  • 16
    • 0024928486 scopus 로고
    • A survey of direct time-integration methods in computational structural dynamics-II, implicit methods
    • Dokainish, M.A. and Subbaraj, K. (1989), "A survey of direct time-integration methods in computational structural dynamics-II, implicit methods", Comput. Struct., 32(6), 1387-1401.
    • (1989) Comput. Struct , vol.32 , Issue.6 , pp. 1387-1401
    • Dokainish, M.A.1    Subbaraj, K.2
  • 17
    • 0030269783 scopus 로고    scopus 로고
    • Unconditionally stable higher-order accurate Hermittian time finite elements
    • Fung, T.C. (1996), "Unconditionally stable higher-order accurate Hermittian time finite elements", Int. J. Numer. Meth. Eng., 39, 3475-3495.
    • (1996) Int. J. Numer. Meth. Eng , vol.39 , pp. 3475-3495
    • Fung, T.C.1
  • 18
    • 0031999770 scopus 로고    scopus 로고
    • Higher order time step integration methods with complex time step
    • Fung, T.C. (1998), "Higher order time step integration methods with complex time step", J. Sound Vib., 210(1), 69-89.
    • (1998) J. Sound Vib , vol.210 , Issue.1 , pp. 69-89
    • Fung, T.C.1
  • 19
    • 0035961282 scopus 로고    scopus 로고
    • Solving initial value problems by differential quadrature method-Part 1: First-order equations
    • Fung, T.C. (2001), "Solving initial value problems by differential quadrature method-Part 1: First-order equations", Int. J. Numer. Meth. Eng., 50, 1411-1427.
    • (2001) Int. J. Numer. Meth. Eng , vol.50 , pp. 1411-1427
    • Fung, T.C.1
  • 20
    • 0035961280 scopus 로고    scopus 로고
    • Solving initial value problems by differential quadrature method-Part 2: Second-and higher-order-order equations
    • Fung, T.C. (2001a), "Solving initial value problems by differential quadrature method-Part 2: Second-and higher-order-order equations", Int. J. Numer. Meth. Eng., 50, 1429-1454.
    • (2001) Int. J. Numer. Meth. Eng , vol.50 , pp. 1429-1454
    • Fung, T.C.1
  • 21
    • 0037127131 scopus 로고    scopus 로고
    • Stability and accuracy of differential quadrature method in solving dynamic problems
    • Fung, T.C. (2002), "Stability and accuracy of differential quadrature method in solving dynamic problems", Comput. Meth. Appl. Mech. Eng., 191, 1311-1331.
    • (2002) Comput. Meth. Appl. Mech. Eng , vol.191 , pp. 1311-1331
    • Fung, T.C.1
  • 22
    • 0037137833 scopus 로고    scopus 로고
    • On the equivalence of the time domain differential quadrature method and dissipative Runge-Kutta collocation method
    • Fung, T.C. (2002a), "On the equivalence of the time domain differential quadrature method and dissipative Runge-Kutta collocation method", Int. J. Numer. Meth. Eng., 53, 409-431.
    • (2002) Int. J. Numer. Meth. Eng , vol.53 , pp. 409-431
    • Fung, T.C.1
  • 23
    • 0037458004 scopus 로고    scopus 로고
    • Imposition of boundary conditions by modifying the weighting coefficient matrices in the differential quadrature method
    • Fung, T.C. (2003), "Imposition of boundary conditions by modifying the weighting coefficient matrices in the differential quadrature method", Int. J. Numer. Meth. Eng., 56, 405-432.
    • (2003) Int. J. Numer. Meth. Eng , vol.56 , pp. 405-432
    • Fung, T.C.1
  • 24
    • 0038007976 scopus 로고    scopus 로고
    • Generalized Lagrange functions and weighting coefficient formulae for the harmonic differential quadrature method
    • Fung, T.C. (2003a), "Generalized Lagrange functions and weighting coefficient formulae for the harmonic differential quadrature method", Int. J. Numer. Meth. Eng., 57, 415-440.
    • (2003) Int. J. Numer. Meth. Eng , vol.57 , pp. 415-440
    • Fung, T.C.1
  • 25
    • 0000263374 scopus 로고
    • A recurrence matrix solution for the dynamic response of elastic aircraft
    • Houbolt, J.C. (1950), "A recurrence matrix solution for the dynamic response of elastic aircraft", J. of Aeronautical Sciences, 17, 540-550.
    • (1950) J. of Aeronautical Sciences , vol.17 , pp. 540-550
    • Houbolt, J.C.1
  • 26
    • 0006451452 scopus 로고
    • Beitrag Zur Näherungsweisen Integration Totaler Differentialgleichungen
    • Kutta, W. (1901), "Beitrag Zur Näherungsweisen Integration Totaler Differentialgleichungen", Zeitschrift für Mathematik un Physik, 46, 435-453.
    • (1901) Zeitschrift für Mathematik un Physik , vol.46 , pp. 435-453
    • Kutta, W.1
  • 27
    • 0002204554 scopus 로고    scopus 로고
    • Three dimensional vibration analysis of rectangular plates based on differential quadrature method
    • Liew, K.M. and Teo, T.M. (1999), "Three dimensional vibration analysis of rectangular plates based on differential quadrature method", J. Sound Vib., 220(4), 577-599.
    • (1999) J. Sound Vib , vol.220 , Issue.4 , pp. 577-599
    • Liew, K.M.1    Teo, T.M.2
  • 28
    • 0000972395 scopus 로고    scopus 로고
    • Comparative accuracy of DQ and HDQ methods for three-dimensional vibration analysis of rectangular plates
    • Liew, K.M., Teo, T.M. and Han, J.B. (1999a), "Comparative accuracy of DQ and HDQ methods for three-dimensional vibration analysis of rectangular plates", Int. J. Numer. Meth. Eng., 45, 1831-1848.
    • (1999) Int. J. Numer. Meth. Eng , vol.45 , pp. 1831-1848
    • Liew, K.M.1    Teo, T.M.2    Han, J.B.3
  • 29
    • 0035400968 scopus 로고    scopus 로고
    • Three-dimensional static solutions of rectangular plates by variant differential quadrature method
    • Liew, K.M., Teo, T.M. and Han, J.-B. (2001), "Three-dimensional static solutions of rectangular plates by variant differential quadrature method", Int. J. Mech. Sci., 43, 1611-1628.
    • (2001) Int. J. Mech. Sci , vol.43 , pp. 1611-1628
    • Liew, K.M.1    Teo, T.M.2    Han, J.-B.3
  • 30
    • 0003124878 scopus 로고    scopus 로고
    • A hybrid moving least squares and differential quadrature (MLSDQ) meshfree method
    • Liew, K.M., Huang, Y.Q. and Reddy, J.N. (2002), "A hybrid moving least squares and differential quadrature (MLSDQ) meshfree method", Int. J. Comput. Eng. Sic., 3(1), 1-12.
    • (2002) Int. J. Comput. Eng. Sic , vol.3 , Issue.1 , pp. 1-12
    • Liew, K.M.1    Huang, Y.Q.2    Reddy, J.N.3
  • 31
    • 0031167220 scopus 로고    scopus 로고
    • Differential cubature method: A solution technique for Kirchhoff plates of arbitrary shape
    • Liew, K.M. and Liu, F.-L. (1997), "Differential cubature method: A solution technique for Kirchhoff plates of arbitrary shape", Comput. Meth. Appl. Mech. Eng., 145, 1-10.
    • (1997) Comput. Meth. Appl. Mech. Eng , vol.145 , pp. 1-10
    • Liew, K.M.1    Liu, F.-L.2
  • 32
    • 0031077934 scopus 로고    scopus 로고
    • A four-node differential quadrature method for straight-sided quadrilateral Reissner/Mindlin plates
    • Liew, K.M. and Han, J.-B. (1997a), "A four-node differential quadrature method for straight-sided quadrilateral Reissner/Mindlin plates", Comm. Numer. Meth. Eng., 13(2), 73-81.
    • (1997) Comm. Numer. Meth. Eng , vol.13 , Issue.2 , pp. 73-81
    • Liew, K.M.1    Han, J.-B.2
  • 33
    • 0030127739 scopus 로고    scopus 로고
    • Differentiel quadrature method for mindlin plates on winkler foundations
    • Liew, K.M., Han, J.-B, Xiao, Z.M. and Du, H. (1996), "Differentiel quadrature method for mindlin plates on winkler foundations", Int. J. Mech. Sci., 38(4), 405-421.
    • (1996) Int. J. Mech. Sci , vol.38 , Issue.4 , pp. 405-421
    • Liew, K.M.1    Han, J.-B.2    Xiao, Z.M.3    Du, H.4
  • 34
    • 0032496861 scopus 로고    scopus 로고
    • Modeling via differential quadrature method: Three-dimensional solutions for rectangular plates
    • Liew, K.M. and Teo, T.M. (1998), "Modeling via differential quadrature method: Three-dimensional solutions for rectangular plates", Comp. Meth. in Appl. Mech. Eng., 159, 369-381.
    • (1998) Comp. Meth. in Appl. Mech. Eng , vol.159 , pp. 369-381
    • Liew, K.M.1    Teo, T.M.2
  • 35
    • 0002689020 scopus 로고
    • A method of computation for structural dynamics
    • Newmark, N.M. (1959), "A method of computation for structural dynamics", J. Eng. Mech. Div., ASCE, 85, 67-94.
    • (1959) J. Eng. Mech. Div., ASCE , vol.85 , pp. 67-94
    • Newmark, N.M.1
  • 36
    • 0012650693 scopus 로고
    • Über die numerische Auflösung von Differentialgleichungen
    • Runge, C. (1895), "Über die numerische Auflösung von Differentialgleichungen", Mathematische Annalen, 46, 167-178.
    • (1895) Mathematische Annalen , vol.46 , pp. 167-178
    • Runge, C.1
  • 37
    • 0021369968 scopus 로고
    • Harmonic accelaration method for dynamic structural analysis
    • Senjanovic, I. (1984), "Harmonic accelaration method for dynamic structural analysis", Comput. Struct., 18(1), 71-80.
    • (1984) Comput. Struct , vol.18 , Issue.1 , pp. 71-80
    • Senjanovic, I.1
  • 38
    • 0031187639 scopus 로고    scopus 로고
    • Explicit computations of weighting coefficients in the harmonic differential quadrature
    • Shu, C. and Xue, H. (1997), "Explicit computations of weighting coefficients in the harmonic differential quadrature", J. Sound Fib., 204(3), 549-555.
    • (1997) J. Sound Fib , vol.204 , Issue.3 , pp. 549-555
    • Shu, C.1    Xue, H.2
  • 39
    • 0037073036 scopus 로고    scopus 로고
    • Block-marching in time with DQ discretization: An efficient method for time-dependent problems
    • Shu, C., Yao, Q. and Yeo, K.S. (2002), "Block-marching in time with DQ discretization: An efficient method for time-dependent problems", Comput. Meth. Appl. Mech. Eng., 191, 4587-4597.
    • (2002) Comput. Meth. Appl. Mech. Eng , vol.191 , pp. 4587-4597
    • Shu, C.1    Yao, Q.2    Yeo, K.S.3
  • 40
    • 0029231934 scopus 로고
    • Harmonic differential quadrature method and applications to analysis of structural components
    • Striz, A.G., Wang, X. and Bert, C.W. (1995), "Harmonic differential quadrature method and applications to analysis of structural components", Acta Mechanica, 111, 85-94.
    • (1995) Acta Mechanica , vol.111 , pp. 85-94
    • Striz, A.G.1    Wang, X.2    Bert, C.W.3
  • 41
    • 0026277945 scopus 로고
    • A post-correction integration algorithm for non-linear dynamic analysis of structures
    • Sun, K., Pires, J.A. and Tao, J.R. (1991), "A post-correction integration algorithm for non-linear dynamic analysis of structures", Earth. Eng. Struct. Dyn., 20, 1083-1097.
    • (1991) Earth. Eng. Struct. Dyn , vol.20 , pp. 1083-1097
    • Sun, K.1    Pires, J.A.2    Tao, J.R.3
  • 42
    • 0035910289 scopus 로고    scopus 로고
    • Dual reciprocity BEM applied to transient elastodynamics problems with differenential quadrature method in time
    • Tanaka, M. and Chen, W. (2001), "Dual reciprocity BEM applied to transient elastodynamics problems with differenential quadrature method in time", Comput. Meth. Appl. Mech. Eng., 190, 2331-2347.
    • (2001) Comput. Meth. Appl. Mech. Eng , vol.190 , pp. 2331-2347
    • Tanaka, M.1    Chen, W.2
  • 43
    • 0034745915 scopus 로고    scopus 로고
    • Coupling dual reciprocity BEM and differential qudrature method for time-dependent diffusion problems
    • Tanaka, M. and Chen, W. (2001a), "Coupling dual reciprocity BEM and differential qudrature method for time-dependent diffusion problems", Appl. Mathematical Modeling, 25(3), 257-268.
    • (2001) Appl. Mathematical Modeling , vol.25 , Issue.3 , pp. 257-268
    • Tanaka, M.1    Chen, W.2
  • 44
    • 0027576566 scopus 로고
    • A new approach in applying differential quadrature to static and free vibrational analyses of beams and plates
    • Wang, X. and Bert, C.W. (1993), "A new approach in applying differential quadrature to static and free vibrational analyses of beams and plates", J. Sound Vib., 162, 566-572.
    • (1993) J. Sound Vib , vol.162 , pp. 566-572
    • Wang, X.1    Bert, C.W.2
  • 46
    • 0033704742 scopus 로고    scopus 로고
    • The generalized differenential quadrature rule for initial-value differential equations
    • Wu, T.Y. and Liu, G.R. (2000), "The generalized differenential quadrature rule for initial-value differential equations", J. Sound Vib., 233, 195-213.
    • (2000) J. Sound Vib , vol.233 , pp. 195-213
    • Wu, T.Y.1    Liu, G.R.2
  • 47
    • 85039216464 scopus 로고    scopus 로고
    • Zienkiewicz, O.C. (1977), The Finite Element Method in Engineering Science, 3rd edt. McGraw- Hill, London.
    • Zienkiewicz, O.C. (1977), The Finite Element Method in Engineering Science, 3rd edt. McGraw- Hill, London.
  • 48
    • 84985839935 scopus 로고
    • An analysis of various time-stepping schemes for initial value problems
    • Zienkiewicz, O.C. and Lewis, R.W. (1973), "An analysis of various time-stepping schemes for initial value problems", Earth. Eng. Struct. Dyn., 1, 407-408.
    • (1973) Earth. Eng. Struct. Dyn , vol.1 , pp. 407-408
    • Zienkiewicz, O.C.1    Lewis, R.W.2


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