Differential quadrature method for free vibration analysis of coupled shear walls

다국어 초록 (Multilingual Abstract)

Differential Quadrature Method (DQM) is a powerful method which can be used to solve numerical problems in the analysis of structural and dynamical systems. In this study the governing equation which represents the free vibration of coupled shear walls is solved using the DQM method. A one-dimensional model has been used in this study. At the end of study various examples are presented to verify the accuracy of the method.

참고문헌 (Reference)

1 Takabatake, H., "Two-dimensional rod theory for approximate analysis of building structures" 1 (1): 1-19, 2010

2 Bert, C. W., "Two new approximate methods for analyzing free vibration of structural components" 26 (26): 612-618, 1987

3 Liew, K.M., "Three dimensional vibration analysis of rectangular plates based on differential quadrature method" 220 (220): 577-599, 1999

4 Liew, K.M., "Three dimensional static solutions of rectangular plates by variant differential quadrature method" 43 : 1611-1628, 2001

5 Civalek, Ö., "Three different type differential quadrature methods (DQM) for linear buckling analysis of uniform elastic columns" 4 (4): 51-58, 2004

6 Coull, A., "Tall buildings 1. Handbook of structural concrete" Pitman Books Limited 1983

7 Resatoglu, R., "Static analysis of laterally arbitrarily loaded non-planar non symmetrical coupled shear walls" 48 (48): 696-708, 2010

8 Birol Kaya, "Solution of the Advection-Diffusion Equation Using the Differential Quadrature Method" 대한토목학회 14 (14): 69-75, 2010

9 Chaallal, O., "Seismic response of flexibly supported coupled shear walls" 122 (122): 1187-1197, 1996

10 Chai, Y.H., "Reexamination of the vibrational period of coupled shear walls by differential transformation" 135 (135): 1330-1339, 2009

11 Zeidabadi, N.A., "Optimized use of the outrigger system to stiffen the coupled shear walls in tall buildings" 13 : 9-27, 2004

12 Striz, A. G., "Nonlinear bending analysis of thin circular plates by differential quadrature" 6 : 51-62, 1988

13 Smith, B. S., "Modified beam method for analyzing symmetrical shear walls" 67 (67): 977-980, 1970

14 Kwan, A.K.H., "Mixed finite elements for analysis of coupled shear/core walls" 119 (119): 1388-1408, 1993

15 Omer Civalek, "Harmonic differntial quadrature(HDQ) for axisymmetric bending analysis of thin isotropic circular plates" 국제구조공학회 17 (17): 1-14, 2004

16 Striz, A. G., "Harmonic differential quadrature method and applications to analysis of structural components" 111 : 85-94, 1995

17 Civalek, Ö., "Geometrically nonlinear dynamic analysis of doubly curved isotropic shells resting on elastic foundation by a combination of HDQ-FD methods" 82 (82): 470-479, 2005

18 Cheung, Y. K., "Frequency analysis of coupled shear wall assemblies" 5 (5): 191-201, 1977

19 Kuang, J.S., "Free vibration of stiffened coupled shear walls" 7 : 135-145, 1998

20 Bert, C.W., "Free vibration analysis of tapered rectangular plates by differential quadrature method : a semi-analytical approach" 190 (190): 41-63, 1996

21 Akso an, O., "Forced vibration analysis of stiffened coupled shear walls using continuous connection method" 25 : 499-506, 2003

22 Chaallal, O., "Finite element model for seismic RC coupled walls having slender coupling beams" 118 (118): 2936-2943, 1992

23 Shu, C., "Explicit computations of weighting coefficients in the harmonic differential quadrature" 204 (204): 549-555, 1997

24 Wang, Q., "Estimating periods of vibration of buildings with coupled shear wall" 131 (131): 1931-1935, 2005

25 Kwan, A. K. H., "Equivalence of finite elements and analogous frame modules for shear/core wall analysis" 57 (57): 193-203, 1995

26 Basu, A., "Dynamic characteristics of coupled shear walls" 105 : 1637-1651, 1979

27 Bert, C.W., "Differential quadrature method in computational mechanics : a review" 49 (49): 1-28, 1996

28 Bert, C. W., "Differential quadrature for static and free vibration analysis of anisotropic plates" 30 (30): 1737-1744, 1993

29 Bellman, R.E., "Differential quadrature and long term integration" 34 : 235-238, 1971

30 Shu, C., "Differential quadrature and its application in engineering" Springer-Verlag London Limited 2000

31 Bellman, R. E., "Differential quadrature : a technique for the rapid solution of nonlinear partial differential equations" 10 : 40-52, 1972

32 Liew, K.M., "Comparative accuracy of DQ and HDQ methods for threedimensional vibration analysis of rectangular plates" 45 : 1831-1848, 1999

33 Chaallal, O, "Classification methodology for coupled shear walls" 122 (122): 1453-1458, 1996

34 Rosman, R., "Approximate analysis of shear walls subject to lateral loads" 61 (61): 717-734, 1964

35 Shu, C., "Application of generalized differential quadrature to solve two-dimensional incompressible navier-stokes equations" 15 : 791-798, 1992

36 Civalek, Ö., "Application of differential quadrature(DQ)and harmonic differential quadrature(HDQ)for buckling analysis of thin isotropic plates and elastic columns" 26 : 171-186, 2004

37 Karami, G., "Application of a new differential quadrature methodology for free vibration analysis of plates" 56 : 847-867, 2003

38 Kim, H.S., "Analysis of shear wall with openings using super elements" 25 : 981-991, 2003

39 Potzta, G., "Analysis of building structures by replacement sandwich beams" 40 : 535-553, 2003

40 Rashed, Y.F., "Analysis of building shear walls using boundary elements" 24 : 287-293, 2000

41 Ha, H.H., "An efficient analysis of continuum shear wall models" 26 : 425-433, 1999

42 Bozdogan, K.B., "An approximate method for static and dynamic analyses of multi-bay coupled shear walls" 18 : 1-12, 2009

43 Aksogan, O., "A simplified dynamic analysis of multi bay stiffened coupled shear walls" 38 : 552-560, 2007

44 Eftekhari, S.A., "A new mixed finite element-differential quadrature formulation for forced vibration of beams carrying moving loads" 78 (78): 011020-1-011020-16, 2011

45 Li, G.Q., "A continous-discrete approach to the free vibration analysis of stiffened pierced walls on flexible foundations" 33 (33): 249-263, 1996

46 Malekzadeh, P., "A DQ large deformation analysis of composite plates on nonlinear elastic foundations" 79 : 251-260, 2007