FEM Analysis and Experimental Study on Monolayer Cable Net for Glass Facades: Dynamic Properties

Abstract

Study of the dynamic properties of a monolayer cable net is described in this part II of the paper. The linear vibration properties of a cable net are analyzed in the form of a lumped-mass system based on the assumption of small-amplitude vibration. The respective influence of two vital factors: geometric shape and cable pretension on the dynamic properties of cable nets at different deflected positions under load is especially focused upon. Results show that when the geometric shape has a small displacement, the displacement influence on frequencies of vibration is almost the same as that of pre-tension, otherwise, the influence of geometric shape is far greater than that of pre-tension. Dynamic tests on the cable net model mentioned in Part I were also carried out at each pre-stretching stage. The results of experiments agree well with those of finite element analysis (FEA). In addition, a modified method called “MML” based on Rayleigh's approach for the calculation of fundamental frequency is put forward in this paper, since it was found that Rayleigh's approach may sometimes introduce large errors. The nonlinear dynamic properties of the cable net were also analyzed. Different from the linear vibration case, nonlinear cases are to some extent amplitude-dependent. Thus explicitly approximate formulae for the first and second nonlinear modal frequencies are derived from continuous theory assuming the cable net to act as a continuous membrane. Transient dynamic analysis using the finite element software ANSYS was carried out to validate the formulae. The results given by the formulae and those via numerical analysis agree with each other well.

Keywords

monolayer cable net pre-tension geometric shape nonlinear frequency

References

Al-Qassab

and Nair

(2003). “Wavelet-galerkin method for free vibrations of elastic cable”, Journal of Engineering Mechanics, ASCE, Vol. 129, No. 3, pp. 350–357.

Bathish

G.N.

(1972). “Free vibrational characteristics of pretensioned cable roofs”, Journal of Engineering for Industry, Vol.7, No. 4, pp. 31–37.

Berlioz

and Lamarque

C.H.

(2005). “Nonlinear vibrations of an inclined cable”, Journal of Vibration and Acoustics-Transactions of the ASME, Vol. 127, No. 4, pp. 315–323.

Cheung

Y.K.

Chan

H.C.

and Cai

C.W.

(1988). “Natural vibration analysis of rectangular networks”, International Journal of Space Structures, Vol. 3, No. 3, pp. 139–152.

Chen

H.H.

and Chen

Z.X.

(2000). “A direct optimization method for solving eigen problems of interval matrices”, Journal of Vibration Engineering, Vol. 13, No. 1, pp. 117–121. (in Chinese)

Clough

R.W.

and Penzien

(2003). Dynamics of Structures. New York: McGraw-Hill.

Krishna

(1978). Cable-Suspended Roofs, McGraw-Hill, New York.

Han

S.M.

and Grosenbaugh

M.A.

(2004). “Non-linear free vibration of a cable against a straight obstacle”, Journal of Sound and Vibration, Vol. 273, pp. 337–361.

Hangai

and Wu

(1999). “Analytical method of structural behaviours of a hybrid structure consisting of cables and rigid structures”, Engineering Structures, Vol. 21, No. 8, pp. 726–736.

10.

Irvine

H.M.

(1981). Cable Structures, Cambridge, Mass. The MIT Press.

11.

Mackerle

(1997). “Finite element linear and nonlinear, static and dynamic analysis of structural elements: A bibliography (1992–1995)”, Engineering Computations, Vol. 14, No. 4, pp. 347–440.

12.

Mehrabi

A.B.

and Tabatabai

(1998). “Unified finite difference formulation for free vibration of cables”, Journal of Structural Engineering, ASCE, Vol. 124, No. 11, pp. 1313–1322.

13.

Moussa

Pons

J.C.

and Crosnier

(1998). “Tension-frequency relation in tensegrity system”, Mecanique Industrielle Et Materiaux, Vol. 51, No.4, pp. 191–193.

14.

Pilipchuk

V.N.

and Ibrahim

R.A.

(1999). “Non-linear modal interactions in shallow suspended cables”, Journal of Sound and Vibration, Vol. 227, No. 1, pp. 1–28.

15.

Shen

S.Z.

C.B.

, and Zhao

(1997). Design of Cable Suspended Structures. Beijing: China Architecture & Building Press. (in Chinese)

16.

Shore

and Chaudhari

(1972). “Free vibrations of cable networks utilizing analogous membranes”, IABSE, pp. 445–451.

17.

Solar

A.I.

and Afshari

(1970). “On the analysis of cable network vibration using Galerkin's method”, Journal of Applied Mechanics, ASME, Vol. 37, No. 92, pp. 606–611.

18.

Stefanou

G.D.

(1995). “Dynamic response analysis of nonlinear structures using step-by-step integration techniques”, Computers and Structures, Vol. 57, No. 6, pp. 1063–1070.

19.

Subramonian

and Reddy

D.V.

(1974). “Frequency analysis of cable networks using finite-difference calculus”, Journal of Applied Mechanics, ASME, Vol. 41, No. 1, pp. 293–294.

20.

Zhang

L.M.

B.Q.

and Yuan

X.R.

(1995). “Shifted-iterative modal method of structural eigenvector derivative computation”, Journal of Vibration Engineering, Vol. 8, No. 3, pp. 247–252. (in Chinese)

21.

Zingoni

(1996). “An efficient computational scheme for the vibration analysis of high tension cable nets”, Journal of Sound and Vibration, Vol. 189, No. 1, pp. 55–79.

22.

Wang

G.Y.

(1978). Vibration of Building Structures. Beijing: Science Press. (in Chinese)

23.

L.L.

Wang

Y.Q.

and Shi

Y.J.

(2005). “Influence of stiffness of glass panels and joint constraints on dynamic properties of monolayer cable net for point-supported facade”, Journal of Shenyang Jianzhu University (Natural Science), Vol. 21, No. 5, pp. 432–437.