The main objective of the present work is to develop an algorithm consisting of the eigenvalue sensitivity and modal updating along with the mode tracking to analyze the dynamic behavior (i.e., vibrational properties) of a tensegrity structure. The optimum values of the design parameters including the pre-tension force, element section area, etc., are obtained to satisfy the desired vibrational properties of the structure. The optimum variables will be acceptable if the design constraints involving the buckling constraint for rod elements and the strength constraints for all components of the system are fully satisfied. The efficiency of the proposed algorithm for finding the optimum values of the design variables of the tensegrity structures is proved through the solution of three examples
AliNBHSmithIFC (2010) Dynamic behaviour and vibration control of a tensegrity structure. International Journal of Solids and Structures47: 1285–1296.
2.
AliNBHBarbarigosLRAlbertoAAlbiPSmithIFC (2010) Design optimization and dynamic analysis of a tensegrity-based footbridge. Engineering Structures32: 3650–3659.
3.
AllemangRJ (2003) The modal assurance criterion–twenty years of use and abuse. Journal of Sound and Vibration37(8): 14–21.
4.
AnacOBasdoganI (2008) Model validation and performance prediction in the design of micro systems. Journal of Vibration and Control14: 1711–1728.
5.
BagchiA (2005) Updating the mathematical model of a structure using vibration data. Journal of Vibration and Control11: 1469–1486.
6.
BarbarigosLRJainHKripakaranPSmithIFC (2010) Design of tensegrity structures using parametric analysis and stochastic search. Engineering with Computers26: 193–203.
7.
BarnesM (1999) Form finding and analysis of tension structures by dynamic relaxation. International Journal of Space Structures14: 89–104.
8.
Ben KahlaNMoussaBPonsJC (2000) Nonlinear dynamic analysis of tensegrity systems. Journal of the International Association for Shell and Spatial Structures41: 49–58.
9.
CalladineCRPellegrinoS (1991) First order infinitesimal mechanisms. International Journal Solids and Structures27: 505–515.
10.
CarstensSKuhlD (2005) Non-linear static and dynamic analysis of tensegrity structures by spatial and temporal Galerkin methods. Journal of the International Association for Shell and Spatial Structures46: 116–134.
11.
CefaloMMirats TurJM (2011) A comprehensive dynamic model for class-1 tensegrity systems based on quaternions. International Journal of Solids and Structures48: 785–802.
12.
Dalilsafaei S, Eriksson A and Tibert G (2011a) Application of flexibility analysis for design of tensegrity structures. In: Proceedings of 4th Structural Engineering World Congress,Como, Italy, April 4–6.
13.
Dalilsafaei S, Eriksson A and Tibert G (2011b) Stiffness modification of tensegrity structures. Technical reports from Royal Institute of Technology Department of Mechanics SE - 100 44 Stockholm, Sweden.
14.
EnomotoHSakamotoS (2009) Algorithm for tracking natural vibration modes using image operation. Journal of System Design and Dynamics3: 82–94.
15.
EstradaGGBungartzHJMohrdieckC (2006) Numerical form finding of tensegrity structures. International Journal of Space Structures43: 6855–6868.
16.
EwinsDJ (2000) Modal Testing: Theory, Practice and Application. 2nd edn. Baldock, Hertfordshire, UK: Research Studies Press.
17.
FelippaCA (2004) Introduction to Finite Element Methods, Boulder, CO: Department of Aerospace Engineering Sciences and Center for Aerospace Structures, University of Colorado.
18.
FuruyaH (1992) Concept of deployable tensegrity structures in space application. International Journal of Space Structures7: 143–151.
19.
GuestS (2006) The stiffness of prestressed frameworks: a unifying approach. International Journal of Solids and Structures43: 842–854.
KennerH (2003) Geodesic Math and How to Use It, Berkeley, CA: University of California Press.
22.
KimTSKimYY (2000) MAC-based mode-tracking in structural topology optimization. Computers and Structures74: 375–383.
23.
LinkwitzK (1999) Form-finding by the direct approach and pertinent strategies for the conceptual design of prestressed and hanging structures. International Journal of Space Structures14: 73–87.
24.
MasicMSkeltonREGillPE (2005) Algebraic tensegrity form-finding. International Journal of Solids and Structures42: 4833–4858.
25.
Mirats-TurJMHernándezS (2009) Tensegrity frameworks: dynamic analysis review and open problems. International Journal of Mechanism and Machine Theory44: 1–18.
26.
MotroR (2003) Tensegrity Structural Systems for the Future, London: Kogan Page Science.
27.
Motro R, Najari S and Jouanna P (1986) Static and dynamic analysis of tensegrity systems. In Proceedings of ASCE International Symposium Shells and Spatial Structure Computer, Computational Aspects. New York: Springer Verlag, pp. 270–279.
28.
MoussaBKahlaNBPonsJC (2001) Evolution of natural frequencies in tensegrity systems: A case study. International Journal of Space Structures16: 57–73.
29.
MurakamiH (2001a) Static and dynamic analyses of tensegrity structures, part 1. Nonlinear equations of motion. International Journal of Solids and Structures38: 3599–3613.
30.
MurakamiH (2001b) Static and dynamic analyses of tensegrity structures, part 2. Quasi static analysis. International Journal of Solids and Structures38: 3615–3629.
31.
OkuboNToiT (2000) Sensitivity analysis and its application for dynamic improvement. SaÅdhanaÅ25: 291–303.
32.
OppenheimIJWilliamsWO (2001a) Vibration and damping in three-bar tensegrity structure. Journal of Aerospace Engineering14: 85–91.
33.
OppenheimIJWilliamsWO (2001b) Vibration of an elastic tensegrity structure. European Journal of Mechanics A Solids20: 1023–1031.
34.
PagitzMMirats-TurJM (2009) Finite element based form-finding algorithm for tensegrity structures. International Journal of Solids and Structures46: 3235–3240.
35.
Paul C, Lipson H and Cuevas F (2005) Evolutionary form-finding of tensegrity structures. In Proceedings of Genetic and Evolutionary Computation Conference, Washington DC, June 25–26, pp. 3–10.
36.
Pellegrino S (1986) Mechanics of kinematically indeterminate structures. Ph.D. Thesis, University of Cambridge, UK.
37.
PrzemienieckiJS (1968) Theory of Matrix Structural Analysis, New York: McGraw-Hill.
38.
SaigalS (1990) Reanalysis for structural modifications in boundary-element response and design sensitivity analysis. American Institute of Aeronautics and Astronautics28: 323–328.
39.
SmailiAMotroR (2007) Foldable/unfoldable curved tensegrity systems by finite mechanism activation. Journal of the International Association for Shell and Spatial Structures48: 153–60.
40.
SultanCCorlessMSkeltonRE (2002) Linear dynamics of tensegrity structures. Engineering Structures24: 671–685.
41.
TanGEBPellegrinoS (2008) Nonlinear vibration of cable-stiffened pantographic deployable structures. Journal of Sound and Vibration314: 783–802.
42.
TranHCLeeL (2010a) Advanced form finding of tensegrity structures. Computers and Structures88: 237–246.
43.
TranHCLeeL (2010b) Initial self- stress design of tensegrity grid structures. Computers and Structures88: 558–566.
VanhonackerP (1980) Differential and difference sensitivities of natural frequencies and mode shapes of mechanical structure. American Institute of Aeronautics and Astronautics18: 1569–1572.
46.
VassartNMotroR (1999) Multi-parameter form finding method: Application to tensegrity systems. International Journal of Space Structures14: 147–154.
47.
VuKKLiewJYRAnandasivamK (2006) Deployable tension-strut structures: from concept to implementation. Journal of Constructional Steel Research62: 195–209.
48.
WangWMottersheadJEIhleASiebertTSchubachHR (2011) Finite element model updating from full-field vibration measurement using digital image correlation. Journal of Sound and Vibration330: 1599–1620.
49.
ZhangJYOhsakiMKannoY (2006) A direct approach to design of geometry and forces of tensegrity systems. International Journal of Solids and Structures43: 2260–2278.
