An accurate method for the dynamic behavior of tensegrity structures

Abstract

Purpose The purpose of this paper is to propose an accurate and efficient numerical method for determining the dynamic responses of a tensegrity structure consisting of bars, which can work under both compression and tension, and cables, which cannot work under compression. Design/methodology/approach An accurate time-domain solution is obtained by using the precise integration method when there is no cable slackening or tightening, and the Newton–Raphson scheme is used to determine the time at which the cables tighten or slacken. Findings Responses of a tensegrity structure under harmonic excitations are given to demonstrate the efficiency and accuracy of the proposed method. The validation shows that the proposed method has higher accuracy and computational efficiency than the Runge–Kutta method. Because the cables of the tensegrity structure might be tense or slack, its dynamic behaviors will exhibit stable periodicity, multi-periodicity, quasi-periodicity and chaos under different amplitudes and frequencies of excitation. Originality/value The steady state response of a tensegrity structure can be obtained efficiently and accurately by the proposed method. Based on bifurcation theory, the Poincaré section and phase space trajectory, multi-periodic vibration, quasi-periodic vibration and chaotic vibration of the tensegrity structures are predicted accurately.

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“…TSs are characterized by presenting dynamic behaviors with stable-periodicity, multi-periodicity, quasi-periodicity or chaos, under different frequencies [55]. Therefore, in the dynamic analysis, the change in their equilibrium configurations is analyzed and allows the development of action strategies [6].…”