This study is to analyse the dynamical instability (or the buckling) of a steel space truss using the accurate solutions obtained by the high-order Taylor series method. One is used to obtain numerical solutions for analysing instability, because it is difficult to find the analytic solution for a geometrical nonlinearity system. However, numerical solutions can yield incorrect analyses in the case of a space truss model with high nonlinearity. So, we use the semi-analytic solutions obtained by the high-order Taylor series to analyse the instability of the nonlinear truss system. Based on the semi-analytic solutions, we investigate the dynamical instability of the truss systems under step, sinusoidal and beating excitations. The analysis results show that the reliable attractors in the phase space can be observed even though various forces are excited. Furthermore, the dynamic buckling levels with periodic sinusoidal and beating excitations are lower, and the responses react sensitively according to the beating and the sinusoidal excitation.
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