Dynamic instability and free vibration analysis of thin-walled structures with arbitrary cross-sections

The finite strip method provides many advantages in the pre-buckling analysis of thin-walled structures (TWS) with arbitrary cross-sections. This study presents a theoretical model for analyzing free vibration and dynamic instability response of TWS under different service conditions by combining the finite strip theory and the Bolotin’s method. The dynamic instability behavior of thin-walled sections subjected to periodic load is also investigated by considering the effects of restraint and loading scenarios. The results of the free vibration analysis of the members show that for certain section parameters, the frequency of the members initially increases with the application of the lateral restraint, but then decreases with increasing length. Moreover, the influence of critical geometric dimensions and restraint on the dynamic instability behavior of members is discussed in detail. Parametric instability response under axial compression shows that the instability regions occur early for members with lateral restraint. It means that the global stiffness of the members enhances as the coefficients of lateral restraint ( h R ) enlarges, which would result in increase in the natural frequency. The instability areas are also affected by the values of the static and dynamic load factors according to the dynamic instability response under various loading conditions. The increase of the static load factor of the periodic load leads to a shift of the dynamic instability zone towards lower frequency side and the increase in the width of the instability zone. The results reveal that the developed model is an efficient tool, which can be used in the dynamic instability and free vibration analyses of TWS. Meanwhile, understanding the vibration and dynamic behavior could help designers conduct safe design in structural stability, capacity, and seismic resistance.