Natural frequencies describe the pre-stress in tensegrity structures

This paper investigates the effect of pre-stress level on the natural frequencies of tensegrity structures. This has been established by using Euler-Bernoulli beam elements which include the effect of the axial force on the transversal stiffness. The axial-bending coupling emphasizes the non-linear dependence of the natural frequencies on the pre-stress state. Pre-stress is seen as either synchronous, considering a variable final pre-stress design or as tuning, when increasing pre-stress is followed in a planned construction sequence. It is shown that for a certain tensegrity structure, increasing the level of pre-stress may cause the natural frequencies to rise or fall. This effect is related to whether the structural behavior can be seen as compression or tension dominant. Vanishing of the lowest natural frequency of the system is shown to be related to the critical buckling load of one or several compressed components. Modes of vibration show that when the force in the compressed components approaches any type of critical buckling load, this results in lower vibration frequencies. The methods in this study can be used to plan the tuning of the considered tensegrity structure towards the design level of pre-stress, and as health monitoring tools.