Vibration and Damping in Three-Bar Tensegrity Structure

The most interesting examples of tensegrity structures are underconstrained and display an infinitesimal flex. In the direction of that flex the force-displacement relationship is highly nonlinear, resulting from geometric stiffening and influenced by the effect of prestress at equilibrium. A tensegrity structure would therefore display nonlinear vibrations when excited in the direction of the infinitesimal flex, the "frequency" decreasing with amplitude. Movement in the direction of the flex occurs with only infinitesimal change in member length, and therefore under conventional models of material damping in members the motion would not vanish as rapidly as it would for a conventional oscillator. We study one particular tensegrity geometry for which we present the force-displacement relationship in analytical form and then examine the nonlinear vibrations. We observe the role of damping and we discuss those implications for the design of tensegrity structures in space applications.