The growing interest in lightweight, deployable, and adaptive space membrane systems motivates the study of tensegrity-membrane systems. Such systems, which are composed of membranes, bars, and tendons, can be treated as extensions of classical tensegrity systems. Therefore, they inherit typical advantages of tensegrity systems, such as reduced mass, extreme flexibility, and the capacity of shape change. Membranes can be part of a certain device, such as a reflector or solar sail, while also offering opportunities for integrated system design. This paper presents a study in the modal analysis and free vibration analysis of a tensegrity-membrane system. Two mathematical models are used in this analysis: a nonlinear finite element model and a control-oriented model. The nonlinear finite element model is of great generality, while several modeling assumptions are introduced in the control-oriented model to simplify the modeling problem and lead to a model that lends itself to modern control design. Numerical results given by the two models are compared in order to ascertain the extent to which the two models agree. Observations related to system mode shapes, coupled dynamic behavior between system components, and system free vibration responses are discussed.

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