Nonlinear primary resonance of a rigid-flexible space symmetric antenna

This paper studies the nonlinear response of a T-shape space antenna structure composed of two rigid arms jointed by a spring and two uniform beams made by isotropic material. Based on the Lagrange equation and the assumed modes method, the nonlinear dynamic equations of in-plane motion of the rigid-flexible coupled antenna are established, with four degrees of freedom. In order to reveal the dynamic characteristics of the nonlinear system, the method of multiple scales expressed in matrix form is used to solve the primary resonance responses of third-order approximation. Analyzing the frequency-amplitude response gives the jumping phenomenon in the primary resonance response. With increase of the excitation amplitude, the frequency-amplitude response curve would have a conversion between the hardening and softening types. Under small excitation amplitude, the frequency-response curve exhibits the hardening-type behavior, whereas the softening-type behavior would appear once the excitation amplitude is out to a critical value. In the case of softening-type behavior, the resonance frequencies decrease with increase of the excitation amplitudes.