Continuous model and nonlinear dynamic responses of circular mesh antenna clamped at one side

The continuous model and nonlinear dynamic responses of a circular mesh antenna subjected to the thermal excitation in the space environment are investigated for the first time. A continuum cantilever circular cylindrical short shell, which is clamped at one side of the shell along the axial direction, is proposed to take place of the circular mesh antenna composed of the repetitive beamlike lattice by the principle of equivalent effect. Based on the first-order shear deformation shell theory and von Karman nonlinear strain-displacement relationship, the nonlinear governing equations of motion are derived by using the Hamilton's principle. The Galerkin approach is used to transform the governing nonlinear partial differential equations into a set of nonlinear ordinary differential equations. The method of multiple scales is utilized to obtain the four-dimensional averaged equation when the 1:1 internal resonance is taken into account. The numerical results, which include the time histories, phase plots, and frequency spectrum, are obtained for the mesh antenna. The influences of the thermal excitation and the damping coefficient on the nonlinear dynamics are analyzed for the mesh antenna.