Membrane structures are extensively employed in aerospace applications to satisfy requirements for large-scale, lightweight designs. However, their intrinsic properties result in complex, poorly attenuated vibrations that can impair spacecraft performance. To address this, a novel analytical model of the membrane structure with non-classical boundary conditions is developed to investigate its nonlinear primary resonance characteristics. Subsequently, the negative velocity feedback control strategy incorporating piezoelectric materials is introduced, and the closed-loop system vibration control equation is derived to analytically explore nonlinear vibration suppression. Numerical simulations demonstrate that the amplitude-frequency response is significantly influenced by the external excitation amplitude, pre-tension, and uniform temperature rise. Furthermore, the appropriate selection of the control gain can effectively mitigate the resonance amplitude.