Nonlinear resonance of rotating solar-sail membrane under solar thermal and pressure excitations

This study explores the nonlinear resonance of a rotating solar sail membrane exposed to time-varying solar thermal and solar radiation pressure. The sail membrane is modeled using a cantilever membrane, applying the von Kármán theory for membrane large deflection. The membrane’s nonlinear equation is derived by employing the Lagrange equation while accounting for excitations from solar thermal and radiation pressure. The equation is solved via the Rayleigh-Ritz method. The bifurcation diagram of membrane motion is applied to reveal membrane resonance responses under different solar sail rotating frequencies. The displacement time history, phase portrait, Poincaré map, frequency spectrum, and the largest Lyapunov exponent are used to study nonlinear vibrations that occur near resonance regions. The results indicate that time-varying thermal loading excites membrane motions with multiple natural frequencies by the parametric resonance mechanics, leading to the onset of membrane chaotic motion. The membrane’s primary resonance is stimulated in harmonic oscillation by the time-varying radiation pressure. The divergence instability caused by thermal excitation is also illustrated by comparing the membrane’s vibration amplitude with and without thermal excitation. The membrane’s nonlinear vibration characteristics vary significantly with solar illumination angles, the membrane’s thermal expansion coefficients, and structural damping.