Nonlinear response characteristics of thin-walled structures under thermo-acoustic loadings

Hypersonic vehicles suffer high intensity acoustic loadings in an elevated temperature. Owning to the temperature loadings, not only will thermal stresses be produced, but the material physical parameters are also changed. The thermal loadings will result in complicated motion forms of thin-walled structures with strong nonlinear characteristics through wide-band noise excitation. The complicated dynamics will decrease the fatigue life seriously. Considering the effect of thermal-acoustic loadings on the structural nonlinear behaviors, a nonlinear partial differential equation of large deflection under thermal-acoustic loadings is derived and then is treated with Galerkin method to obtain an ordinary differential equation under modal coordinates. The thermal-acoustic responses of simply supported rectangular titanium plates with different temperature and sound pressure levels (SPL) combinations are obtained, including random vibration in pre-buckled region, snap-through motion between post-buckled equilibrium positions and nonlinear vibration around one post-buckled position. Then the restoring force term and power spectral density (PSD) characteristics with temperature and SPL are analyzed for further research on nonlinear characteristics. Research results show that thermal loadings and acoustic loadings affect nonlinear characteristics differently. Thermal loadings will change the shape of stiffness curves. Taking the stiffness of critical buckling as standard, thermal loadings can reduce the stiffness of a structure in the pre-buckled region and increase the stiffness in post-buckled region. Due to the influences of acoustic loadings, the structures will work at different stiffness curve regions. Taking the stiffness of the structure without loadings as standard, the structures will work at hardened area while undergoing persistent snap through and work at softened area while undergoing intermittent snap through.