Future flight vehicle structures will encounter severe loading conditions, a combination of aerodynamic, thermal, acoustic and mechanical loads. Although the analysis methods for responses of structures under acoustic loads have been developed to some extent, but with thermal loads considered, the responses show fundamental differences, which complicate the analysis immensely. It was reported that hypersonic flight may give rise to surface temperature as high as and intense noise whose overall sound pressure level (OSPL) may reach 180dB. Thin-walled structures subjected to such loadings will exhibit nonlinear responses. Large temperature increments may cause thermal buckling, large thermal deflections and large thermal stresses superimposed on dynamic stresses, coupled with changes in material properties. Both the geometry change by thermal buckling and stiffness change by thermal stress account for the changes of natural frequencies and mode shapes. When the acoustic loading increases to a high enough level, the post-buckled structures will exhibit snap-through motion, a large amplitude nonlinear vibration between different equilibrium positions, which will introduce extra large mean stress. As a result, thermo-acoustic fatigue may be caused, which will reduce the structure's fatigue life dramatically. Therefore it is an urgent need to estimate the influences of thermal loads on the nonlinear response of structures. A numerical investigation of the influences of thermal loads on the dynamic response of thin-walled structure under thermo-acoustic loadings is implemented. With clamped-clamped thin flat plate selected, the response characteristics related to temperature are investigated by changing thermal loads. The thermal load is considered as constant both on the surface and across the thickness. The acoustic load is simulated using stationary Gaussian white noise. Firstly, a thermal buckling analysis is proceeded to obtain critical buckling temperatures, followed by modal analysis under different thermal loads. The pre-buckled and post-buckled mode frequencies and shapes are obtained. Then three types of snap-though motions are predicted: i) vibration around one post-buckled equilibrium position, ii) intermittent snap-through, and iii) persistent snap-through. The relations between thermal loads and the occurrence of snap-though is obtained together with results about the statistics characteristic of dynamic response and their relations with thermal loads, which include critical thermal buckling loads, natural frequencies and mode shapes, RMS response and snap-through frequency. Good agreements have been achieved with previous analytical solutions, which demonstrate the effectiveness and reliability of the method employed.
An analytical formulation to evaluate natural frequencies and mode shapes of high-rise buildings