Dynamic snap-through of thin-walled structures by a reduced-order method

The goal of this investigation is to further develop nonlinear modal numerical simulation methods for application to geometrically nonlinear response of structures exposed to combined high-intensity random pressure fluctuations and thermal loadings. The study is conducted on a flat aluminum beam, which permits a comparison of results obtained by a reduced-order analysis with those obtained from a numerically intensive simulation in physical degrees of freedom. A uniformly distributed thermal loading is first applied to investigate the dynamic instability associated with thermal buckling. A uniformly distributed random loading is added to investigate the combined thermalacoustic response. In the latter case, three types of response characteristics are considered, namely: 1) smallamplitude vibration around one of the two stable buckling equilibrium positions, 2) intermittent snap-through response between the two equilibrium positions, and 3) persistent snap-through response between the two equilibrium positions. For the reduced-order analysis, four categories of modal basis functions are identified, including those having symmetric transverse, antisymmetric transverse, symmetric in-plane, and antisymmetric in-plane displacements. The effect of basis selection on the quality of results is investigated. It is found that despite symmetric geometry, loading, and boundary conditions, the antisymmetric transverse and symmetric in-plane modes participate in the snap-through behavior.