Nonlinear bifurcation structure of panels subject to periodic acoustic fluid-structure interaction

Motivated by a benchmark NASA experiment in 1992, the spatiotemporal, nonlinear, acoustic fluid-structure interaction of a two-dimensional panel in an inviscid compressible fluid is numerically investigated. The numerical coupling between the quadratic Euler fluid field and the acoustically excited viscoelastic panel with a cubic nonlinearity is obtained via a loose-coupling approach with grid adaption. Simulations reveal an intricate bifurcation structure near the fifth-mode panel resonance that includes coexisting symmetric and asymmetric periodic solutions. Furthermore, the emergence of a nonstationary, chaoticlike, spatiotemporal solution is established as an outcome of orbital stability loss of an m/n = 3/2 ultrasubharmonic response. It is also noted that the biharmonic acoustic input of the Maestrello experiment reveals distinct sum and difference frequency combination resonances that yield spatially stationary periodic and quasi-periodic panel dynamics. The former incorporates a combined interplay of third- and sixth-mode spatial responses, whereas the latter exhibits a significant widebanded spectral content at half of the fundamental exciting frequency corresponding to a combination resonance between the fifth-mode subharmonic and a superharmonic of the seventh mode. The scattered pressure field reveals a complex wave pattern in the acoustic near field, which becomes less significant with increasing distance from the panel.