Flutter of rectangular simply supported plates at low supersonic speeds

Aeroelastic instability of skin panels, known as panel flutter, can occur in the form of coupled mode or single-mode flutter, While the first type of flutter usually occurs in one eigenmode (composed of the first and the second natural modes in vacuum) and yields well-studied nonlinear limit cycle oscillations, the single mode flutter can occur in several simultaneously growing eigenmodes, leading to complex nonlinear panel dynamics, including different coexisting limit cycles, periodic and non-periodic higher-mode oscillations. Structural nonlinearity and linear aeroelastic growth mechanism play the major role in this dynamic. While the linear panel flutter boundaries in the two-dimensional formulation have been studied in detail, there are only few investigations of the boundaries in the three-dimensional case. Since the linear growth mechanism plays an essential role in nonlinear oscillations, its comprehensive study is an important step toward understanding of complex dynamics of skin panels in the three-dimensional case. In this paper, we investigate the flutter boundaries of rectangular panels simply supported at all edges, and use potential flow theory to calculate the unsteady pressure. The problem is considered in two formulations: a series of rectangular plates, attached to each other, and a single rectangular plate. Flutter boundaries of the first four modes are calculated, and their transformations with the change of the spanwise plate width are studied in detail.