Reexamination of Unsteady Fluid Dynamic Forces on a Two-Dimensional Finite Plate at Small Mach Numbers

The Fourier transform theory is applied to the analytical determination of the disturbance velocity potential and pressure acting on a two-dimensional plate, in order to reexamine those of previous analyses by other investigators. Simplified expressions of the generalized forces are presented for incompressible and nearly incompressible flows. As the Mach number tends to zero, the virtual mass induced by an oscillating fluid becomes infinitely large for a natural mode symmetric with respect to the midchord point. It is recommended to take into account a symmetric mode which changes no fluid volume contained in a control surface, when a coupled flutter oscillation at very low Mach numbers is analyzed. Incorrectness in the generalized forces of the previous analyses is pointed out by comparing with the present analysis.