THE ACCURACY OF LINEAR PISTON THEORY WHEN APPLIED TO CYLINDRICAL SHELLS

Abstract

P theory was introduced into aeroelasticity in the linearized form by Ashley and Zartarian as a handy tool in 1956. This theory furnishes an approximation for the aerodynamic pressure acting on a slightly deformed flat plate in a supersonic airstream. The linearized piston theory is used widely in the investigation of the flutter of flat panels. Because of the lack of appropriate approximations for the aerodynamic pressure acting on a vibrating cylindrical shell, linear piston theory is used also in investigations of the flutter of cylindrical shells.' 4 There are doubts about the accuracy of using the linear piston theory for cylindrical shells. This opinion was strengthened by recent studies at California Institute of Technology.'In the following, a short survey of an investigation of the accuracy of the linear piston theory when applied to cylindrical shells is given. For further details, the reader is referred to Ref. 6. An infinitely long circular cylindrical shell of radius R, which is exposed externally to a uniform airstream parallel to the cylinder axis, is considered. The Mach number, the density, and the velocity of sound of the undisturbed airstream are denoted by M, p0, and a0, respectively. Let a cylinder coordinate system x, r, 6 be chosen, where the positive direction of the x axis coincides with the positive direction of the airstream (i.e., a negative Mach number means that the airstream is moving in the negative x direction). The shell is assumed to be slightly deformed by a harmonically oscillating standing wave of the form w = w0 cos(nO)s(x)e co £ 0 (la) with s(x) = sm(vx) or s(x) = cos(vx) v ^ 0 (Ib)