Abstract: This paper is concerned with propagation of thermoelastic longitudinal vibrations of an infinite circular cylinder, in the context of the linear theory of generalized thermoelasticity with two relaxation time parameters (Green and Lindsay theory). Three displacement potential functions are introduced to uncouple the equations of motion. The frequency equation, by using the traction free boundary conditions, is given in the form of a determinant involving Bessel functions. The roots of the frequency equation give the value of the characteristic circular frequency as function of the wave number. These roots, which correspond to various modes, are numerically computed and presented graphically for different values of the thermal relaxation times. It is found that the influences of the thermal relaxation times on the amplitudes of the elastic and thermal waves are remarkable. Also, it is shown in this study that the propagation of thermoelastic longitudinal vibrations based on the generalized thermoelasticity can differ significantly compared with the results under the classical formulation. A comparison of the results for the case with no thermal effects shows well agreement with some of the corresponding earlier results.
Abstract: In a previously developed fast vortex method, the
diffusion of the vortex sheet induced at the solid wall by the no-slip
boundary conditions was modeled according to the approximation
solution of Koumoutsakos and converted into discrete blobs in the
vicinity of the wall. This scheme had been successfully applied to a
simulation of the flow induced with an impulsively initiated circular
cylinder. In this work, further modifications on this vortex method are
attempted, including replacing the approximation solution by the
boundary-element-method solution, incorporating a new algorithm for
handling the over-weak vortex blobs, and diffusing the vortex sheet
circulation in a new way suitable for high-curvature solid bodies. The
accuracy is thus largely improved. The predictions of lift and drag
coefficients for a uniform flow past a NASA airfoil agree well with the
existing literature.