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 the paper we submit the non-local modification of
kinetic Smoluchowski equation for binary aggregation applying to
dispersed media having memory. Our supposition consists in that that
intensity of evolution of clusters is supposed to be a function of the
product of concentrations of the lowest orders clusters at different
moments. The new form of kinetic equation for aggregation is
derived on the base of the transfer kernels approach. This approach
allows considering the influence of relaxation times hierarchy on
kinetics of aggregation process in media with memory.