关键词: viscoelastic Timoshenko beam, fractional derivative constitutive relation, weakly singular Volterra integro-differential equation, dynamical response

Abstract: By using the physical analysis described in Paper I (Part I of this paper), we shall establish, in a certain way,the quantitative relation between the Markov process theory of two particle dispersion in a turbulence of very large Reynolds number and the Kolmogoroff’s theory. In terms of this relation and the results of two-particle dispersion,we shall obtain the structure functions, the correlation functions and the energy spectrum, which are applicable not only to the inertial subrange, but also to the whole range of the wave numberless than that in the inertial subrange. The Kolmogoroff ’s"2/3 law" and"-5/3 Law" are the asymptotic cases of the present result for large k. Thus, the present resuit is an extension of Kolmogoroff s laws.

Key words: viscoelastic Timoshenko beam, fractional derivative constitutive relation, weakly singular Volterra integro-differential equation, dynamical response