V.3 No 1

41

On the nature of red shift of Metagalaxy

On the basis of (57), the mass of the  i th element of line will be

As the elementary volumes vary, the elasticity of constraints  s_i   between the line elements will vary too. Actually, "we cannot speak of stresses, doing not determining the cross-section through which this stress is passed. So we speak of the stress on such-and-such area" [17, p. 21]. Since the constraint elasticity in the lumped line is determined as the relation of the constraint rigidity to the distance between the elements [18, p. 95],

Finally, we will take into account the viscosity of the elastic medium by way of introducing into the modelling differential equations the additional impedance forces obeying the above regularity (55). We have to notice that for each element of elastic line, the velocity gradients as to the neighbouring elements will be, in general case, different. So the regularity (55) in our case separates into two regularities - for the right and left elements correspondingly:

where  y_i  is the transverse shift of the i th element of elastic line.

On the basis of the established regularities, the modelling system of differential equations takes the following form:

Given the statement of problem, we are interesting in the law of wave propagation out of the excitation region. Proceeding from this, it will be sufficient to investigate the common term of (61)

Substituting (56) - (61) into (62), we yield

Tending r   to zero, we finally obtain the wave equation describing the excitation propagation in the infinite elastic space with the viscosity :

Using the standard transformation (see, e.g., [19, p. 139])

where = ry and c ² = /  is the velocity of wave propagation in the ideal non-viscose medium.