SELF

68

S.B. Karavashkin, O.N. Karavashkina

Suppose that zero of the distributed line is the location of  n + 1-st mass of a lumped line in the unexcited state. Then

Using (39) and (40), transform some multipliers of the system (2)–(4), noting the smallness of a:

where x_k  is the external force application point, and   are the wave propagation velocities in the sections having related densities ₀₁   and ₀₂ .

Substituting (41) to the basic system and finding the limit at a 0 , we yield the sought solution:

for the section x₀ x_k

for the section x_k x₀ 0

and for the section x₀ 0

We can see from (42)- (44) that at the limit passing, the distributed line retains its distinctions considered above for a lumped line.