130859713

Mathematical model analysis of sample from...

The value we are interested in: X (s) = X,(s). can be calculated from the eąuation

(6)

where:

|A,„| is the main determinant of a matrix derived earlier A_m

- (&,£ + )    F{^S)

|A_ot3| = (/n, + /n₂).y² +(i, +b₂ +63)5' + ^, +k₂ +k₂    0

-[(6, +b₂)s + k_t+k₂]    0

0		^an	F(s) 0
-[(£>, + Z>2)s + fc, +A:2]	=	^a2\	0	^a23
mĄs^2 + (6, + b2 + b4 )s + kt + k2 + k4		°2\	0

is a auxiliary determinant associated with the variable X(s) = x₂(s).

Therefore, the main determinant takes the form:

| ^Am | = \^au^an^an +^ai\^a\i^a2i ~^a2\^an^av\ =

= {b₂s + k_7i'f \jn_Ąs² +(6, +b₂ +b_i)s+k_l +k₂ + &,] +

+[(Z>, + 6₂)s + (&, +fc₂)]² (^m3^,y2 +b₃s+k₃}+    (7)

-[(w, +m₂)s² + (Z>, +b₂ +63)5+^, +k₂ +k₂](m,5² -ł-Z>₃5--ł-Ar₃)

[m₄s² +(6, +b₂ +b₄)s+k_t +k₂ + £₄]

However, determinant |A_m3| has fonn:

\K3\ = {^a3i^a23~^a2i^an)^F(^s) =

|[(6, +b₂)s+k_t +A:₂]² -[(/w, +m₂)s² +(Z>, +b₂ +b₃)s + k_l +k₂ + fc₃]    (8)

[m₄s² + (&, +b₂ +b₄)s + k_t +k₂ +k₄ ]}f(s)

The transfer fiinction is defined as the ratio of the Laplace transform of the output ^(s) to the Laplace transform of the input F(s) is given by (9):

(9)

After substituting s = ico for the Laplace operator, where co is angular freąuency of driying force F{co)), we get a spectral transfer function G{ico),