130859712

Weronika DZIKOWSKA

where:

X, =^(s) means the Laplace transformed outputs (displacements), m, F(s) - the Laplace transformed input (driving force), N,

5 - Laplace operator, [s"‘], other symbols as in formula (3).

The system defined by eąuations (3) can be written in matrix form

- [b₃s + k₃)    m₃s² + b₃s + k₃

(m, + m₂)s² + (Z>, +b₂ +Z>,)s + £, +k₂ + k₃    —(b₃s+k₃)

(5a)

(5b)

-[(^ft1+*₂)^{s +} (*i⁺*₂)]    0

0	^xi		F(s)
-[(Z), +b2)s + kx +k2]	X3	=	0
m4s^2 + (Z>, +b2 + Z>4) 5 + Ar, +k2 +k4	X4		0

or in short form:

A„,X = F

where:

A_m

-(b₃s + k₃)

(w, -\-m₂)s² +(6, +b₂+b₃)s+k_x+k₂+k₃ -[(6, +Z)₂ )5- -ł-(Ar, +&₂)]

m_ys² + b_ys + k₃ ~(b₃s+k₃)

0

0    a_u a_n 0

-[(Z?! + Z>₂).s + k_x +fc₂]    = a_2X a₂₂ a₂₃

m_xs² + (Z>, +b₂ +Z>₄ )$' + &, +k₂ +k_Ą _^ji b ^33.

is a matrix of coefficients resulting from the materiał properties of particular elements of this sample

'X_x

X ₃

x₄

X =

is output ąuantity vector (in our case the images of deviations of

the upper surface of the particular elements from stable balance

F =

0

0

is a vector of inputs, reduced in the present case to one

driying force.