130859715

Mathematical model analysis of sample from...

where in formulas (10) and (11):

b, - damping coefficient of i-th element of the sample, N s m"¹, k. - stiffness of i-th element of the sample, N m'¹,

- h

h= — h₀ = im - relative height i-th element of the sample,

K

» A

Ą = — Ą = lm² - relative area i-th element of the sample, -,

4)

h - real height of i-th element of the sample, measured along the axis of driving force, m,

A - real surface perpendicular to the direction of the driving force of i-th element of the sample, m².

Possibilities of manufacturing different samples are presented in Fig. 4. Distribution of the skin on tested sample depends on whether it is cut or manufactured. Different samples allow to determine the materiał properties by the experimental methods for porous foam and skin.

Fig. 4. The possibilities of skin position in the sample Rys. 4. Możliwości rozmieszczenia lica próbki

Eąuations (3) for simplified samples presented in Fig. 4 are reduced eąuations as written below, respectively:

m,x, +6,x, + k_lx_i = F (ot)    (12)

(m, +m₂)x_l +(b_{ +6₂)x, +(£, +k₂)x_{ =F{o)t)    (13)

(14)

(15)

m₃3ć₃ +b₃ (x₃ -x,) + ^₃ (x, -x,) = F(ot)

m,x, +    + k_ix_l = 6₃ (x₃ - x,) + k₂ (x₃ - x,)

m₃ (x₃ - 3ć,) + b₃ (x₃ - x,) + k₂ (x₃ - x,) = F ((ot)

(w, +w₂)x, +(b_l +b₂)x_l +(k_{ +^₂)x, =b₃ (x₃ -x,) + &₃ (x₃ -x,)

In generał, to determine the four parameters k_l, k₂=k₃= k₄ b_x, and

b₂=b₃= b₄ it is sufficient to study only two types of samples because the obtained transfer functions are complex numbers and each of them enables