Compute the natural periodT of the system in Figure 5 Neglec

Compute the natural period(T) of the system in Figure 5. Neglect damping. 2EI EI L/2 Figure 5

Solution

Solution:-

1/K = 1/K₁ + 1/K₂

1/K = 1/(12*2EI/(L/2)³) + 1/(12 *EI/(L/2)³)

K = 64EI/L³

Total stiffness = K + 3k

Total stiffness = 64EI/L³ + 3k

We know that

Natural period(T_n) = 2(pi)* root(M/stiffness)

Natural period(T_n) = 2(pi) * root((W/g)/(64EI/L³ +3k))         Answer