Vibration Control of Fractionally-Damped Beam Subjected to a Moving Vehicle and Attached to Fractionally-Damped Multiabsorbers

Table 1

Material and geometrical properties of beam, vehicle, and absorbers.

Problem	Properties
Verification problem I in Section 3.1	𝐿=25m, 𝐸=82.7GPa, 𝐼=9.2m^4, 𝜇=2303kg/m, 𝑚𝑣=5750kg, 𝑘𝑣=1595000N/m, 𝑐𝑣=0Ns/m, 𝐾𝑖=0N/m, 𝜔𝑖=0rad/s.
Verification problem II in Section 3.2	𝛽=1, 𝛾=1, 𝑁=1:𝑑1=𝐿/2(m), (𝑖=1,2,…,𝑁); 𝑑𝑁=2:^1=𝐿2m𝑑−𝛿2=𝐿2+𝛿m,  𝑑𝑁=3:^1=𝐿2m𝑑−𝛿2=𝐿2m𝑑3=𝐿2+𝛿m, 𝛿=0.02m.; 𝑘𝑣=0.0N/m, 𝜁𝑣=0.1, 𝑚𝑣=1kg.
Problem in Section 3.4	𝑁=1,𝑑1=(𝐿/2)m , 𝑣=25m/s , 𝑚𝑣=1kg, 𝑘𝑣=700N/m, 𝜁𝑣=0.1 , 𝜁=0.15.
Problem in Section 3.5	𝛽=1.245, 𝛾=1.19, 𝑘𝑣=700.0N/m, 𝜁𝑣=0.1, 𝑚𝑣=1kg,; 𝑁=1:𝑑1=𝐿2(m),  𝑑𝑁=2:^1=𝐿2m𝑑−𝛿2=𝐿2+𝛿m,; 𝑑𝑁=3:^1=𝐿2m𝑑−𝛿2=𝐿2m𝑑3=𝐿2+𝛿m,  𝛿=0.02m.
For all problems (except verification Problem I)	𝐿=4m, 𝐸=206.8GPa , 𝜌=7820kg/m^3, 𝐴=0.03×0.03m^2, 𝑀𝑖=1.4076kg, 𝐾𝑖=877.767N/m ,  𝜁̂𝑖=0.1846356 for 𝑖=1,2,…,𝑁.