On the synthesis of optimal dampers

Review: Optimal Shock and Vibration Isolation

“…Sometimes, if the function Φ is independent of u, the maximum-type functional is replaced by a terminal functional with an unknown time for the termination of the process. This approach was used, for example, by Kuznetsov and Chernousko [107] and Troitskii [197] to solve some problems of optimal control in mechanical systems whose performances were evaluated by maximum-type functionals. The condition of the vanishing of the total derivative of the function Φ(x(t), t) with respect to time is adopted as the condition of the process termination.…”

“…Troitskii [197] solved the problem of synthesis of the optimal isolator feedback characteristic for a single-degree-of-freedom system. The performance index to be minimized was the peak displacement J 1 .…”

“…There are numerous publications on these problems, some of which will be cited here. Problems of optimal shock isolation were investigated by Afimiwala and Mayne [1], Babitskii and Izrailovich [5], Balandin [7][8][9][10] [197], and Wilmert and Fox [211]. Various problems of optimal vibration isolation were considered by Akulenko and Bolotnik [2], Akulenko, Bolotnik, and Kaplunov [3], Bolotin [30,31], Furunzhiev [64], Guretskii [73], Guretskii and Mazin [75], Haug and Arora [78], Kolovskii [100], Maksimovich [120,121], Ryaboy [168,169,[172][173][174][175], Saranchuk and Troitskii [179,180], Sevin and Pilkey [189], and Wang and Pilkey [207].…”