Abstract
In this paper, the two positive position feedback controllers (PPF) are used to reduce the vertical vibration in the vertical conveyors. An investigation is presented of the response of a four-degree-of-freedom system (4-DOF) with cubic nonlinearities and external excitations at primary resonance
(
Ω
1
≅
ω
1
,
Ω
2
≅
ω
2
)
in the presence of 1:1 internal resonance
(
ω
3
≅
ω
1
,
ω
4
≅
ω
2
)
. Method of multiple scales is applied to the equations of the system to find approximate analytical solutions. Then, we derived the frequency response equation and the stability criteria for the system. Numerical solution show that the time histories of the main system and the PPF controllers to present the response with and without control. The frequency response curves for the system and the controllers are studied numerically. To discuss the validity of the results, we make comparison between the analytical and numerical solutions and also compared them with the available published work.