An Optimal Distribution of Actuatorsin Active Beam Vibration – Some Aspects, Theoretical Considerations

Analytical Determination of Optimal Actuators Position for Single Mode Active Reduction of Fixed-free Beam Vibration Using the Linear Quadratic Problem Idea

“…The p-reduction is possible for separate mode and it is realized with actuators [14]. The quantity of the reduction depends on many factors [510]; they are enumerated in [3]. It seems that the most important is an optimal distribution of actuators on the structure [5,6].…”

“…It seems that the most important is an optimal distribution of actuators on the structure [5,6]. A lot of optimization techniques are distinguished; an excellent survey of them may be found in [11] and is repeated in [3]. Two main approaches to this problem are classied.…”

Comparison of Formulas Obtained for Analytical and LQ Idea Approaches to Determine the Optimal Actuator Location in Active Multimodal Beam Vibration Reduction

“…and κ ν (x a ) -curvature of X ν (x) at the point x = x a ; the sign κ ν (x a ) arises from the directions of the forces f a (Brański, 2011), ω q -excitation frequency, K ν (.) -Krylov functions (Kaliski, 1986), λ ν -they are the solution of the equation…”

“…The a-reduction, via actuators, is described for example in (de Silva, 2000; Hansen, Snyder, 1997; Fuller et al, 1997;Wiciak, 2008). It depends on many factors enumerated in (Bruant, 2010;Brański, Lipiński, 2011;Brański, 2011). It seems that the most important factor is the distribution of the actuator on the structure, because once bonded actuator cannot change the place.…”

“…There are also many structures of which the vibrations are reduced via actuators, from the simple beam (Augustyn et al, 2014;Brański, 2011), through the plate (Wiciak, 2007) to the very complicated structure (Kozień, Wiciak, 2008).…”