Effectiveness Analysis of the Beam Modes Active Vibration Protection with Different Number of Actuators

Abstract

This paper deals with an active vibration protection (p-reduction) of the beam-actuators mechanical system, hence it concerns separate modes. The paper's aim is an eectiveness analysis of the p-reduction assuming dierent number of actuators. It is assumed a priori that actuators are bonded to the beam in the sub-domain with the largest curvatures and they are exactly the same. The beam clamped at one end is chosen as the research object. Next, as required by the p-reduction condition, the number and distribution of actuators are changed. It turns out that the best reduction eectiveness, measured via any eectiveness coecient, is obtained for one actuator bonded in the sub-domain with the largest curvature. The validation of theoretical considerations is conrmed numerically.

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

“…The results obtained with this method conrm the results obtained on the analytical way for separate mode presented in [2,4]. To the authors' knowledge, such problem has not been considered yet.…”

“…This theory is repeated after papers [3,4]. Let the beam be clamped at one side; geometrical data of the beam are: length, S area of the cross-section, q E = q E (x, t) distributed load force.…”

“…where ω q is the angular frequency. The solution of the above problem, for the steady-state case, can be proposed, after [3,4] as…”

Evaluation of the Effect of a Step Change in Piezo Actuator Structure on Vibration Reduction Level in Plates

“…Since the works of Dimitriadis, Fuller, and Rogers (1991) these materials have been typically used for beams (Brański, 2013;Ferdek, Kozień, 2013 (Wiciak, 2007;2008; Trojanowski, Wiciak, 2010;Iwański, Wiciak, 2013;Jabłoński, Ozga, 2012). In most cases, a significant reduction of vibration or/and acoustic pressure can be achieved.…”

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

“…From mathematical point of view, this distribution is called an optimal one (O-distribution). In (Brański, 2013) it is proved that the maximum efficiency of p-reduction is obtained for the O-distribution of the single actuator.…”