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

• Authors: E. Żołopa , A. Brański
• Languages of publication: EN

Abstracts

EN

An analytical solution is obtained, based on linear quadratic problem well-known in the control theory. The problem is formulated for fixed-free beam vibration (fourth order partial differential equation) in Hilbert space and the point control and distributed output is considered. Beam deflection at any point is chosen as a criterion of optimization. In this case it means the linear quadratic problem. Up to now, the linear quadratic problem was formulated many times, but only for the time-dependent equation. The aim of the paper is to obtain the value of the cost functional formulated as the function of distribution of actuators. The minimum of this function leads to the optimal actuators location. The results obtained with this method confirm the results obtained in heuristic way and pure analytical one for separate mode; it is pointed out that the actuators ought to be bonded on the beam sub-regions in which the mode curvatures take their local maximums and the highest value.

Keywords

EN

43.40.Tm; 43.40.Vn; 77.84.Dy; 77.65.-j; 46.40.-f; 62.25.Jk

Discipline

• 62.25.Jk: Mechanical modes of vibration
• 46.40.-f: Vibrations and mechanical waves(see also 43.40.+s Structural acoustics and vibration; 62.30.+d Mechanical and elastic waves; vibrations in mechanical properties of solids)
• 77.65.-j: Piezoelectricity and electromechanical effects

• Publisher: Institute of Physics, Polish Academy of Sciences
• Journal: Acta Physica Polonica A
• Year: 2014
• Volume: 125
• Issue: 4A
• Pages: A-155-A-158

Dates

published

2014-04

Contributors

author

E. Żołopa

• Halszki 31/12, 30-611 Kraków, Poland

author

A. Brański

• Laboratory of Acoustics, Department of Electrical and Computer Engineering, Rzeszów University of Technology, Wincentego Pola 2, 35-959 Rzeszów, Poland

References

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Identifiers

DOI

10.12693/APhysPolA.125.A-155