https://doi.org/10.1140/epjp/i2016-16232-2
Regular Article
Quasi-optimal locations of piezo-elements on a rectangular plate
Faculty of Mechanical Engineering, Department of Automatic Control and Robotics, Bialystok University of Technology, Wiejska 45C Street, 15-351, Bialystok, Poland
* e-mail: a.koszewnik@pb.edu.pl
Received:
25
November
2015
Accepted:
3
June
2016
Published online:
7
July
2016
The optimal location of piezo-actuators and piezo-sensors for the vibration control of a rectangular plate with SFSF (Simply Supported - Free - Simply Supported - Free) boundary conditions is presented in the paper. Based on bending moments, 
and 
, the modal control forces generated by the piezo-stripes are calculated for the first five mode shapes. Calculations are carried out for different locations of two piezo-strips directed along the X and Y axes. The obtained results are used to define performance indexes of modal control forces for the two considered directions of vibration. In a similar way the modal unit elongations of the piezo-sensors are calculated for two different orientations of the piezos on the plate. Based on these results the objective cost functions 
and 
are defined separately for odd and even modes. The quasi-optimal locations of the piezo-actuators and piezo-sensors are determined by maximizing the proposed cost functions. After analytical and numerical investigations the process of the full model identification is carried out at the laboratory stand. A chirp signal is applied in the identification process. The rectangular plate is excited with the chirp force while output signals are measured by the piezo-sensors oriented in the perpendicular directions X and Y. In such a way two mathematical models are obtained to control the vibration of the plate separately for odd and even natural modes.-1
© The Author(s), 2016
