Experiments on vibration control of a piezoelectric laminated paraboloidal shell

Significance Statement

Aerospace structures are typically made into shape of a thin-walled paraboloidal shells. These paraboloidal shells are usually made of very light and thin materials offering features such as low modal frequencies, small damping ratio and large flexibility. Vibrations in outer space area due to scarce air resistance in major concern as it can lead to failures in structure and defective instruments and equipment. Hence, adaptive and active vibration control to key structures are needed.

Researchers from Harbin Institute of Technology and Nanjing University of Aeronautics and Astronautics in China led by Prof. Honghao Yue established the mathematical model of control systems and proved the experimental platform for adaptive modal control of precision paraboloidal shell where two from eight polyvinylidene fluoride (PVDF) actuators could be selected by control systems to alleviate the oscillation caused by external excitations. This study was recently published in Mechanical Systems and Signal Processing.

Piezoelectric materials have been used as sensors and actuators for plates and shell structures with further research proving that distributed PVDF piezoelectric film layers laminated on one side of flexible cantilever, increases the modal damping ratio 4.5 times.

Control methods and strategies are of importance to vibration control effectiveness. The control methods include positive position feedback (PPF) control, optimal control, fuzzy control, neutral network control and adaptive feed forward control.

Due to complexity of analytical procedures and unavailability of analytical solutions, Yue et al. (2016) study focused on an experimental study of the active modal vibration control of a flexible paraboloidal shells with free boundary conditions. For establishment of mathematical method of control systems; controllers of first order mode as well as coupled mode of first and second order paraboloidal shell was developed based on PPF algorithm.

Experimental setup was composed of two systems; a vibrating paraboloidal shell and an active vibration controller. For modal analysis of the paraboloidal shell, a flexible model of DSM Somos-14120 resin where height, radial distance and thickness are 0.1, 0.2 and 0.001m respectively. The mass density of the shell is 1120Kg/m3 at 250C with elastic modulus of 2800MPa. Mobile point extraction method were obtained by modal VIEW Software showing its frequency response analysis.

For active vibration control setup, A/D card (PXI-6284) and a D/A card (PXI-6723) (NI-DAQ) were employed in the experimental setup for data acquisitions of sensors and outputs of the control signs. Eight pieces of PVDF sensor patches are uniformly arranged on the outside of flexible paraboloidal thin shell with an interval of 22.5 degrees between each in circumferential direction while eight actuators were inside the shell on the opposite side of the sensors.

Appropriate gains for PDVF sensors and actuators are selected as Ksen=20 and Kact=50 respectively. Impulse response method and frequency response method were the two identification methods used to test the shell model and it was revealed that vibration frequencies mainly concentrated in the vicinity of 8.9Hz and 23.6Hz, natural frequencies ω1 and ω2 are 55.9 rad/s and 148.2 rad/s respectively with static gain KS=0.0007.

Results from independent modal control effect indicated that damping of first shell mode was increased by controller and this independent modal controller can restrain the vibration amplitude thereby shortening the stability time observably. Amplitude of first mode decreases by approximately 62.3% while the rest modes of shell structure remained unchanged indicating feasibility of design PPF controller for an independent mode without influencing others. A 13Hz mode was generated by a controller and its amplitude larger than first mode under suppression which indicated system uncertainties of model imperfections and unpredicted non-linear behaviors by the paraboloidal shell, PVDF sensors or actuators and hardware circuit.

A coupled modal controller together for controlling natural frequencies ω1=8.9Hz and ω2=23.6Hz indicated that suppression ratio of first mode was more significant than the second mode. Vibration of the first mode is larger than that of second mode at the point where the chosen sensor and actuator in the experiment nears the excitation position which contributes to suppression difference between the two nodes.

Results from adaptive modal control from different areas and regions indicated larger initial vibration amplitudes in odd areas (1, 3, 5, 7) than those in even areas (2, 4, 6, 8). Time domain response of odd areas 5 and 7 with active control decay more quickly than odd areas 1 and 3. This indicates that sensing signals of odd areas contain more high-frequency components than even areas.

This control system identified areas with largest vibration amplitude thereby selecting the best two actuators to exert control force and moments to structure in order to control modal vibration effectively.

Yue et al. (2016) experimental setup proves good real-time performance which is of great help to practical application in space smart structures and structonic system.

REFERENCE

Yue, H., Lu, Y., Deng, Z., Tzou, H. Experiment on Vibration Control of a Piezoelectric Laminated Paraboloidal Shell. Mechanical Systems and Signal Processing, 2016, Volume 82, pp 279-295.     

About the author

 Prof. Honghao Yue, Ph.D., graduated in Harbin Institute of Technology, is the director of Dept. Aeronautics and Astronautics Manufacturing Engineering in Harbin Institute of Technology. His main research interests include smart structure system and space structure and mechanism. He works in the area of advanced space connection and separation technology, smart material structure system design and space structure active vibration control, to which he has given many contributions. He has more than forty academic papers published in international famous journals and academic conferences, plus one monograph and six patents of invention.

Journal Reference

Honghao Yue1, Yifan Lu1 , Zongquan Deng1, Hornsen Tzou. Experiment on Vibration Control of a Piezoelectric Laminated Paraboloidal Shell.  Mechanical Systems and Signal Processing, Volume 82, 1 January 2017, Pages 279–295.
[expand title=”Show Affiliations”]
  1. School of Mechatronics Engineering, Harbin Institute of Technology, Harbin, Heilongjiang Province 150001, PR China
  2. College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, PR China
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