Journal of Applied and Computational Mechanics

Stress Control of a Piezoelectric Lumped-element Model − ‎Theoretical Investigation and Experimental Realization

Document Type : Special Issue Paper

Authors

Institute of Technical Mechanics, Johannes Kepler University Linz, Altenberger Strasse 69, 4040 Linz, Austria‎

Abstract

This contribution focuses on force- and stress-tracking of a multi-degree of freedom system by eigenstrain actuation. The example under consideration is an axially excited piezoelectric bar which can be modeled as a lumped parameter system. The piezoelectric effect serves as actuation source and the question is answered how to prescribe the piezoelectric actuation in order to achieve a desired stress distribution, or, in the lumped case, a desired distribution of internal forces. First, the equations of motion are set up in matrix notation where the state vector contains the displacement components. After some basic manipulations, the governing equation can be written in terms of the internal force vector. Now, if one intends to have a certain desired internal force distribution, it is straightforward to find a condition for the piezoelectric control actuation. The developed theory is first verified by using a continuous piezoelectric bar, where the motion of one end is prescribed. Then the theory is experimentally verified: a lumped two-degree of freedom system is investigated and the goal is to reduce the stress or the internal force in order to avoid mechanical damage. The force-controlled configuration is exposed to a sweep-signal excitation between 1000−4900 Hz, running for 22 minutes without any signs of damage. Then the same system is excited by the same excitation but without piezoelectric control. After some seconds the test sample is visibly damaged, going along with a significant reduction of the first eigenfrequency. This gives strong evidence for the appropriateness of the proposed stress or force control methodology.

Keywords

Main Subjects

[1] Yang, J., Analysis of Piezoelectric Devices, World Scientific, Hackensack, NJ, 2006.
[2] Preumont, A., Mechatronics: Dynamics of Electromechanical and Piezoelectric Systems, Springer, 2006.
[3] Safari, A., Akdogan, E.K. (Eds.), Piezoelectric and Acoustic Materials for Transducer Applications, Springer, 2008.
[4] Moheimani, S.O.R., Fleming, A.J., Piezoelectric Transducers for Vibration Control and Damping, Springer, London, 2006.
[5] Irschik, H., A review on static and dynamic shape control of structures by piezoelectric actuation, Engineering Structures, 24, 2002, 5–11.
[6] Irschik, H., Krommer, M., Nader, M., Schöftner, J., Zehetner, C., Active and Passive Shape Control of Structures, Proceedings 5th European Conference on Structural Control (EACS 2012), E. Del Grosso, P. Basso. (Eds.), Genua, Italy 2012, Paper No. 146, 8 pages, 2012.
[7] Irschik, H., , Krommer, M., A Review on Static and Dynamic Shape Control of Structures: The Period 2002-2012, Proceedings Vienna Congress on Recent Advances in Earthquake Engineering and Structural Dynamics 2013(VEESD 2013), C. Adam, R. Heuer, W. Lenhardt, C. Schranz (Eds.), Vienna, Austria 2013, Paper No. 581, 2013.
[8] Irschik, H., Krommer, M., Zehetner, Ch., Displacement tracking of pre-deformed smart structures, Smart Structures and Systems, 18, 2016, 139-154.
[9] Austin, F., Rossi, M.J., Van Nostrand, W., Knowles, G., Static shape control of adaptive wings, AIAA Journal, 32, 1994, 1895–1901.
[10] Agrawal, B.N., Treanor, K.E., Shape control of a beam using piezoelectric actuators, Smart Materials and Structures, 8, 1999, 729–740.
[11] Schoeftner, J., Irschik, H., Passive damping and exact annihilation of vibrations of beams using shaped piezoelectric layers and tuned inductive networks, Smart Materials and Structures, 18, 2009, 125008 (9pp).
[12] Schoeftner, J., Irschik, H., Passive shape control of force-induced harmonic lateral vibrations for laminated piezoelastic Bernoulli–Euler beams—theory and practical relevance, Smart Structures and Systems, 7, 2011, 417–432.
[13] Schoeftner, J., Buchberger, G., Brandl, A., Irschik, H., Theoretical prediction and experimental verification of shape control of beams with piezoelectric patches and resistive circuits, Composite Structures, 133, 2015, 746–755.
[14] Schoeftner, J., Irschik, H., Buchberger, G., Static and dynamic shape control of slender beams by piezoelectric actuation and resistive electrodes, Composite Structures, 111, 2014, 66–74.
[15] Schoeftner, J., Buchberger, G., Active shape control of a cantilever by resistively interconnected piezoelectric patches, Smart Structures and Systems, 12, 2013, 501–521.
[16] Giorgio, I., Culla, A., Del Vescovo, D., Multimode vibration control using several piezoelectric transducers shunted with a multiterminal network, Archive of Applied Mechanics, 79, 2009, 859–879.
[17] Lossouarn, B., Deü, J. F., Aucejo, M., Multimodal vibration damping of a beam with a periodic array of piezoelectric patches connected to a passive electrical network, Smart Materials and Structures, 24(11), 2015, 115037.
[18] Rosi, G., Pouget, J., dell'Isola, F., Control of sound radiation and transmission by a piezoelectric plate with an optimized resistive electrode, European Journal of Mechanics-A/Solids, 29(5), 2010, 859-870.
[19] Trindade, M.A., Maio, C.E.B, Multimodal passive vibration control of sandwich beams with shunted shear piezoelectric materials, Smart Materials and Structures, 17(5), 2008, 055015 (10 pages).
[20] Benjeddou, A., Ranger, J. A., Use of shunted shear-mode piezoceramics for structural vibration passive damping, Computers and Structures, 84, 2006, 1415–1425.
[21] Lediaev, L., Finite element modeling of piezoelectric bimorphs with conductive polymer electrodes, doctoral thesis Montana State University, Bozeman, Montana, 2010.
[22] Suresh, S., Fatigue of Materials, 2nd Edition, Cambridge University Press, 1998.
[23] Schijve, J., Fatigue of Structures and Materials, 2nd Edition, Springer, 2009.
[24] Weisshaar, T., Aerospace Structures – an Introduction to Fundamental Problems, West Lafayette, In: Purdue University, 2011, (https://engineering.purdue.edu/AAECourses/aae352/2013/AAE%20352%20Course%20Text%­20Weisshaar%202011.pdf).
[25] Irschik, H., Generation of transient desired displacement or stress fields in force loaded solids and structures by smart actuation, in: Proc. XXXV Summer School Advanced Problems in Mechanics (APM2007), Saint-Petersburg, Russia, 2007.
[26] Irschik, H., Krommer, M., Gusenbauer, M., Tracking of Stresses: A Further Step towards Ageless Structures. in: H. Irschik, M. Krommer, K. Watanabe, T. Furukawa (Eds.), Proc. 1st Joint Japan-Austria Workshop Mechanics and Model Based Control of Smart Materials and Structures, September, 2008, Linz, Austria, Springer Wien New York, 77–84, 2009.
[27] Irschik, H., Gusenbauer, M., Pichler, U., Dynamic stress compensation by smart actuation, in: R.C. Smith (Ed.), Proceedings of SPIE on Smart Structures and Materials 2004: Modeling, Signal Processing, and Control, San Diego, CA, 2004, SPIE vol. 5383, Paper No. 386, 2004.
[28] Schoeftner, J., Irschik, H., Stress tracking of piezoelectric bars by eigenstrain actuation, Journal of Sound and Vibration, 383, 2016, 35–45.
[29] Schoeftner, J., Bending moment tracking and the reduction of the axial stress in vibrating beams by piezoelectric actuation, Acta Mechanica, 228, 2017, 3827–3838.
[30] Schoeftner, J., Brandl, A., Irschik, H., Control of stress and damage in structures by piezoelectric actuation: 1D theory and monofrequent experimental validation, Structural Control and Health Monitoring, 26(5), 2019, e2338 (14pp).
[31] Schoeftner, J., Irschik, H., A comparative study of smart passive piezoelectric structures interacting with electric networks: Timoshenko beam theory versus finite element plane stress calculations, Smart Materials and Structures, 20, 2011, 025007 (13pp).
[32] Website of the manufacturer of the piezoelectric stack: https://www.piezosystem.com/fileadmin/ Piezocomposite/Datenblaetter/Aktoren/en/Stapel/VS/PSt_1000_VS_35_ds_Rev00_2017_01_09.pdf (February 26th, 2018).
[33] Website of the manufacturer of the piezoelectric transducer: https://www.physikinstrumente.de/ fileadmin/user_upload/physik_instrumente/files/datasheets/P-882-Datenblatt.pdf (February 26th, 2018).
[34] Dent, A.C.E, Bowen, C.R., Stevens, R., Cain, M.G., Stewart, M., Tensile Strength of Active Fibre Composites Prediction and Measurement, Ferroelectrics, 368, 2008, 209–215.
Journal of Applied and Computational Mechanics
Volume 7, Special Issue
June 2021
Pages 1110-1120