Piezoelectric actuator/sensor modeling with finite element method using Chebyshev polinomials
UDC
539.3Abstract
Piezoelectric sensors are widely used in the structural health monitoring applications. The failure of a number of the actuators can result in the wrong answer of the whole monitoring system. Therefore dynamic behaviour of the damaged sensors should be investigated. For this purpose a coupled mathematical model of the sensor attached to the composite layer must be developed. In such a model the actuator could be simulated with a high precision finite element method. In this paper the usage of the Chebyshev and Gauss-Legendre-Lobatto polynomials in the high precision finite element model is discussed. The convergence of the displacements and discrepancy between the solution and the boundary conditions are analyzed. The resonance properties of the actuator are studied. The advisability of the Chebyshev polynomials usage for the finite element actuator model is discussed in the conclusion.
Keywords:
high precision finite element method, Chebyshev polynomials, Gauss-Legendre-Lobatto polynomials, piezoelasticity, sensor, resonance, integral approach, coupled modelFunding information
Работа выполнена при финансовой поддержке РФФИ (14-08-00370).
References
- Glushkov E., Glushkova N., Kvasha O., Seemann W. Integral equation based modeling of the interaction between piezoelectric patch actuators and an elastic substrate // Smart Materials and Structures. 2007. No. 16. С. 650-664.
- Giurgiutiu V. Structural health monitoring with piezoelectric wafer active sensors (second edition). Elsevier Academic Press, 2014. 1024 p.
- Moll J., Fritzen C.-P., Golub M.V., Glushkov E., Glushkova N. Non-axisymmetric lamb wave excitation by piezoelectric wafer active sensors // Sensors and Actuators A:Physical. 2012. Vol. 174. No. 1. С. 173-180.
- Голуб М.В., Шпак А.Н., Бюте И., Фритцен К.-П. Моделирование гармонических колебаний и определение реонансных частот полосового пьезоэлектрического актуатора методом конечных элементов высокого порядка точности // Вычислительная механика сплошных сред. 2015. № 4. С. 397-407. [Golub M.V., Shpak A.N., Buethe I., Fritzen C.-P. Modelirovanie garmonicheskikh kolebaniy i opredelenie reonansnykh chastot polosovogo p'ezoelektricheskogo aktuatora metodom konechnykh elementov vysokogo poryadka tochnosti [Harmonic motion simulation and resonance frequencies determination of a piezoelectric strip-like actuator using high precision finite element method]. Vychislitel'naya mekhanika sploshnykh sred [Computational continuum mechanics], 2015, no. 4, pp. 397-407. (In Russian)]
- Бубенчиков А.М., Попонин В.С., Мельникова В.Н. Математическая постановка и решение пространственных краевых задач методом спектральных элементов // Вестник томского государственного университета. Математика и механика. 2008. Vol. 4. № 3. С. 70-76. [Bubenchikov A.M., Poponin V.S., Melnikova V.N. Matematicheskaya postanovka i reshenie prostranstvennykh kraevykh zadach metodom spektral'nykh elementov [The mathematical statement and solution of spatial boundary value problems by means of spectral element method]. Vestnik tomskogo gosudarstvennogo universiteta. Matematika i mekhanika [Bulletin of Tomskiy State University. Mathematics and Mechanics], 2008, vol. 4, no.3, pp. 70-76. (In Russian)]
- Iovane G., Nasedkin A.V. Modal analysis of piezoelectric bodies with voids. II. Finite element simulation // Applied mathmatical modeling. 2010. Vol. 34. No. 1. С. 47-59.
- Бабешко В. А., Глушков Е.В., Зинченко Ж.Ф. Динамика неоднородных линейно-упругих сред. М: Наука, 1989. 344 c. [Babeshko V.A., Glushkov E.V., Zinchenko Zh.F. Dinamika neodnorodnyh lineino-uprigih sred [The dynamics of the heterogeneous linear-elastic solids]. Moscow, Nauka Publ., 1989, 344 p. (In Russian)]
- Glushkov E., Glushkova N., Eremin A. Forced wave propagation and energy distribution in anisotropic laminate composites // Journal of the Acoustical Society of America. 2011. No. 126. С. 2923-2934.
- Komatitsch D., Vilotte J.-P., Vai R., Castillo-Covarrubias J.M., Sanchez-Sesma F.-J. The spectral element method for elastic wave equations - application to 2-D and 3-D seismic problems // International journal for numerical methods in engineering. 1999. № 45. С. 1139-1164.
- Priolo E., Carlione J. M., Seriani G. Numerical simulation of interface waves by high-order spectral modeling techniques // Journal of the Acoustical Society of America. 1994. Vol. 95. № 2. С. 681-693.
- Ostachowicz W., Kudela P., Krawczuk M., Zak A. Guided waves in structures for SHM. The time-domain spectral element method. Polish Academy of Sciences. Institute of Fluid Flow Machinery, 2012. 337 c.
- Glushkov E.V., Glushkova N.V., Golub M.V., Boström A. Natural resonance frequencies, wave blocking, and energy localization in an elastic half-space and waveguide with a crack // Journal of the Acoustical Society of America. 2006. № 119. С. 3589-3598.
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Dates
Submitted
December 14, 2015
Accepted
December 17, 2015
Published
December 28, 2015
How to Cite
[1]
Shpak, A.N., Piezoelectric actuator/sensor modeling with finite element method using Chebyshev polinomials. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2015, № 4, pp. 75–85.
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Copyright (c) 2015 Шпак А.Н.
This work is licensed under a Creative Commons Attribution 4.0 International License.
