Identyfikatory
Warianty tytułu
Języki publikacji
Abstrakty
A powerful computational methodology, named the barycentric Lagrange interpolation iteration collocation method (BLIICM), for solving nonlinear bending problems of a doubly clamped microbeam under electrostatic loads is presented. The nonlinear governing equation of the microbeam is converted into a linear differential equation by assuming the initial function. The barycentric Lagrange interpolation collocation method (BLICM) is used to solve the linear differential equation. The direct linearization formulations and Newton linearization calculation formulations for the nonlinear differential equation have been given. The calculation method and formulation of the nonlinear integral term have been discussed in details. By applying a barycentric Lagrange interpolation differential matrix, a matrix-vector calculation formula of BLIICM has been established. Numerical results of calculation examples show that the advantages of the proposed methodology are efficient, simple and of high precision.
Czasopismo
Rocznik
Tom
Strony
741--749
Opis fizyczny
Bibliogr. 21 poz., rys., tab.
Twórcy
autor
- Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, Southeast University, Nanjing, China and School of Civil Engineering, Southeast University, Nanjing, China
autor
- Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, Southeast University, Nanjing, China and School of Civil Engineering, Southeast University, Nanjing, China
autor
- Institute of Mechanics, Shandong Jianzhu University, Jinan, China
Bibliografia
- 1. Batra R.C., Porfir M., Spinello D., 2008, Vibrations of narrow microbeams predeformed by an electric field, Journal of Sound and Vibration, 309, 3-5, 600-612
- 2. Berrut J.P., Baltensperger R., Mittelmann H.D., 2005, Recent developments in barycentric rational interpolation, [In:] Trends and Applications in Constructive Approximation, D.H. Mache, J. Szabados, M.G. de Bruin (Edit), 27-51
- 3. Berrut J.P., Trefethen L.N., 2004, Barycentric Lagrange interpolation, SIAM Review, 46, 3, 501-517
- 4. Brusa E., Bona F.D., Gugliotta A., 2004, Modeling and prediction of the dynamic behaviour of microbeams under electrostatic load, Analog Integrated Circuits and Signal Processing, 40, 2, 155-164
- 5. Choi B., 1992, Diaphragm Stretching and Contact Problems for Microelectromechanical Pressure Transducers, Madison: University of Wisconsin
- 6. Choi B., Lovell E.G., 1997, Improved analysis of microbeams under mechanical and electrostatic loads, Journal of Micromechanics and Microengineering, 7, 1, 24-29
- 7. Floater M.S., Hormann K., 2007, Barycentric rational interpolation with no poles and high rates of approximation, Numerische Mathematik, 107, 2, 315-331
- 8. Karami G., Malekzadeh P., 2002, A new differential quadrature methodology for beam analysis and the associated differential quadrature element method, Computer Methods in Applied Mechanics and Engineering, 191, 32, 3509-3526
- 9. Kuang J.H., Chen C.J., 2004, Dynamic characteristics of shaped micro-actuators solved using the differential quadrature method, Journal of Micromechanics and Microengineering, 14, 4, 647-655
- 10. Li S.C., Wang Z.Q., 2012, Algorithm, Program and Engineering Application on High Precision and Meshless Barycentric Interpolation Collocation Method, Beijing: Science Press
- 11. Najar F., Choura S., Elborgi S., Abdelrahman E.M., Nayfeh A.H., 2004, Modeling and design of variable-geometry electrostatic microactuators, Journal of Micromechanics and Microengineering, 15, 3, 419-429
- 12. Nayfeh A.H., Mook D.T., Lobitz D.W., 1974, Numerical-perturbation method for the nonlinear analysis of structural vibrations, AIAA Journal, 12, 9, 1222-1228
- 13. Refwield L.W., 2015, Nonlinear flexural oscillations of shallow arches, AIAA Journal, 12, 1, 91-93
- 14. Rezazadeh G., Tahmasebi A., Ziaei-Rad S., 2009, Nonlinear electrostatic behavior for two elastic parallel fixed-fixed and cantilever microbeams, Mechatronics, 19, 6, 840-846
- 15. Sadeghian H., Rezazadeh G., Osterberg P.M., 2007, Application of the generalized differential quadrature method to the study of pull-in phenomena of MEMS switches, Journal of Microelectromechanical Systems, 16, 6, 1334-1340
- 16. Shu C., Du H., 1997, Implementation of clamped and simply supported boundary conditions in the GDQ free vibration analysis of beams and plates, International Journal of Solids and Structures, 34, 7, 819-835
- 17. Tomasiello S., 1998, Differential quadrature method application to initial-boundary-value problems, Journal of Sound and Vibration, 218, 4, 573-585
- 18. Wang Z.Q., Jiang J., Tang B.T., Zheng W., 2014, Numerical solution of bending problem for elliptical plate using differentiation matrix method based on barycentric Lagrange interpolation, Applied Mechanics and Materials, 638-640, 1720-1724
- 19. Wang Z.Q., Li S.P., Tang B.T., 2007., Formulations, algorithms and applications on barycentric interpolation in 1D, Journal of Shandong Jianzhu University, 22, 4, 448-453
- 20. Wang Z.Q., Li S.C., Ping Y., Jiang J., Ma T.F., 2014, A highly accurate regular domain collocation method for solving potential problems in the irregular doubly connected domains, Mathematical Problems in Engineering, 2014, 4, 1-9
- 21. Zand M.M., Ahmadian M.T., Rashidian B., 2009, Semi-analytic solutions to nonlinear vibrations of microbeams under suddenly applied voltages, Journal of Sound and Vibration, 325, 1, 382-396
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-d5887b28-1fb6-4b4d-8f78-8962570d6758
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