EDP Sciences logo
Subscriber Authentication Point
Search
Menu
All issues Volume 28 (2022) ESAIM: COCV, 28 (2022) 39 References
Open Access
Issue
ESAIM: COCV
Volume 28, 2022
Article Number 39
Number of page(s) 26
DOI https://doi.org/10.1051/cocv/2022036
Published online 29 June 2022
  1. V. Barbu, Nonlinear Differential Equations of Monotone Types in Banach Spaces. Springer Monographs in Mathematics. Springer, New York (2010). [CrossRef] [Google Scholar]
  2. C. Baur, D.J. Apo, D. Maurya, S. Priya and M. Voit, Piezoelectric polymer composites for vibrational energy harvesting. Am. Chem. Soc. (2014), Chapter 1, pp. 1–27. [Google Scholar]
  3. I. Chueshov, M. Eller and I. Lasiecka, On the attractor for a semilinear wave equation with critical exponent and nonlinear boundary dissipation. Commun. Partial Differ. Equ. 27 (2002) 1901–1951. [CrossRef] [Google Scholar]
  4. I. Chueshov, M. Eller and I. Lasiecka, Finite dimensionality of the attractor for a semilinear wave equation with nonlinear boundary dissipation. Commun. Partial Differ. Equ. 29 (2004) 1847–1876. [Google Scholar]
  5. I. Chueshov and I. Lasiecka, Global attractors for von Karman evolutions with a nonlinear boundary dissipation. J. Differ. Equ. 198 (2004) 196–231. [CrossRef] [Google Scholar]
  6. I. Chueshov and I. Lasiecka, Long-time dynamics of von Karman semi-flows with non-linear boundary/interior damping. J. Diff. Equ. 233 (2007) 42–86. [CrossRef] [Google Scholar]
  7. I. Chueshov and I. Lasiecka, Long-time behavior of second order evolution equations with nonlinear damping. Vol. 195 of Mem. Amer. Math. Soc. Providence (2008). [Google Scholar]
  8. I. Chueshov and I. Lasiecka, Von Karman Evolution Equations. Well-posedness and Long Time Dynamics. Springer Monographs in Mathematics. Springer, New York (2010). [CrossRef] [Google Scholar]
  9. A.N. Darinskii, E. Le Clezio and G. Feuillard, The role of electromagnetic waves in the reflection of acoustic waves in piezoelectric crystals. Wave Motion. 45 (2008) 428–444. [CrossRef] [MathSciNet] [Google Scholar]
  10. S. Devasia, V. Eleftheriou and S.O. Reza Moheimani, A survey of control issues in nanopositioning. IEEE Trans. Control Syst. Technol. 15 (2007) 802–823. [CrossRef] [Google Scholar]
  11. W. Dong, L. Xiao, W. Hu, C. Zhu, Y. Huang and Z. Yin, Wearable human—machine interface based on PVDF piezoelectric sensor. Trans. Inst. Measur. Control. 39 (2017) 398–403. [CrossRef] [Google Scholar]
  12. F. Ebrahimi and M.R. Barati, Vibration analysis of smart piezoelectrically actuated nano-beams subjected to magnetoelectrical field in thermal environment. J. Vibr. Control. 24 (2016) 549–564. [Google Scholar]
  13. A. Erturk, Assumed-modes modeling of piezoelectric energy harvesters: Euler-Bernoulli, Rayleigh, and Timoshenko models with axial deformations. Comput. Struct. 106/107 (2012) 214–227. [CrossRef] [Google Scholar]
  14. G.Y. Gu et al., Modeling and control of piezo-actuated nanopositioning stages: a survey. IEEE Trans. Autom. Sci. Eng. 13 (2016) 313–332. [CrossRef] [Google Scholar]
  15. P.G. Geredeli and I. Lasiecka, Asymptotic analysis and upper semicontinuity with respect to rotational inertia of attractors to von Karman plates with geometrically localized dissipation and critical nonlinearity. Nonlinear Anal. 91 (2013) 72–92. [CrossRef] [MathSciNet] [Google Scholar]
  16. B. Feng and A.O. Ozer, Long-time behavior of a nonlinearly-damped three-layer Rao-Nakra sandwich beam (2022). [Google Scholar]
  17. J.K. Hale and G. Raugel, Upper semicontinuity of the attractor for a singulary perturbed hyperbolic equation. J. Differ. Equ. 73 (1988) 197–214. [CrossRef] [Google Scholar]
  18. M.A. Horn and I. Lasiecka, Asymptotic behavior with respect to thickness of boundary stabilizing feedback for the Kirchhoff plate. J. Differ. Equ. 114 (1994) 396–433. [CrossRef] [Google Scholar]
  19. M.A. Jorge Silva and V. Narciso, Attractors and their properties for a class of nonlocal extensible beams. Discrete Contin. Dyn. Syst. 35 (2015) 985–1008. [CrossRef] [MathSciNet] [Google Scholar]
  20. D.H. Kim et al., Microengineered platforms for cell mechanobiology. Annu. Rev. Biomed. Eng. 11 (2009) 203–233. [CrossRef] [PubMed] [Google Scholar]
  21. J.E. Lagnese and G. Leugering, Uniform stabilization of a nonlinear beam by nonlinear boundary feedback. J. Differ. Equ. 91 (1991) 355–388. [CrossRef] [Google Scholar]
  22. I. Lasiecka, Finite-dimensionality of attractors associated with von Karman plate equations and boundary damping. J. Diff. Equ. 117 (1995) 357–389. [CrossRef] [Google Scholar]
  23. I. Lasiecka, Local and global compact attractors arising in nonlinear elasticity: the case of noncompact nonlinearity and nonlinear dissipation. J. Math. Anal. Appl. 196 (1995) 332–360. [CrossRef] [MathSciNet] [Google Scholar]
  24. I. Lasiecka and D. Tataru, Uniform boundary stabilization of semilinear wave equations with nonlinear boundary damping. Differ. Integr. Equ. 6 (1993) 507–533. [Google Scholar]
  25. T.F. Ma and R.N. Monteiro, Singular limit and long-time dynamics of Bresse systems. SIAM J. Math. Anal. 4 (2017) 2468–2495. [Google Scholar]
  26. G.P. Menzala and E. Zuazua, Timoshenko’s beam equation as limit of a nonlinear onedimensional Von Karman system. SIAM J. Math. Anal. 130A (2000) 855–875. [Google Scholar]
  27. K.A. Morris and A.Ö. Özer, Strong stabilization of piezoelectric beams with magnetic effects. In: The Proceedings of 52nd IEEE Conference on Decision & Control (2013) 3014–3019. [CrossRef] [Google Scholar]
  28. K.A. Morris and A.Ö. Özer, Modeling and stabilizability of voltage-actuated piezoelectric beams with magnetic effects. SIAM J. Control Optim. 52 (2014) 2371–2398. [CrossRef] [MathSciNet] [Google Scholar]
  29. A.Ö. Özer and A.K. Aydin, Uniform observability of filtered approximations for a three-layer Mead-Marcus beam equation. Preprint. [Google Scholar]
  30. A.Ö. Özer and W. Horner, Uniform boundary observability of Finite Difference approximations of non-compactly-coupled piezoelectric beam equations. Appl. Anal. 101 (2021) 1571–1592. [Google Scholar]
  31. A.Ö. Özer, Further stabilization and exact observability results for voltage-actuated piezoelectric beams with magnetic effects. Math. Control Signals Syst. 27 (2015) 219–244. [CrossRef] [Google Scholar]
  32. A.Ö. Özer, Dynamic and electrostatic modeling for a piezoelectric smart composite and related stabilization results. Evol. Equ. Control Theory 7 (2018) 639–868. [CrossRef] [MathSciNet] [Google Scholar]
  33. A.J.A. Ramos, C.S.L. Gonçalves and S.S. Corrêa Neto, Exponential stability and numerical treatment for piezoelectric beams with magnetic effect. Modélisation Mathématique et Analyse Numérique. 52 (2018) 255–274. [Google Scholar]
  34. A.Ö. Özer, Stabilization results for well-posed potential formulations of a current-controlled piezoelectric beam and their approximations. Appl. Math. Optim. (2020) 1–38. [Google Scholar]
  35. A.J.A. Ramos, M.M. Freitas, D.S. AlmeidaJr., S.S. Jesus and T.R.S. Moura, Equivalence between exponential stabilization and boundary observability for piezoelectric beams with magnetic effect. Z. Angew. Math. Phys. 70 (2019) 60. [CrossRef] [Google Scholar]
  36. A. Ruiz, Unique continuation for weak solutions of the wave equation plus a potential. J. Math. Pures Appl. 71 (1992) 455–467. [MathSciNet] [Google Scholar]
  37. J. Simon, Compact sets in the space Lp(0,T; B). Annali di Matematica Pura ed Applicata. 146 (1987) 65–96. [Google Scholar]
  38. R.C. Smith, Smart Material Systems. Society for Industrial and Applied Mathematics, Philladelphia, PA (2005). [Google Scholar]
  39. D. Tallarico, N. Movchan, A. Movchan and M. Camposaragna, Propagation and filtering of elastic and electromagnetic waves in piezoelectric composite structures. Math. Meth. Appl. Sci. 40 (2017) 3202–3220. [CrossRef] [Google Scholar]
  40. D. Tataru, Uniform decay rates and attractors for evolution PDE’s with boundary dissipation. J. Diff. Equ. 121 (2005) 1–27. [Google Scholar]
  41. J. Yang, Fully-dynamic theory, in Special Topics in the Theory of Piezoelectricity, edited by J. Yang. Springer, New-York (2009). [CrossRef] [Google Scholar]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.