-
Previous Article
Optimal control problems for some ordinary differential equations with behavior of blowup or quenching
- MCRF Home
- This Issue
-
Next Article
Feedback stabilization with one simultaneous control for systems of parabolic equations
Weak stability of a laminated beam
1. | College of Mathematics and Information Science, Henan Normal University, Xinxiang 453007, China |
2. | Department of Mathematics and Statistics, University of Minnesota, Duluth, MN 55812, USA |
3. | College of Information Science and Technology, Donghua University, School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai 201620, China |
In this paper, we consider the stability of a laminated beam equation, derived by Liu, Trogdon, and Yong [
References:
[1] |
A. A. Allen and S. W. Hansen,
Analyticity of a multilayer Mead-Markus plate, Nonliear Anal., 71 (2009), e1835-e1842.
doi: 10.1016/j.na.2009.02.063. |
[2] |
A. A. Allen and S. W. Hansen,
Analyticity and optimal damping for a multilayer Mead-Markus sandwich beam, Discrete Contin. Dyn. Syst. Ser. B., 14 (2010), 1279-1292.
doi: 10.3934/dcdsb.2010.14.1279. |
[3] |
A. Borichev and Y. Tomilov,
Optimal polynomial decay of functions and operator semigroups, Math. Ann., 347 (2010), 455-478.
doi: 10.1007/s00208-009-0439-0. |
[4] |
S. W. Hansen and Z. Liu, Analyticity of semigroup associated with a laminated composite
beam, Control of Distributed Parameter and Stochastic Systems (Hangzhou, 1998), Kluwer
Acad. Publ., Boston, MA, 1999, 47–54. |
[5] |
S. W. Hansen and R. Spies,
Structural damping in a laminated beam due to interfacial slip, J. Sound and Vibration, 204 (1997), 183-202.
doi: 10.1006/jsvi.1996.0913. |
[6] |
Z. Liu, S. A. Trogdon and J. Yong,
Modeling and analysis of a laminated beam, Math. Comput. Modeling, 30 (1999), 149-167.
doi: 10.1016/S0895-7177(99)00122-3. |
[7] |
Z. Liu and S. Zheng,
Semigroup Associated with Dissipative System, Res. Notes Math., Vol 394, Chapman & Hall/CRC, Boca Raton, 1999. |
[8] |
D. J. Mead and S. Markus,
The forced vibration of a three-layer, damped sandwich beam with arbitrary boundary conditions, J. Sound Vibr.(2), 10 (1969), 163-175.
doi: 10.1016/0022-460X(69)90193-X. |
[9] |
A. Özkan Özer and S. W. Hansen,
Uniform stabilization of a multilayer Rao-Nakra sandwich beam, Evol. Equ. Control Theorey, 2 (2013), 695-710.
doi: 10.3934/eect.2013.2.695. |
[10] |
Y. V. K. S Rao and B. C. Nakra, Vibrations of unsymmetrical sanwich beams and plates with viscoelastic cores, J. Sound Vibr.(3), 34 (1974), 309-326. Google Scholar |
[11] |
C. A. Raposo,
Exponential stability of a structure with interfacial slip and frictional damping, Applied Math. Letter, 53 (2016), 85-91.
doi: 10.1016/j.aml.2015.10.005. |
[12] |
J. M. Wang, G. Q. Xu and S. P. Yung,
Stabilization of laminated beams with structural damping by boundary feedback controls, SIAM Control Optim., 44 (2005), 1575-1597.
doi: 10.1137/040610003. |
[13] |
M. J. Yan and E. H. Dowell, Governing equations for vibratory constrained-layer damping sandwich plates and beams, J. Appl. Mech.(4), 39 (1972), 1041-1046. Google Scholar |
show all references
References:
[1] |
A. A. Allen and S. W. Hansen,
Analyticity of a multilayer Mead-Markus plate, Nonliear Anal., 71 (2009), e1835-e1842.
doi: 10.1016/j.na.2009.02.063. |
[2] |
A. A. Allen and S. W. Hansen,
Analyticity and optimal damping for a multilayer Mead-Markus sandwich beam, Discrete Contin. Dyn. Syst. Ser. B., 14 (2010), 1279-1292.
doi: 10.3934/dcdsb.2010.14.1279. |
[3] |
A. Borichev and Y. Tomilov,
Optimal polynomial decay of functions and operator semigroups, Math. Ann., 347 (2010), 455-478.
doi: 10.1007/s00208-009-0439-0. |
[4] |
S. W. Hansen and Z. Liu, Analyticity of semigroup associated with a laminated composite
beam, Control of Distributed Parameter and Stochastic Systems (Hangzhou, 1998), Kluwer
Acad. Publ., Boston, MA, 1999, 47–54. |
[5] |
S. W. Hansen and R. Spies,
Structural damping in a laminated beam due to interfacial slip, J. Sound and Vibration, 204 (1997), 183-202.
doi: 10.1006/jsvi.1996.0913. |
[6] |
Z. Liu, S. A. Trogdon and J. Yong,
Modeling and analysis of a laminated beam, Math. Comput. Modeling, 30 (1999), 149-167.
doi: 10.1016/S0895-7177(99)00122-3. |
[7] |
Z. Liu and S. Zheng,
Semigroup Associated with Dissipative System, Res. Notes Math., Vol 394, Chapman & Hall/CRC, Boca Raton, 1999. |
[8] |
D. J. Mead and S. Markus,
The forced vibration of a three-layer, damped sandwich beam with arbitrary boundary conditions, J. Sound Vibr.(2), 10 (1969), 163-175.
doi: 10.1016/0022-460X(69)90193-X. |
[9] |
A. Özkan Özer and S. W. Hansen,
Uniform stabilization of a multilayer Rao-Nakra sandwich beam, Evol. Equ. Control Theorey, 2 (2013), 695-710.
doi: 10.3934/eect.2013.2.695. |
[10] |
Y. V. K. S Rao and B. C. Nakra, Vibrations of unsymmetrical sanwich beams and plates with viscoelastic cores, J. Sound Vibr.(3), 34 (1974), 309-326. Google Scholar |
[11] |
C. A. Raposo,
Exponential stability of a structure with interfacial slip and frictional damping, Applied Math. Letter, 53 (2016), 85-91.
doi: 10.1016/j.aml.2015.10.005. |
[12] |
J. M. Wang, G. Q. Xu and S. P. Yung,
Stabilization of laminated beams with structural damping by boundary feedback controls, SIAM Control Optim., 44 (2005), 1575-1597.
doi: 10.1137/040610003. |
[13] |
M. J. Yan and E. H. Dowell, Governing equations for vibratory constrained-layer damping sandwich plates and beams, J. Appl. Mech.(4), 39 (1972), 1041-1046. Google Scholar |
[1] |
Bopeng Rao. Optimal energy decay rate in a damped Rayleigh beam. Discrete & Continuous Dynamical Systems - A, 1998, 4 (4) : 721-734. doi: 10.3934/dcds.1998.4.721 |
[2] |
Qiong Zhang. Exponential stability of a joint-leg-beam system with memory damping. Mathematical Control & Related Fields, 2015, 5 (2) : 321-333. doi: 10.3934/mcrf.2015.5.321 |
[3] |
Maya Bassam, Denis Mercier, Ali Wehbe. Optimal energy decay rate of Rayleigh beam equation with only one boundary control force. Evolution Equations & Control Theory, 2015, 4 (1) : 21-38. doi: 10.3934/eect.2015.4.21 |
[4] |
Farah Abdallah, Denis Mercier, Serge Nicaise. Spectral analysis and exponential or polynomial stability of some indefinite sign damped problems. Evolution Equations & Control Theory, 2013, 2 (1) : 1-33. doi: 10.3934/eect.2013.2.1 |
[5] |
Kai Liu, Zhi Li. Global attracting set, exponential decay and stability in distribution of neutral SPDEs driven by additive $\alpha$-stable processes. Discrete & Continuous Dynamical Systems - B, 2016, 21 (10) : 3551-3573. doi: 10.3934/dcdsb.2016110 |
[6] |
Xun-Yang Wang, Khalid Hattaf, Hai-Feng Huo, Hong Xiang. Stability analysis of a delayed social epidemics model with general contact rate and its optimal control. Journal of Industrial & Management Optimization, 2016, 12 (4) : 1267-1285. doi: 10.3934/jimo.2016.12.1267 |
[7] |
Luis Barreira, Claudia Valls. Delay equations and nonuniform exponential stability. Discrete & Continuous Dynamical Systems - S, 2008, 1 (2) : 219-223. doi: 10.3934/dcdss.2008.1.219 |
[8] |
Augusto Visintin. Structural stability of rate-independent nonpotential flows. Discrete & Continuous Dynamical Systems - S, 2013, 6 (1) : 257-275. doi: 10.3934/dcdss.2013.6.257 |
[9] |
Emine Kaya, Eugenio Aulisa, Akif Ibragimov, Padmanabhan Seshaiyer. A stability estimate for fluid structure interaction problem with non-linear beam. Conference Publications, 2009, 2009 (Special) : 424-432. doi: 10.3934/proc.2009.2009.424 |
[10] |
Emine Kaya, Eugenio Aulisa, Akif Ibragimov, Padmanabhan Seshaiyer. Stability analysis of inhomogeneous equilibrium for axially and transversely excited nonlinear beam. Communications on Pure & Applied Analysis, 2011, 10 (5) : 1447-1462. doi: 10.3934/cpaa.2011.10.1447 |
[11] |
Leif Arkeryd, Raffaele Esposito, Rossana Marra, Anne Nouri. Exponential stability of the solutions to the Boltzmann equation for the Benard problem. Kinetic & Related Models, 2012, 5 (4) : 673-695. doi: 10.3934/krm.2012.5.673 |
[12] |
Sigurdur Freyr Hafstein. A constructive converse Lyapunov theorem on exponential stability. Discrete & Continuous Dynamical Systems - A, 2004, 10 (3) : 657-678. doi: 10.3934/dcds.2004.10.657 |
[13] |
Hichem Kasri, Amar Heminna. Exponential stability of a coupled system with Wentzell conditions. Evolution Equations & Control Theory, 2016, 5 (2) : 235-250. doi: 10.3934/eect.2016003 |
[14] |
István Györi, Ferenc Hartung. Exponential stability of a state-dependent delay system. Discrete & Continuous Dynamical Systems - A, 2007, 18 (4) : 773-791. doi: 10.3934/dcds.2007.18.773 |
[15] |
Litan Yan, Wenyi Pei, Zhenzhong Zhang. Exponential stability of SDEs driven by fBm with Markovian switching. Discrete & Continuous Dynamical Systems - A, 2019, 39 (11) : 6467-6483. doi: 10.3934/dcds.2019280 |
[16] |
Yaru Xie, Genqi Xu. The exponential decay rate of generic tree of 1-d wave equations with boundary feedback controls. Networks & Heterogeneous Media, 2016, 11 (3) : 527-543. doi: 10.3934/nhm.2016008 |
[17] |
M'hamed Kesri. Structural stability of optimal control problems. Communications on Pure & Applied Analysis, 2005, 4 (4) : 743-756. doi: 10.3934/cpaa.2005.4.743 |
[18] |
Cónall Kelly, Alexandra Rodkina. Constrained stability and instability of polynomial difference equations with state-dependent noise. Discrete & Continuous Dynamical Systems - B, 2009, 11 (4) : 913-933. doi: 10.3934/dcdsb.2009.11.913 |
[19] |
Reza Kamyar, Matthew M. Peet. Polynomial optimization with applications to stability analysis and control - Alternatives to sum of squares. Discrete & Continuous Dynamical Systems - B, 2015, 20 (8) : 2383-2417. doi: 10.3934/dcdsb.2015.20.2383 |
[20] |
Cruz Vargas-De-León, Alberto d'Onofrio. Global stability of infectious disease models with contact rate as a function of prevalence index. Mathematical Biosciences & Engineering, 2017, 14 (4) : 1019-1033. doi: 10.3934/mbe.2017053 |
2018 Impact Factor: 1.292
Tools
Metrics
Other articles
by authors
[Back to Top]