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Study of the stability properties for a general shape of damped Euler-Bernoulli beams under linear boundary conditions. (English) Zbl 07902030

MSC:

74K10 Rods (beams, columns, shafts, arches, rings, etc.)
74H55 Stability of dynamical problems in solid mechanics
35Q74 PDEs in connection with mechanics of deformable solids

References:

[1] Aouragh, M. D.; Yebari, N., Stabilisation exponentielle d’une équation de poutres d’Euler-Bernoulli à coefficients variables, Annales Mathématiques Blaise Pascal, 16, 2, 483-510 (2009) · Zbl 1422.74057 · doi:10.5802/ambp.275
[2] Guo, B.-Z., Riesz basis property and exponential stability of controlled Euler-Bernoulli beam equation with variable coefficients, SIAM Journal on Control and Optimization, 40, 6, 1905-1923 (2002) · Zbl 1015.93025 · doi:10.1137/S0363012900372519
[3] Koffi, C. J. J.; Bomisso, G. J.-M.; Touré, K. A.; Coulibaly, A., Riesz basis property and exponential stability for a damped system and controlled dynamically, International Journal of Numerical Methods and Applications, 22 (2022) · Zbl 1538.35056
[4] Touré, K. A.; Coulibaly, A.; Hermith Kouassi, A. A., Riesz basis, exponential stability of variable coefficients Euler-Bernoulli beams with an indefinite damping under a force control in position and velocity, Electronic Journal of Differential Equations, 2015, 54, 1-20 (2015) · Zbl 1310.93073
[5] Wang, J.-M.; Xu, G.-Q.; Yung, S.-P., Riesz basis property, exponential stability of variable coefficient Euler-Bernoulli beams with indefinite damping, IMA Journal of Applied Mathematics, 70, 3, 459-477 (2005) · Zbl 1157.34062 · doi:10.1093/imamat/hxh043
[6] Jean-Marc, B. G.; Augustin, T. K.; Gozo, Y., Stabilization of variable coefficients euler-bernoulli beam with viscous damping under a force control in rotation and velocity rotation, Journal of Mathematics Research, 9, 6, 1-13 (2017) · doi:10.5539/jmr.v9n6p1
[7] Wang, J.-M., Riesz basis property of some infinite-dimensional control problems and its applications (2004), The University of Hong Kong, Ph.D. Thesis
[8] Birkhoff, G. D., On the asymptotic character of the solutions of certain linear differential equations containing a parameter, Transactions of the American Mathematical Society, 9, 2, 219-231 (1908) · JFM 39.0386.01 · doi:10.1090/S0002-9947-1908-1500810-1
[9] Birkhoff, G. D., Boundary value and expansion problems of ordinary linear differential equations, Transactions of the American Mathematical Society, 9, 4, 373-395 (1908) · JFM 39.0386.02 · doi:10.1090/S0002-9947-1908-1500818-6
[10] Guo, B. Z., On the boundary control of a hybrid system with variable coefficients, Journal of optimization Theory and Applications, 114, 2, 373-395 (2002) · Zbl 1061.93055 · doi:10.1023/A:1016039819069
[11] Guo, B.-Z.; Wang, J.-M., Riesz basis generation of abstract second order partial differential equation systems with general non-separated boundary conditions, Numerical Functional Analysis and Optimization, 27, 3-4, 291-328 (2006) · Zbl 1137.35344 · doi:10.1080/01630560600657265
[12] Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations, 44 (1983), New York: Springer-Verlag, New York · Zbl 0516.47023
[13] Naimark, M. A., Linear Differential Operators, 1 (1967), New York: F. Ungar, New York · Zbl 0219.34001
[14] Curtain, R. F.; Zwart, H., An introduction to infinite dimensional linear system theory, Texts in Applied Mathematics, 21 (1995), Berlin: Springer-Verlag, Berlin · Zbl 0839.93001
[15] Brezis, H., Analyse fonctionnelle, Théorie et Applications (1983), Paris: Masson, Paris · Zbl 0511.46001
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