- 期刊
Asymptotics and Stabilization for Dynamic Models of Nonlinear Beams
Mittelineaarsete talade dünaamiliste mudelite asümptootika ja stabiliseerimine
並列摘要
We prove that the von Kármán model for vibrating beams can be obtained as a singular limit of a modified Mindlin-Timoshenko system when the modulus of elasticity in shear k tends to infinity, provided a regularizing term through a fourth-order dispersive operator is added. We also show that the energy of solutions for this modified Mindlin-Timoshenko system decays exponentially, uniformly with respect to the parameter k, when suitable damping terms are added. As k→∞, one deduces the uniform exponential decay of the energy of the von Kármán model.
延伸閱讀
- Pinarbasi, S. (2012). Stability Analysis of Nonuniform Rectangular Beams Using Homotopy Perturbation Method. Mathematical Problems in Engineering, 2012(), 1055-1072-066. https://doi.org/10.1155/2012/197483
- Soize, C., & Batou, A. (2008). Identification of Stochastic Loads Applied to a Nonlinear Dynamical System Using an Uncertain Computational Model. Mathematical Problems in Engineering, 2008(), 116-131. https://doi.org/10.1155/2008/181548
- Seroka, E. (2015). Asymptotic Stabilizability of a Class of Stochastic Nonlinear Hybrid Systems. International Journal of Stochastic Analysis, 2015(), 14-22. https://doi.org/10.1155/2015/231214
- YUAN, X., & TADA, Y. (2001). Nonlinear Analysis of Flexible Beams Undergoing Large Rotations Via Symbolic Computations. Mathematical Problems in Engineering, 2001(), 241-252. https://doi.org/10.1155/S1024123X01001636
- Chiang, W. Y. (2012). Effects of Coupling in Nonlinear Dynamical Systems: Model study and Nonlinear Analysis [doctoral dissertation, National Central University]. Airiti Library. https://www.airitilibrary.com/Article/Detail?DocID=U0031-1903201314433865