https://doi.org/10.1140/epjp/s13360-020-00203-3
Regular Article
Kernel sections and global dynamics of nonautonomous Euler–Bernoulli beam equations
1
Division of Dynamics and Control, School of Mathematics and Statistics, Shandong University of Technology, Zibo, 255000, China
2
Departamento de Matemática Aplicaday Estadística, Universidad Politécnica de Cartagena, 30203, Cartagena, Spain
3
Division of Dynamics and Control, School of Astronautics, Harbin Institute of Technology, 150001, Harbin, China
4
School of Mathematics, Southwest Jiaotong University, Chengdu, 610031, China
* e-mail: juan.garcia@upct.es
Received:
10
May
2019
Accepted:
22
December
2019
Published online:
23
January
2020
This paper concerns with dynamical behavior for nonautonomous Euler–Bernoulli beam equations with either weakly damping or strongly damping. Issues relevant to existence and Hausdorff dimension estimation of Kernel sections are investigated. It is shown that there exist Kernel sections for the beams, in the case of strongly damping, the techniques rely on splitting method, when the damping is weakly, the proof depends on the stabilization estimations of the system. Moreover, the Hausdorff dimension of Kernel sections is proved to be finite. Eventually, the global dynamics of the beams are studied by numerical simulation on the Kernel Sections and Kernel.
© Società Italiana di Fisica (SIF) and Springer-Verlag GmbH Germany, part of Springer Nature, 2020
