Optimal boundary control for the Timoshenko–Ehrenfest truncated model
College
Engineering and Computer Science
Department
Ocean and Mechanical Engineering
Document Type
Article
Publication/Event/Conference Title
Archive of Applied Mechanics
Publication Status
Version of Record
Abstract
In this work, we investigate the optimal control problem associated with a truncated version of the Timoshenko–Ehrenfest beam model, which captures essential features of transverse vibrations in elastic structures. We begin by establishing the well-posedness of the system through the Faedo–Galerkin approximation method, ensuring existence and uniqueness of solutions. The associated optimal control problem is then formulated, and the Pontryagin maximum principle is employed to characterize the optimality conditions. To obtain the analytical solution aiming numerical issues, we apply a Fourier series expansion, which allows for the explicit representation of both the state and the adjoint variables. Finally, we present numerical simulations that demonstrate the efficiency of the proposed control strategy in suppressing unwanted vibrations, confirming the theoretical results and highlighting the practical relevance of the method.
DOI
10.1007/s00419-025-02945-x
Publication Date
10-1-2025
Recommended Citation
da Silva Rodrigues, Leonardo Rogério; da Silva Almeida Júnior, Dilberto; and Elishakoff, Isaac, "Optimal boundary control for the Timoshenko–Ehrenfest truncated model" (2025). Faculty Scholarship. 147.
https://digitalcommons.fau.edu/faculty_papers/147