On the controllability of laminated beams with Venttsel-type boundary conditions

TL;DR

This paper investigates the boundary controllability of a Timoshenko laminated beam system with Venttsel-type boundary conditions, demonstrating controllability through observability inequalities and duality methods for a novel three-beam configuration.

Contribution

It introduces a new controllability analysis for a system of three beams with Venttsel boundary conditions, expanding the understanding of boundary control in complex beam systems.

Findings

Controllability achieved with three boundary controls.

Derived observability inequality for the adjoint system.

Established controllability for a novel three-beam Venttsel boundary system.

Abstract

This paper examines the boundary controllability of a Timoshenko laminated beam system subject to Venttsel-type boundary conditions. The study focuses on a novel configuration in which three controls are applied solely at the boundary of the beam. Controllability is established by deriving an appropriate observability inequality for the corresponding adjoint system, which is then employed within the framework of the duality method in the setup of the classical Hilbert uniqueness method (HUM) to achieve the control problem. The main contribution lies in the analysis of a system comprising three beams governed by dynamic Venttsel-type boundary conditions, as introduced by Venttsel in [Theory Probab. Appl., 4 (1959)].