A Timoshenko beam with tip body and boundary damping

Zietsman, Lizette; Rensburg, N.F.J. van; Merwe, A. J. van der

doi:10.1016/j.wavemoti.2003.08.003

Cited by 22 publications

(17 citation statements)

References 8 publications

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“…However, the rotary inertia of the rigid body is not taken into account in the model. A numerical approach to the problem, using the finite element method, was undertaken by Zietsman et al [29] who from their empirical studies could not conclude uniform stabilization, neither in the case of non-zero rotary inertia, I m , of the tip load, nor when I m is neglected. Their FEM approach was followed most recently by a finite difference approach due to F. Li et al [17] in which unique solvability, unconditional stability (to the initial values and inhomogeneous terms) and convergence of their difference scheme of the problem, which includes the rotary inertia of the tip load, are proved.…”

Section: Introduction and Statement Of The Problemmentioning

confidence: 99%

Uniform stability for the Timoshenko beam with tip load

Dalsen¹

2010

Journal of Mathematical Analysis and Applications

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In this paper we consider a hybrid elastic model consisting of a Timoshenko beam and a tip load at the free end of the beam. We show that uniform stabilization of the model which includes the rotary inertia of the tip load can be obtained when feedback boundary moment and force controls are applied at the point of contact between the beam and the tip load. However, in the presence of the load stabilization is "slower" and subject to a restriction on the boundary data at the free end of the beam.

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Section: Introduction and Statement Of The Problemmentioning

confidence: 99%

Uniform stability for the Timoshenko beam with tip load

Dalsen¹

2010

Journal of Mathematical Analysis and Applications

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“…We take α = 1200, β = 300, m = 0.125, I m = 0, k 0 = 0.005 and k 1 = 0.0025 (see [16]). The right hand functions f 1 (x, t), f 2 (x, t) and the functions in the initial and boundary conditions are determined by the exact solution w(x, t) = e −t sin π…”

Section: Numerical Examplementioning

confidence: 99%

“…A number of authors (see [4,6,9,[13][14][15][16]) have considered control problems associated with the Timoshenko beam and obtained many interesting results. At the same time, the finite element method and the finite difference method are effectively applied to the Timoshenko beam for solving the boundary stabilization, calculating the eigenvalues and the numerical solution (see [1][2][3]5,7,8]).…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we consider the finite difference simulation for the following Timoshenko beam equations with tip body and boundary damping, given by [16] …”

Section: Introductionmentioning

confidence: 99%

“…This mathematical model is presented and written in dimensionless form. L. Zietsman et al [16] established the efficiency and accuracy for the model given in (1.1)-(1.6) using the finite element method for calculating the eigenvalues and eigenmodes. The difference of the Timoshenko beam equations between [7,13] and the present work is the boundary condition at x = 1.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A difference scheme for solving the Timoshenko beam equations with tip body

Huang

2008

Acta Math. Appl. Sin. Engl. Ser.

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In this article, a Timoshenko beam with tip body and boundary damping is considered. A linearized three-level difference scheme of the Timoshenko beam equations on uniform meshes is derived by the method of reduction of order. The unique solvability, unconditional stability and convergence of the difference scheme are proved. The convergence order in maximum norm is of order two in both space and time. A numerical example is presented to demonstrate the theoretical results.

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Stabilization of a Timoshenko Beam With Disturbance Observer‐Based Time Varying Boundary Controls

Liu

Shang

2017

Asian Journal of Control

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This paper is concerned with the boundary feedback stabilization for a Timoshenko beam with external disturbances in the boundary inputs. Based on the idea of active disturbance rejection controls, extended state observers with the time‐varying gains are designed to estimate disturbances and then a control strategy is presented by canceling the disturbances via the feedback channels. The well‐posedness of the resulting closed‐loop system is proved by the dual theory and admissibility theory, and the relationship between the stability and the disturbance is interpreted by Lyapunov's second method. At the end, the numerical experiment illustrate the effectiveness of the proposed control strategy.

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A Timoshenko beam with tip body and boundary damping

Cited by 22 publications

References 8 publications

Uniform stability for the Timoshenko beam with tip load

Uniform stability for the Timoshenko beam with tip load

A difference scheme for solving the Timoshenko beam equations with tip body

Stabilization of a Timoshenko Beam With Disturbance Observer‐Based Time Varying Boundary Controls

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