The Imbedding Equations for the Timoshenko Beam

Billger, Dag; Folkow, Peter D.

doi:10.1006/jsvi.1997.1286

Cited by 8 publications

(13 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The corresponding rotation angle and the bending moment are given in Figure 8 4 • In the unrestrained case, i.e. a free beam, this scattering problem was treated in [16], and the case where the suspension is semi-infinite was treated in [6]. These results are reproduced here to enable a comparison with the finite suspension solution presented here.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…Then the inverse problem of recovering a geometrical variation of the beam, from knowledge of boundary data, can be considered. Furthermore, numerical solutions of the reflection equation are needed when numerical solution of the transmission problem is addressed, since the reflection kernel appears as a source term in the equation for the transmission kernel [6].…”

Section: Discussionmentioning

confidence: 99%

“…The reflected and transmitted fields are related to the incident field by reflection and transmission operators, which are independent of the incident field. These operators are described in [6]. The wave problem considered in this paper is that of scattering of a right-moving wave, in a homogeneous Timoshenko beam, by the region of the beam that resides on a viscoelastic suspension.…”

Section: On the Timoshenko Beammentioning

confidence: 99%

“…In [6], the imbedding equation for the reflection kernel, along with its initial values and discontinuities, is derived. It has been found that this reflection kernel grows exponentially with time.…”

Section: On the Timoshenko Beammentioning

confidence: 99%

“…In the case of a homogeneous beam on a viscoelastic suspension, the reflection kernel R(x, s) is continuous everywhere in its domain [6]. However, there are discontinuities in the derivatives of the reflection kernel across the characteristic traces emanating from the point (1, 0).…”

Section: On the Timoshenko Beammentioning

confidence: 99%

See 4 more Smart Citations

A time domain algorithm for the reflection of waves on a viscoelastically supported Timoshenko beam

Billger¹

1999

The Quarterly Journal of Mechanics and Applied Mathematics

View full text Add to dashboard Cite

This paper presents a time domain algorithm for solving the direct wave scattering problem for a Timoshenko beam. The beam is assumed to be made of a homogeneous material and to be restrained by a viscoelastic suspension of finite length. In the Timoshenko beam, the characteristic wave-fronts propagate with two distinct velocities. This implies that the equation satisfied by the reflection operator contains three separate families of characteristic curves. Furthermore, the equation is both temporally and spatially dependent due to the finite extent of the suspension. The mathematical problem this paper addresses is the construction of an algorithm to solve an associated partial integro-differential equation with three distinct wave-front velocities. The mathematical techniques that are developed are applicable to any set of matrix-valued, functional, first order equations appropriate for reflection kernels. Some numerical examples are presented in order to validate the algorithm.

show abstract

Section: Numerical Resultsmentioning

confidence: 99%

Section: Discussionmentioning

confidence: 99%

Section: On the Timoshenko Beammentioning

confidence: 99%

Section: On the Timoshenko Beammentioning

confidence: 99%

Section: On the Timoshenko Beammentioning

confidence: 99%

See 3 more Smart Citations

A time domain algorithm for the reflection of waves on a viscoelastically supported Timoshenko beam

Billger¹

1999

The Quarterly Journal of Mechanics and Applied Mathematics

View full text Add to dashboard Cite

show abstract

Dispersion free wave splittings for structural elements

Johansson

Folkow

Olsson

2006

Computers & Structures

Self Cite

View full text Add to dashboard Cite

Wave splittings are derived for three types of structural elements: membranes, Timoshenko beams, and Mindlin plates. The Timoshenko beam equation and the Mindlin plate equation are inherently dispersive, as is each Fourier component of the membrane equation in an angular decomposition of the eld. The distinctive feature of the wave splittings derived in the present paper is that, in homogeneous regions, they transform the dispersive wave equations into simple one-way wave equations without dispersion. Such splittings have uses bothfor radial scattering problems in the 2D cases and for scattering problems in dispersive media. As an example of how the splittings may be applied, a direct scattering problem is solved for a membrane with radially varying density. The imbedding method is utilised, and agreement is obtained with an FE simulation.

show abstract

A purely directional wave splitting for the homogeneous Timoshenko beam

Johansson

2004

Journal of Sound and Vibration

View full text Add to dashboard Cite

The Imbedding Equations for the Timoshenko Beam

Cited by 8 publications

References 0 publications

A time domain algorithm for the reflection of waves on a viscoelastically supported Timoshenko beam

A time domain algorithm for the reflection of waves on a viscoelastically supported Timoshenko beam

Dispersion free wave splittings for structural elements

A purely directional wave splitting for the homogeneous Timoshenko beam

Contact Info

Product

Resources

About