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**Harvard**

Billger, D. och Folkow, P. (1998) *The imbedding equations for the Timoshenko beam*.

** BibTeX **

@article{

Billger1998,

author={Billger, Dag V. J. and Folkow, Peter D.},

title={The imbedding equations for the Timoshenko beam},

journal={Journal of Sound and Vibration},

issn={0022-460X},

volume={209},

pages={609-634},

abstract={Wave reflection in a Timoshenko beam is treated, using wave splitting and the imbedding technique. The beam is assumed to be inhomogeneous and restrained by a viscoelastic suspension. The viscoelasticity is characterized by constitutive relations that involve the past history of deflection and rotation of the beam through memory functions of the suspension. By applying wave splitting, the propagating fields are decomposed into left- and right-moving parts. An integral representation of the split fields in impulse responses is presented. This representation gives the reflected and transmitted fields as convolutions of the incident field with the reflection and transmission kernels, respectively. The kernels are independent of the incident field and depend only on the material properties. Invariant imbedding is used to obtain equations for these kernels. In general, the kernels contain discontinuities for which transport equations are derived and solved. Some numerical solutions are presented for the reflection by a homogeneous beam suspended on two separated, semi-infinite layers of continuously distributed, viscoelastically damped, local acting springs. },

year={1998},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 170227

A1 Billger, Dag V. J.

A1 Folkow, Peter D.

T1 The imbedding equations for the Timoshenko beam

YR 1998

JF Journal of Sound and Vibration

SN 0022-460X

VO 209

SP 609

OP 634

AB Wave reflection in a Timoshenko beam is treated, using wave splitting and the imbedding technique. The beam is assumed to be inhomogeneous and restrained by a viscoelastic suspension. The viscoelasticity is characterized by constitutive relations that involve the past history of deflection and rotation of the beam through memory functions of the suspension. By applying wave splitting, the propagating fields are decomposed into left- and right-moving parts. An integral representation of the split fields in impulse responses is presented. This representation gives the reflected and transmitted fields as convolutions of the incident field with the reflection and transmission kernels, respectively. The kernels are independent of the incident field and depend only on the material properties. Invariant imbedding is used to obtain equations for these kernels. In general, the kernels contain discontinuities for which transport equations are derived and solved. Some numerical solutions are presented for the reflection by a homogeneous beam suspended on two separated, semi-infinite layers of continuously distributed, viscoelastically damped, local acting springs.

LA eng

DO 10.1006/jsvi.1997.1286

LK http://dx.doi.org/10.1006/jsvi.1997.1286

OL 30