| 1. |
|
|
| 2. |
- Billger, Dag V. J., 1969, et al.
(author)
-
The imbedding equations for the Timoshenko beam
- 1998
-
In: Journal of Sound and Vibration. - : Elsevier BV. - 1095-8568 .- 0022-460X. ; 209, s. 609-634
-
Journal article (peer-reviewed)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.
|
|
| 3. |
- Folkow, Peter, 1968, et al.
(author)
-
Direct and inverse problems on nonlinear rods
- 1999
-
In: Mathematics and Computers in Simulation. - 0378-4754. ; 50, s. 577-595
-
Journal article (peer-reviewed)abstract
- In this paper a class of models on nonlinear rods, which includes spatial inhomogeneities, varying cross-sectional area and arbitrary memory functions, is considered. The wave splitting technique is applied to provide a formulation suitable for numerical computation of direct and inverse problems. Due to the nonlinearity of the material, there are no well defined characteristics other than the leading edge, so the method of characteristics, highly successful in the computation of linear wave splitting problems, is abandoned. A standard finite difference method is employed for the direct problem, and a shooting method is introduced for the inverse problem. The feasibility of the inverse algorithm is presented in various numerical examples.
|
|
| 4. |
- Folkow, Peter, 1968
(author)
-
Time domain inversion of a viscoelastically restrained Timoshenko beam
- 1999
-
In: Inverse Problems. - : IOP Publishing. - 1361-6420 .- 0266-5611. ; 15, s. 551-562
-
Journal article (peer-reviewed)abstract
- This paper deals with the inverse scattering problem for a homogeneous Timoshenko beam suspended on a semi-infinite viscoelastic layer. The purpose is to derive the properties of the suspension from knowledge of the reflection data. The method used is the imbedding technique, which render solutions that are independent of the excitation. From a numerical point of view, the reflection equation in its usual form is inappropriate when solving the inverse problem. In order to bypass such complications, the reflection equation is modified and solved. In the numerical results, the properties of the layer are calculated using noisy reflection data.
|
|
| 5. |
|
|
| 6. |
- Folkow, Peter, 1968
(author)
-
Wave Propagation in Structural Elements - Direct and Inverse Problems in the Time Domain
- 1998
-
Doctoral thesis (other academic/artistic)abstract
- The subject of this thesis is direct and inverse wave propagation problems in structural elements. The considered structures are beams, plates and rods. The models for the beams and the plates are based on linear theory, while the rods are assumed to be nonlinear. The greater part of the work concerns the Timoshenko beam. The analysis is performed in the time domain using wave splitting. Wave splitting in conjunction with scattering operator techniques is used for the linear problems. For the nonlinear problems, a finite difference scheme is adopted. The basis for the solution of the scattering problems considered in this thesis is the wave splitting concept. Wave splitting is a change of the dependent variables that diagonalizes the dynamic equations for a nonvarying medium. The diagonalization implies that the transformed variables propagate independently in definite directions. In a varying medium, these fields couple as the waves scatters. Information on the scattered fields is the main subject for both the direct and the inverse problems. The scattering operators that are used for the linear problems are the imbedding technique, the Green function approach and the propagator formalism. The two former are special cases of the latter. In general, the different operators map the incident field to the scattered fields in the varying region. The operators are represented by integral kernels that are convolved with the incident field. These kernels are independent of the wave fields, and depend only on the properties of the scatterer. The integral kernels satisfy integro-differential equations. The key to the direct and the inverse problems is to derive and solve these equations. This is done numerically, using the method of characteristics. The direct wave propagation problems on Timoshenko beams are studied using Green functions for a free, homogeneous beam, and imbedding techniques as well as propagator formalism for a viscoelastically restrained, inhomogeneous beam. The inverse problem is addressed for a homogeneous beam on a viscoelastic layer, using the imbedding technique. Both direct and inverse problems on a Mindlin plate with varying thickness in one direction are presented. Green functions are used for the direct problem, while the imbedding approach is used for the inverse problem. Concerning the nonlinear rod, both direct and inverse problems are studied for various types of viscoelastic, inhomogeneous rods. The inverse algorithm is based on a minimization of a functional, using iterative procedures.
|
|
