- Tytuł:
- Dynamic displacement tracking in viscoelastic solids by actuation stresses: a one-dimensional analytic example involving shock waves
- Autorzy:
-
Irschik, Hans
Krommer, Michael - Powiązania:
- https://bibliotekanauki.pl/articles/27311394.pdf
- Data publikacji:
- 2023
- Wydawca:
- Polska Akademia Nauk. Czasopisma i Monografie PAN
- Tematy:
-
displacement tracking
eigenstrains
actuation stresses
linear viscoelasticity
shock waves
symbolic computation
śledzenie przemieszczenia
naprężenia własne
lepkosprężystość liniowa
fale uderzeniowe
obliczenia symboliczne
naprężenie uruchamiające - Opis:
- A one-dimensional (1D) analytic example for dynamic displacement tracking in linear viscoelastic solids is presented. Displacement tracking is achieved by actuation stresses that are produced by eigenstrains. Our 1D example deals with a viscoelastic half-space under the action of a suddenly applied tensile surface traction. The surface traction induces a uni-axial shock wave that travels into the half-space. Our tracking goal is to add to the applied surface traction a transient spatial distribution of actuation stresses such that the total displacement of the viscoelastic half-space coincides with the shock wave produced by the surface traction in a purely elastic half-space. We particularly consider a half-space made of a viscoelastic Maxwell-type material. Analytic solutions to this tracking problem are derived by means of the symbolic computer code MAPLE. The 1D solution presented below exemplifies a formal 3D solution derived earlier by the present authors for linear viscoelastic solids that are described by Boltzmann hereditary laws. In the latter formal solution, no reference was made to shock waves. Our present solution demonstrates its validity also in the presence of singular wave fronts. Moreover, in our example, we show that, as was also indicated in our earlier work, the actuation stress can be split into two parts, one of them producing no stresses, and the other no displacements in two properly enlarged problems.
- Źródło:
-
Bulletin of the Polish Academy of Sciences. Technical Sciences; 2023, 71, 3; art. no. e144616
0239-7528 - Pojawia się w:
- Bulletin of the Polish Academy of Sciences. Technical Sciences
- Dostawca treści:
- Biblioteka Nauki
Artykuł