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Analytical Solution of In-Plane Response of a Thin Viscoelastic Disc Under Impact Load

Citace: [] ADÁMEK, V., VALEŠ, F. Analytical Solution of In-Plane Response of a Thin Viscoelastic Disc Under Impact Load. In Vibration Problems ICOVP 2011. Heidelberg: Springer, 2011. s. 715-721. ISBN: 978-94-007-2068-8 , ISSN: 0930-8989
Druh: STAŤ VE SBORNÍKU
Jazyk publikace: eng
Anglický název: Analytical Solution of In-Plane Response of a Thin Viscoelastic Disc Under Impact Load
Rok vydání: 2011
Místo konání: Heidelberg
Název zdroje: Springer
Autoři: Ing. Vítězslav Adámek Ph.D. , František Valeš
Abstrakt CZ: This paper concerns the analytical solution of the in-plane response of a thin viscoelastic disc to a dynamic load applied to its rim. The exact analytical relations for the Laplace transforms of radial and circumferential displacements are derived in terms of Bessel functions for the case of radial and torsional loads defined by even and odd functions of angular variable, respectively. The numerical evaluation of the analytical solution is then made for the case of an impulse radial load and transient wave phenomena are studied in the disc. With respect to the complexity of presented formulae, the multi-precision implementation of FFT based numerical algorithm for the inverse Laplace transform is used. The obtained analytical results are then compared to the results of numerical simulation performed in the finite element system MSC.Marc. The presented analytical solution can be used as a benchmark solution for the testing of numerical methods.
Abstrakt EN: This paper concerns the analytical solution of the in-plane response of a thin viscoelastic disc to a dynamic load applied to its rim. The exact analytical relations for the Laplace transforms of radial and circumferential displacements are derived in terms of Bessel functions for the case of radial and torsional loads defined by even and odd functions of angular variable, respectively. The numerical evaluation of the analytical solution is then made for the case of an impulse radial load and transient wave phenomena are studied in the disc. With respect to the complexity of presented formulae, the multi-precision implementation of FFT based numerical algorithm for the inverse Laplace transform is used. The obtained analytical results are then compared to the results of numerical simulation performed in the finite element system MSC.Marc. The presented analytical solution can be used as a benchmark solution for the testing of numerical methods.
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