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Analytical solution for wave propagation in a viscoelastic wall strip under transverse impact loading

Citace: ADÁMEK, V., VALEŠ, F. Analytical solution for wave propagation in a viscoelastic wall strip under transverse impact loading. In Proceedings of the 11th International Conference on Vibration Problems. Lisbon: APMTAC, 2013. s. 1-9. ISBN: 978-989-96264-4-7
Druh: STAŤ VE SBORNÍKU
Jazyk publikace: eng
Anglický název: Analytical solution for wave propagation in a viscoelastic wall strip under transverse impact loading
Rok vydání: 2013
Místo konání: Lisbon
Název zdroje: APMTAC
Autoři: Ing. Vítězslav Adámek Ph.D. , Ing. František Valeš CSc.
Abstrakt EN: This work concerns the investigation of non-stationary waves propagated in a viscoelastic strip of infinite length. The strip is subjected to a transverse pressure load the amplitude of which is described by cosine function in spatial domain and by Heaviside function in time. Using the exact 2D theory, the equations of motion are derived for the standard model of linear viscoelastic solid. The system of two integro-differential equations is then solved by means of integral transforms and the exact formulae for the Laplace transforms of relevant displacement components are derived. The inverse Laplace transform is then performed by means of a numerical algorithm based on FFT and Wynn?s epsilon accelerator. To prevent the precision and the quality of the solution derived, multi-precision implementation of this algorithm was performed in Maple, so the results obtained can be considered of analytical accuracy. Finally, these results are compared to numerical ones obtained by the help of finite element software MSC.Marc/Mentat. It is clear from presented results that very good agreement between both solutions was achieved, both close and far from the area of excitation. Presented analytical solution can be utilised in problems of optimal design of structures with viscoelastic layers subjected to impact loading.
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