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Journal of Applied Mechanics and Technical Physics

2018 year, number 3

Identification of Parameters of Short-Time Creep of Plexiglas by Means of Studying Decaying Flexural Oscillations of Test Samples

V. N. Paimushin1,2, V. A. Firsov1, V. M. Shishkin3
1Kazan National Research Technical University named after A. N. Tupolev, Kazan, Russia, 420111
2Kazan Federal University, Kazan, Russia, 420008
3Vyatka State University, Kirov, Russia, 610000
Keywords: вязкоупругий материал, ядро наследственности, конечный элемент, метод прямого поиска, целевая функция, viscoelastic material, hereditary kernel, finite element, direct search method, object function

Abstract

A technique for identification of hereditary properties under conditions of short-time creep of Plexiglas is developed. The technique is based on experimental determination of shifting of the center of decaying flexural oscillations of vertically fixed test samples after their preliminary curing in a static bent state. Mathematically, the technique is based on using the finite element method and integral equations of the theory of hereditary viscoelasticity with the Koltunov-Rzhanitsyn hereditary kernel. An object function is constructed for identification of rheological parameters of this kernel. The minimum of this function is found by the direct search method, which does not require the function gradient to be known. The hereditary kernel of Plexiglas averaged on the basis of data for several test samples is obtained as a function of time.