The analysis of the impact of different shape functions in tolerance modeling on natural vibrations of the rectangular plate with dense system of the ribs in two directions

The main concern of this paper are thin rectangular plates with dense system of the ribs in two directions. The aim of the analysis is the examination of the impact of different shape functions in tolerance modeling on natural vibrations of the plates. The plate is made of two different materials, both for matrix and ribs. The thickness of the plate is comparable to the width of the ribs. This provides a powerful tool for getting a desirable frequency of natural vibrations of the plate. The tolerance averaging approach is the base for the formulation of averaged model equations. The most accurate readings presenting this method are described in Wozniak et al. [1]. By application of the tolerance averaging technique to the known differential equations of considered plates, the averaged equations of the tolerance model have been derived. The general results of the contribution are illustrated using the analysis of natural vibrations. The effect of different shape functions on free vibration frequencies is examined.

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Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę.