Analytical Method for the Vibrations Fundamental Frequency Determining of a Three-Layer Panel with a Pyramidal Truss Core

Design of the Flying Vehicles Elements from Polymer Composite Materials


Аuthors

Pikulin S. A.1, Lopatin A. V.2

1. Compani «Information satellite systems of academician M.F. Reshetnev», 52, Lenin str., Zheleznogorsk, Krasnoyarsk region, 662972, Russia
2. Federal Research Center for Information and Computing Technologies,

Abstract

This article presents an analytical solution to the problem of the fundamental frequency of vibrations determining of a three-layer panel with a pyramidal truss core. The solution was obtained for panel, which edges are fixed rigidly around the perimeter. This problem was solved based on the averaged mechanical characteristics of the truss core and by the Galerkin method for solving the equations of motion. Solutions to the classical problem of bending a beam clamped at the two ends with account for the effect of shear deformations were used as basic functions for the panel deformed shape approximation.

The problem relevance is stipulated by the need to study a new type of cores for the three-layer panels, namely, the truss core. This type of core has high mechanical characteristics, which makes it especially prospective for application in the aerospace structures where high strength and lightness are required. The fundamental oscillation frequency of the panels is a key characteristic that determines the structure dynamic behavior, which stresses the importance of this work for dynamically loaded structures, including aerospace ones.

To confirm correctness of the obtained analytical solution, verification by the finite element models was performed. The verification procedure allowed determining the range of the truss core parameters, in which the analytical solution demonstrates sufficient accuracy. The identified range is critically important for practical application, as it allows focusing on the area of parameters where analytical and numerical results agreed.

Besides, the article provides recommendations for the core average characteristics adjusting, which will allow achieving greater accuracy within the entire range of the parameters studied. The presented analytical solution can be successfully applied in the design of the three-layer panels with truss cores of any type, since its accuracy is mainly determined by the accuracy of the specified average characteristics of the core.

If necessary, this solution can be easily adapted to apply to other boundary conditions. Thus, the obtained results can serve as a basis for further research and development in the field of the multilayer structures with the truss core, which is relevant for the state-of-the-art engineering solutions in the aerospace industry.

Keywords:

three-layer panel, truss core, fundamental frequency of vibrations, Galerkin method

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