Experimental verification of mathematical model of forced oscillations of an open thin-walled shell with a small attached mass and rigidly clamped edges


Аuthors

Dobryshkin A. Y.*, Sysoev O. E.**, Sysoev E. O.**

Komsomolsk-na-Amure State University, 27, Lenina str., Komsomolsk-on-Amur, 681013, Russia

*e-mail: wwwartem21@mail.ru
**e-mail: fks@knastu.ru

Abstract

The article regards the problem of numerical characteristics determining of a rectangular in-plan view open thin-walled shell, rigidly pinched along one of its sides.

A theoretical analysis of theories of oscillations of an open cylindrical shell and a curved plate was performed. The shell calculation was performed based on the Germain-Lagrange equation using asymptotic methods for solving differential equations, the Padé approximation, and the recursive perturbation theory. Approximation was performed by expansion in a series in a variable of wave-forming parameter. Analytical dependencies were obtained between the shell oscillation frequency and the wave-forming parameter of a cylindrical open shell. The performed studies were verified by the experimental studies. For these purposes, a special test facility was developed, test samples were fabricated, and a program of experimental studies was developed. Mathematical models and the shell vibrations studies refinement is necessary to reduce the onset of resonance effects and prevent accidents. The numerical data determined with the Padé approximation is very accurate, and describes perfectly frequency characteristics of the oscillatory process at the wave-forming parameter staying within the range from zero to unity. The data obtained in the course of the experiment setting up, represents minimal discrepancies for the RTV method (recursive formulation of perturbation theory). In the range of the wave-forming parameter less than 0.5, the data obtained during the experiment setting up, are inconsistent with numerical data determined using the Padé approximation method. The refined mathematical model demonstrates significant conformity with the experimental data at ε > 0.4. Thus, the range of ε > 0.4 is excellent for the calculation applying the mathematical model obtained in this article.

Keywords:

thin-walled shell, natural vibrations, attached mass, experiment

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