6TH International Congress on Technology - Engineering - Kuala Lumpur3 - Malaysia (2018-07-19)

Free Vibrations Of Three-layered Closed Shell Supported By Longitudinal Stiffness Ribs

A computational model is described and an algorithm for research of free vibrations of a three-layer closed shell with a lightweight aggregate supported by longitudinal stiffness ribs is developed. In a variational way, using the Ostrogradskii-Hamilton functional-action, differential equations of bending vibrations of the shell section closed between the ribs are obtained, as well as conditions along the edge lines and along the edges of the shell. Kirchhoff-Love hypotheses are accepted for the outer bearing layers, and the linear law for changing the tangential displacements along the thickness is used for the aggregate. Transverse deformations of the aggregate are not taken into account. Bernoulli hypothesis are accepted for the edges, and only the bending of the ribs in the vertical plane is taken into account. For the numerical implementation of the author’s methodology there was developed a program. It was implemented in the Wolfram Mathematica environment. The transcendental frequency equation of a three-layer closed cylindrical shell with the hinged support of the edges, supported by regular longitudinal stiffness ribs, is obtained. The values of the parameter of the first frequency of free vibrations of the shell, which is supported by one and three stiffeners, are determined. The value was determined both taking into account the edge Reissner effect, and without taking it into account. It is found that the shear deformations in the ribs and the edge Reissner effect have an insignificant effect on the frequency of free vibrations. With an increase in the number of ribs, the frequency of free vibrations decreases, and a further increase in the number of ribs does not increase the frequency of this mode. An increase in the ratio of the sides of the shell leads to an increase in the frequencies of free vibrations.
T.A. Yemelianova, M.G. Surianinov, O.S. Shyliaiev