The Effect of Winkler-Pasternak Foundation Coefficients on the Natural Frequency of Cylindrical Lattice Structures Using Galerkin Method

Composite Lattice structures are one of the most widely used structures in the aerospace industry in recent years. These structures are composed of a large number of oblique and circumferential ribs with specific distances from each other and in addition to strength, they are very light in terms of weight. The present study includes an analytical expression and a solution to the problem of free vibrations of a composite lattice cylindrical shell. The continuous formula for calculating the natural frequency of a cylindrical lattice structure was obtained by considering the Winkler-Pasternak elastic foundation from the governing equations of the shell based on Galerkin methods. This formula, in addition to being used to estimate the frequency in the initial design phase, is also a tool for evaluating the vibration analysis of composite lattice shells in mechanical analysis. The results have been calculated analytically in two cases with and without elastic foundation and the accuracy of the results has been confirmed by finite element modeling. For finite element method simulations, Winkler and Pasternak coefficients have been replaced by shear and radial springs, respectively. The natural base frequency of the system depends on the properties of the elastic substrate, so changing the stiffness of the radial and shear springs causes a change in the natural frequencies.