An analytical expression for fundamental frequency of the composite lattice cylindrical shell with clamped edges

A solution of the free vibrations problem formulated for a composite lattice cylindrical shell with clamped edges is presented in this paper. The lattice shell is composed of a large number of helical and hoop ribs and modelled as a continuous orthotropic thin cylinder with effective stiffness parameters. A solution of the equations of motion of the shell is based on the Fourier decomposition and the Galerkin method and yields an analytical formula for the calculation of a fundamental frequency. It is demonstrated that starting from a certain density of the lattice structure the value of fundamental frequency does not depend on the number of helical ribs. This result is verified and confirmed using finite-element analysis. Applications of this formula to the determination of the parameters of lattice structures and design of composite lattice shells with required fundamental frequencies are demonstrated using numerical examples. It is shown that the analytical formula presented in this article provides an efficient tool for rapid calculation of the fundamental frequency which can be used for the assessment of the structural stiffness of the composite lattice shells in the design analysis.