Dynamic theory of composite anisogrid lattice conical shells with nonconstant stiffness and density

Abstract

Composite anisogrid lattice conical shells have been applied in rocket adapters and the fundamental frequency is the basic design parameter. Free vibrations of three types composite anisogrid lattice conical shells under arbitrary boundary conditions are considered in the paper to theoretically evaluate the fundamental frequency. The lattice conical shell is modelled as continuous conical shell with nonconstant stiffness and density by equivalent continuum method. Employing Fourier decomposition and power series method, the governing equations of motion based on Donnell-type thin shell theory are converted into the recurrence relations through identity transformation. Displacement and stress resultants expressions containing the unknown frequency and initial terms are obtained through the recurrence relations, respectively. Compared with the previous and numerical results, the analytical solution is remarkably accurate and efficient in dealing with lattice conical shells with variable cross-sectional radius, nonconstant stiffness and density for different number of circumferential waves and geometric parameters. The effect of radius ratio, height of cone and thickness of ribs on the value of frequencies is studied using a parametric analysis. It is shown that the fundamental frequency increase with the thickness of rib and decrease with increasing height of cone.