Nonlinear Free Vibration of Anisogrid Lattice Cylindrical Panel Using the 2D Double Exponential Sinc Collocation Method

Abstract

This study explores the nonlinear free vibrations of anisogrid lattice cylindrical panels under clamped circumstances for the first time. The lattice panel is made of repeating circumferential hexagonal unit cells with helical and circumferential isotropic ribs. The panel’s stiffness and mass are calculated using a continuous model based on orthotropic deep panel theory. The strain–displacement relationships are based on von-Kármán’s geometrically nonlinear theory. Using the Hamilton principle, nonlinear two-dimensional (2D) motion equations are extracted in their strong form. A 2D collocation approach based on the Sinc functions with double exponential (DE) transformation with a high convergence rate is used to solve the governing motion equations. The time variable is then eliminated from the equations using the weighted residual Galerkin procedure. Finally, the system’s nonlinear natural frequencies are computed using an iterative algorithm based on the bilateral displacement control. The influence of unit cell features, such as the angle of helical ribs, the number and thickness of ribs, and the panel dimensions, is examined in detail on the panel’s linear and nonlinear vibration behavior.