The Rotary Inertia Effect In The Large Reference Displacement Analysis Of Initially Curved Plates

Abstract

The objective of this investigation is to examine the effect of rotary inertia on the dynamics of initially curved plates that undergo large reference displacements. Non-linear terms that represent the coupling between the rotary inertia and the initial curvature are identified and their dependence on the finite rotation of the plate is demonstrated. The effect of rotary inertia on the kinematic relationships as well as the centrifugal and Coriolis force components is examined. It is shown in this investigation that the non-linear mass matrix of the initially curved plate can be decomposed into four inertia matrices, which all depend on the finite rotation as well as the elastic deformation of the plate. The first of these inertia matrices is the conventional mass matrix that arises in the analysis of the plates without considering the effect of the rotary inertia. The second and third inertia matrices are the curvature inertia matrix and the rotary inertia matrix, and they represent, respectively, the separate effect of the initial curvature and the rotary inertia. The last inertia matrix is the curvature-rotary inertia matrix , which represents the effect of the coupling between the initial curvature and the rotary inertia. Consequently, the non-linear curvature-rotary inertia matrix exists only when the effects of the initial curvature and rotary inertia are both considered. The non-linear dynamic differential equations of motion of the initially curved plate are formulated using the principle of virtual work in dynamics. These equations are solved using direct numerical integration methods that have variable order and variable step size. The use of the formulation presented in this paper is demonstrated using a spatial multi-body RSSR mechanism that consists of interconnected rigid and deformable bodies. The effects of the rate of the finite rotation and the thickness of the plate coupler on the non-linear dynamics of the mechanism are examined numerically.