A finite-patch model of a flexible plate via Kane's dynamics

Abstract

Military hardware must undergo extensive shock-response analysis to predict survivability to mechanical shock. Although finite element modeling is commonly used to model such hardware, alternative methods which offer the possibility of shorter modeling, modification, or simulation times continue to be desirable. This research effort applies Kane's dynamics to the problem of plate modeling, toward shock-response analysis of homogeneous plates having various geometries and boundary conditions. Analytical equations of motion are found for a continuous flexible plate that is discretised in checkerboard fashion as a patchwork of rigid rectangular patches connected by flexible springs and damped modally. A MATLAB implementation is used to validate the model against pertinent analytical and numerical benchmark analyses, for a variety of boundary conditions. The model is then reduced by applying non-holonomic constraints directly using Kane's method, and revalidated via MATLAB for a rectangular plate in simple support.