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

Authors: R. David Hampton

Addresses: Mechanical Engineering Division, Civil and Mechanical Engineering Department, Mahan Hall (Bldg. 752), US Military Academy, West Point, NY 10996, USA

Abstract: Military hardware must undergo extensive shock-response analysis to predict survivability to mechanical shock. Although finite element modelling is commonly used to model such hardware, alternative methods which offer the possibility of shorter modelling, modification, or simulation times continue to be desirable. This research effort applies Kane's dynamics to the problem of plate modelling, 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.

Keywords: Kane's dynamics; shock response analysis; discretised; finite patch modelling; dynamic modelling; flexible plates; plate modelling; military hardware; simulation; severe shocks; mechanical shocks.

DOI: 10.1504/IJVSMT.2012.049433

International Journal of Vehicle Systems Modelling and Testing, 2012 Vol.7 No.4, pp.303 - 350

Received: 20 Aug 2011
Accepted: 04 Apr 2012
Published online: 13 Sep 2014 *

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