Determination of continuum and wave propagation characteristics for geometrically engineered materials

Date of Completion

January 2004


Applied Mechanics|Engineering, Civil|Engineering, Mechanical




A general method to establish the equivalent continuum plate properties, referred to as the Continuum Plate Model (CPM), has been developed for Geometrically Engineered Material Systems (GEMS), such as Lattice Block Material (LBM). The method is general in the sense that it can be applied to any plate-like structure comprised of repetitive unit cells having arbitrary lattice geometry. The method is also practical, since it is based on the stiffness and inertia matrices formed using standard Finite Element Analysis (FEA) models of a representative unit cell. The CPM properties can easily be incorporated within a general FEA program to analyze complex structures containing GEMS substructures. The CPM has been demonstrated to accurately compare to discretely modeled FEA for a variety of static and dynamic problems. ^ For a special case of GEMS, in which the unit cell and its geometric reciprocal have coupling terms that are equal in magnitude but opposite in sense, the CPM method is extended to calculate a neutral set of properties. For GEMS of this type, the structural boundary conditions have been demonstrated to play a significant role in the overall behavior of finite structures. A border of CPM elements containing the coupled properties is shown to reasonably account for the moments generated in finite structures. For GEMS filled with a damping treatment, Guyan reduction is shown to capture the internal mechanics of the structure and allow the CPM process to be used. ^ A general method to evaluate the wave propagation characteristics in GEMS has also been developed. The CPM properties are used to establish wave propagation characteristics corresponding to axial, shear, and flexural waves. Due to the repetitive structure of GEMS, periodic structure theory (PST) is expected to predict more complicated behavior, including pass and stop bands. A general method to represent GEMS as a quasi-one-dimensional structure is developed so that a direct transfer matrix approach may be used to determine the propagation constants as a function of frequency. The two theories agree well at low frequencies; while at higher frequencies, PST predicts extremely complicated behavior containing many stop bands and mode shifts. ^