On some problems of choice of the shape function in the tolerance averaging technique in modeling free vibrations of the composite plate resting on elastic foundation

摘要

The paper presents a detailed analysis of the vibration of the composite plate resting on a heterogeneous composite elastic foundation. The plate has a non-uniform geometry, periodic in one direction and functionally graded variable in the second direction. The research method was the tolerance averaging technique. At the stage of modeling, a comparison of the adopted shape function with the exact solution on the cell periodicity was performed. Next, modeling of free vibrations of the plate was conducted. The resulting equations were solved numerically using the finite difference method. It has been shown that, the adapted material of the walls and the matrix, and the assumed shape function, have influence on the accuracy of the solutions. The range of applicability of tolerance averaging technique for selecting a shape function for the analyzed problem was specified.