VIBRATION ANALYSIS OF STEPPED THICKNESS PLATES

Abstract

Investigation has been made into various approaches for analyzing the vibration of plates with stepped thicknesses. First, attention has been paid to updating a classical approach for the analysis of such problems, correcting the boundary conditions cited in an earlier paper and dealing with the difficulties that can arise when calculating high order modes. Secondly, contribution has been made to improving the classical finite strip method (FSM) by replacing the “static” shape function of the strip element by a “dynamic” function. This leads to the development of a dynamic finite strip method which improves solution accuracy without compromising model size and which therefore is more efficient than the classical FSM. When compared with the finite element method (FEM), which is also considered here, the advantages of smaller model size and higher accuracy of the dynamic FSM are significant. In order to demonstrate the application of the above approaches, the modes of simply supported plates with uniform and stepped thicknesses have been analyzed. From this numerical study, it is noted that the updated classical approach can be used to obtain a solution for any order mode to any specified accuracy and is the most efficient approach considered in the present study. It is also noted that, compared with the FEM of similar solution accuracy, the dynamic finite strip method normally produces a much smaller model size, so that such calculations are significantly more efficient than for the FEM. The aim of this work is to establish methods for the analysis of stepped plates that might be used in optimization studies where speed of formulation and solution are at a premium. There are, of course, a number of other methods that could be used to tackle such problems, but they lie outside the scope of this work; see for example the papers of Liew and co-authors [1, 2].