VIBRATION ANALYSIS OF STEPPED THICKNESS PLATES

Investigation has been made into various approaches for analyzing the vibration of plates with stepped thicknesses. First, attention has bee n paid to updating a classical approach for the analysis of such probl ems, correcting the boundary conditions cited in an earlier paper and dealing with the difficulties that can arise when calculating high ord er modes. Secondly, contribution has been made to improving the classi cal finite strip method (FSM) by replacing the ''static'' shape functi on of the strip element model by a. ''dynamic'' function. This leads t o the development of a dynamic finite strip method which improves solu tion accuracy without compromising model size and which therefore is m ore efficient than the classical FSM. When compared with the finite el ement method (FEM), which is also considered here, the advantages of s maller model size and higher accuracy of the dynamic FSM are significa nt. In order to demonstrate the application of the above approaches, t he modes of simply supported plates with uniform and stepped thickness es have been analyzed. From this numerical study, it is noted that the updated classical approach can be used to obtain a solution for any o rder 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 calculation s are significantly more efficient than for the FEM. The aim of this w ork is to establish efficient methods for the analysis of stepped plat es that might be used in optimization studies where speed of formulati on and solution are at a premium. There are, of course, a number of ot her methods that could be used to tackle such problems, but they lie o utside the scope of this work; see for example the papers of Liew and co-authors [1,2]. (C) 1997 Academic Press Limited.