Vibration Analysis of a Variable Thickness Kirchhoff rectangular Plate Using Modified Wave Method

In this contribution, based on Kirchhoff plate theory, natural frequencies and mode shapes of an arbitrary variable thickness rectangular plate in one direction with two opposite edgessimply supported is investigated by employing a semi-analytical method referred to as modified wave method (MWM). The plate is partitioned into several continues segment withconstant thickness, for which there exists exact analytical solution. By using continuity condition,the waves entering a segment in positive and negative directions are calculated in terms of waves that entered in first segment. By satisfying boundary conditions, characteristicequations are achieved and all natural frequencies and mode shapes are computed. For validatingthe proposed technique, the results are compared with the investigations available on the technical literature. The results reveal that the introduced technique is highly accuratewhich is applicable for plates with two opposite edges simply supported, and two other edge can have any combination of simply (S) and clamped (C) boundary conditions, while also the frequencies of plate are obtained by lower numbers of segments, because all segments are solved analytical.

Keywords:

vibration , variable thickness plate , semi-analytical , modified wave method