Fundamental Frequency of Tapered Plates Using Modi ed Modes


Department of Civil Engineering,Amirkabir University of Technology


The fundamental frequency of a rectangular orthotropic plate having an arbitrary thickness
variation is computed by using the method of Modi ed Vibrational Mode (MVM) shapes. The change of
thickness within a plate is characterized by introducing a tapering index. It is shown that the vibrational
mode shapes of a tapered plate is in fact a linear combination of various mode shapes of intact plates.
This phenomenon is used to estimate the vibrational mode shapes of stepped plates. In turn, these mode
shapes are incorporated to evaluate their fundamental frequency. Many numerical analyses are carried
out to represent the accuracy and robustness of the proposed method by comparing the results to the works
presented by other researchers. The major advantage of the present method over the existing ones is its
simplicity for handling the problem of force vibration of tapered plates.