Fundamental Frequency of Tapered Plates Using Modi ed Modes

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.