Cluster Frequencies of Continuous Uniform Plates

Abstract

The numerical formulas are presented for quick determination of natural frequencies of orthotropic and isotropic continuous uniform plates. A one‐way continuous plate consists of two types of independent vibration modes in both directions. The transverse mode represents the number of half‐waves across the width of a plate. The longitudinal mode possesses more implicit characteristics, nevertheless it may represent shape distribution across all the panels. It has been noted that the frequencies of continuous uniform plates can be grouped in formation of clusters. The frequency clusters analyzed in this paper are based on the transverse modes. Therefore, each cluster consists of the number of longitudinal frequencies equal to the number of panels or spans in a continuous system. An example of twelve‐span continuous plate and 164 natural frequencies is included. Over sixty percent of the frequencies has error percentage less than 0.01. The maximum error is only 0.044%.