Eigenfrequencies of tapered rectangular plates with intermediate line supports

Abstract

The free vibrations of a wide range of tapered rectangular plates with an arbitrary number of intermediate line supports in one or two directions are investigated. The domain of the plate is bounded by x = αa, a (0 ≤ α < 1) and y = βb, b (0 ≤ β < 1) in the rectangular co-ordinates. The thickness of the plate is continuously varying and proportional to a power function xsyt. A variety of tapered rectangular plates can be described by giving the taper factors s and t various values. The intermediate line supports run parallel to the edges of the plate. A new set of admissible functions, which are the static solutions of the tapered beam with intermediate point supports, or a strip taken from the plate structure in one or the other direction under a Taylor series of loads, is developed. Consistent convergency independent of the truncation factors α and β of the plate can be obtained by taking the midpoint of the beam as the expanding point of the Taylor series. Unlike conventional admissible functions, this set of static beam functions can appropriately vary with the thickness variation of the plate. The eigenfrequency equation of the plate is derived by the Rayleigh-Ritz approach. A general computer program has been compiled. It can be seen that the convergency of the numerical computation is very rapid and that the first few eigenfrequencies can be obtained with good accuracy by using only a small number of terms of the static beam functions. Sets of first-time reported eigenfrequency data are included for future reference.