Sudden Drop Phenomena in Natural Frequencies of Composite Plates or Panels With a Non-Central (or Eccentric) Stiffening Plate Strip

Abstract

Abstract In this study the free bending vibrations of compsite base plates or panels reinforced by a non-central (or eccentric) stiffening plate strip are considered. The base plate and the stiffening plate strip are dissimilar orthotropic plates. They are connected by a very thin and flexible adhesive layer. The dynamic equations of the entire composite plate system are obtained from the “Mindlin Plate Theory” for orthotropic plates. The set of the governing partial differential equations of the composite plate or panel system are reduced to a set of first order ordinary differential equations by the elimination of the time variable and one of the space variables. This final system of the first order differential equations in one space variable is integrated by the “Modified Version of the Transfer Matrix Method”. It was shown that the natural frequencies, at any mode, of the plate or panel system gradually increase at first with the increasing “Bending Cross Stiffness Ratio”. After then, for certain values of this “Ratio”, the natural frequencies for each mode, suddenly drop to a lower value and subsequently start to go up, although slowly, regardless of the support conditions. This unusual “Sudden Drop Phenomena” is explained in detail and, also, the mode shapes corresponding to the sudden drop are presented. The effect of the “hard” and the “soft” adhesive layer on the “Phenomena” are also shown.