A METHOD FOR THE VIBRATION ANALYSIS OF BUILT-UP STRUCTURES, PART I: INTRODUCTION AND ANALYTICAL ANALYSIS OF THE PLATE-STIFFENED BEAM

This is the first of two companion papers which collectively present a method for the analysis of built-up structures. One such structure is the machinery foundation of a ship which is constructed from a collection of large beams and flexible plates. The heavy vibration sources are supported by the large stiff beams. The power injected into and the power transmitted around the structure is controlled by long-wavelength waves generated in these beams by the vibration sources. As these long waves propagate along the stiff beams they generate short-wavelength flexural waves in the attached flexible plates. The long waves transmit some of their energy to the short-wavelength waves which therefore damp the long waves. The difference between the wavelengths of the long waves in the stiff beams and the short waves in the flexible plates is often very large. In this case, the short waves present a locally reacting impedance to the long waves at the structural joints. This paper argues that such a condition allows the vibration to predicted in three steps. First, the long-wave response of the stiff beams is analyzed in isolation of the short-wave response of the flexible plates; second, the short-wave response of the flexible plates is analyzed in isolation of the long-wave response; third, the two separate responses are combined to yield the response of the complete structure due to both the long and the short waves. The method is applied to a simple plate-stiffened beam consisting of a directly excited stiff beam attached to a large flexible plate which is broadly representative of the machinery foundation. The method predicts the frequency response of the plate-stiffened beam which compares well with laboratory measurements, thereby supporting the method. In this paper, all three steps are performed analytically which restricts the method to geometrically simple structures. The companion paper presents a hybrid numerical/analytical implementation which accommodates geometrically more diverse structures.