Dynamics of periodically stiffened structures using a wave approach

Sen Gupta, Gautam (1970) Dynamics of periodically stiffened structures using a wave approach. University of Southampton, Doctoral Thesis.

Record type: Thesis (Doctoral)

Abstract

The vibrations of beams and plates, periodically stiffened in one or two directions, have been analysed in terms of free flexural wave groups. The normal modes of finite periodic beams, skin-stringer structures and "doubly periodic structures" (i.e. structures consisting of the repetition of a basic unit which is a periodic structure in itself) have been studied in these terms, utilising the concept of an equivalent internal restraint. Natural frequencies of finite structures of this type are readily determined from the wave propagation constant curves. The free propagation zones of doubly periodic structures exhibit a somewhat doubly periodic pattern. Theorems relating to the free flexural waves and their propagation constants have been developed and relationships with the transfer matrix theory established. Two orthogonal free wave groups have been identified for simple rib-skin structures. The knowledge of these waves is useful in understanding the mechanism of coincidence excitation of these structures due to convected random pressure fields. Two dimensional structures such as orthogonally stiffened plates have been found to possess an infinite number of discrete propagation constants at a given frequency. Both free and forced plane wave propagation across the structure have been studied, the direction of propagation being varied. A preferred direction is shown to exist, along which the free propagation zone is widest and the vibration response is greatest. This study has also led to the development of an approximate method of determining the natural frequencies of skin stringer structures, allowing for the frame torsional stiffnesses

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