Wave propagation in periodically stiffened plates and shells

Bardell, Nicholas Simon (1990) Wave propagation in periodically stiffened plates and shells. University of Southampton, Doctoral Thesis.

Abstract

This work investigates how the vibration-transmission characteristics of periodically stiffened plates and shells might be exploited to reduce propfan-induced noise and vibration in the fuselage cabins of civil aircraft. Initially, steady state harmonic wave propagation is considered in stringer-stiffened and frame-stiffened cylinders. Generality of stringer and frame section is allowed. Both types of structure are analyzed as one-dimensional periodic systems. Exact, closed-form relationships are established between the frequency and the propagation constants. Computed values are presented in graphical form, and clearly show the existence of distinct frequency stop and pass bands. The phase constant part of these curves is used to deduce the natural frequencies and normal modes for a number of specific structures. Provision is made for the inclusion of hysteretic damping. Steady state harmonic wave propagation is then considered in orthogonally stiffened plates and shells. Although the vibration modes and waves of these structures do not admit closed-form, exact solutions, approximate modes and frequencies can be deduced using energy methods. Both types of structure are therefore analyzed as two-dimensional periodic systems by using wave propagation techniques in conjunction with the hierarchical finite element method. Results are presented in the form of phase constant surfaces plotted against frequency. In general, wave propagation is found to commence at zero frequency; at higher frequencies a large number of overlapping pass bands are found to occur. However, a small frequency stop band has been identified for the orthogonally stiffened cylinder in which predominantly flexural waves cannot propagate. Experimental work conducted on two differently stiffened cylinders provides additional substantiation to the theoretical analyses.

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