Finite Element Vibration Analysis of Cracked Plates in Tension

摘要

A finite element method of analysis is developed to determine the vibration characteristics of an aircraft fuselage panel, containing a fatigue crack. Experimental observations show that as the length of the crack increases, the frequency of vibration reaches a minimum when the free edge of the crack buckles. The variation in this phenomena with increasing plate width is studied both experimentally and theoretically. The analysis is developed in a systematic manner, and calculations are performed, at each stage, on problems with known solutions, in order to determine the accuracy of the method. The problems considered include the vibrations of flat plates of varying platform, the vibrations of a cylindrical shell, the buckling of a rectangular plate, and the vibrations of a rectangular plate in compression. The method is finally applied to the problem of a cracked plate in tension and the results compared with experimental measurements. The post buckling behaviour is calculated using a step-by-step analysis to permit linearisation of the governing equations. By considering the calculated stress distributions, the variation in buckling stress with crack length and plate width is explained. (Author)