Natural Frequencies and Mode Shapes of Deterministic and Stochastic Non-Homogeneous Rods
In this study the natural frequencies and mode shapes of the kth order of nonhomogeneous (deterministic and stochastic) rods are found. The solution is based on the functional perturbation method (FPM). The natural frequency and mode shape of the kth order is found analytically to any desired degree of accuracy. In the deterministic it is shown that the FPM accuracy range for the frequency ω and the mode shape is less then 1%. The stochastic case demonstrates the power of this method. The material and geometrical properties will be considered as statistically homogeneous random field with exponential two-point correlation. It is shown that the accuracy depends on the stochastic information used, the correlation distance (roughly the “grain size”), and whether we are interested in the properties of ω or ω2.
Patrick Sean Keogh
S. Nachum and E. Altus, "Natural Frequencies and Mode Shapes of Deterministic and Stochastic Non-Homogeneous Rods", Applied Mechanics and Materials, Vols. 5-6, pp. 207-216, 2006