A transfer matrix method capable of determining the exact solutions of a twisted Bernoulli-Euler beam with multiple edge cracks

In this paper, an improved numerical method is developed to obtain the accurate natural frequencies and mode shapes for the coupled bending vibrations of a twisted Bernoulli-Euler beam with multiple edge cracks, and this method can compute the desired number of natural frequencies by dividing the minimum number of subdivisions for a whole structural element with multiple open edge cracks. The development of a method that can simply and accurately compute the variation of the natural frequencies due to the effect of cracking is possible using the distributed mass, transcendental function, and local coordinate systems varying along the length of a twisted beam. Because the in-plane and out-of-plane bending stiffnesses are coupled in two principal planes by the effect of twisting, each crack is modeled as rotational springs in the in-plane and out-of-plane directions. With these assumptions, the effect of cracking for twisted beams is investigated using a parametric study for the various crack depths and locations.