A hybrid analytical/numerical solution method is developed that permits the efficient evaluation of eigensolutions for a vibration beam with an arbitrary finite number of transverse open cracks. The method utilizes a numerical implementation of a transfer matrix solution to an analytical form of the equation of motion. The dimension of the matrix is independent of the number of cracks in this method. The proposed methods are used to solve the beam vibration problems with multiple open cracks. By using the proposed method in this article, the eigensolutions of the beam with multiple cracks can be obtained easily. The results show that the variations on eigenvalues are more sensitive when only a few cracks exist. As the number of the cracks N increases, the dynamic behavior becomes more and more insensitive. This method is used to decrease the dimension of the matrix involved in the finite element method and some other analytical methods.
All Science Journal Classification (ASJC) codes
- Condensed Matter Physics
- Acoustics and Ultrasonics
- Mechanics of Materials
- Mechanical Engineering