Comparisons of matched interface and boundary (MIB) method and its interpolation formulation for free vibration analysis of stepped beams and plates

This work conducts a comparison study of matched interface and boundary (MIB) method and its interpolation formulation for free vibration analysis of stepped beams and plates. Two types of schemes are used to describe the relations between interfaces and grid points in one-dimensional and two-dimensional domains. In the first scheme, the interfaces are located on grid points, while, in the second scheme, the interfaces lie between grid points. Detailed procedures of MIB and the interpolation formulation of MIB (IMIB) are presented in these two schemes. Based on the in-depth understanding of MIB, a new algorithm is also developed to deal with cross derivatives of interface conditions of plates with interfaces lying between grid points to improve the accuracy. Various examples of stepped beams and plates are chosen to illustrate the performance of MIB and IMIB. This research work reveals that on the whole, MIB and IMIB are equivalent in the solutions of eigenvalues of beams and plates. However, some differences can also be observed for very large computational bandwidths. Some important conclusions are drawn at the end of this study.