Resonance Behaviors of the Plate-Structured Rock with Minute Defects Under the Action of Multiple Types of Excitations

Plate-structured rocks are prevalent in rock engineering applications such as stratified formation and underground gas storage, and the breakage driven by dynamic loads is significantly influenced by resonance. However, the current literature discloses a research gap regarding the theoretical analysis of the natural frequency of porous and cracked rock under vibro-impact conditions. In this study, we develop and verify an analytical model for predicting the natural frequencies of plate-structured rock with minute pores and cracks, thus an idealized solid plate model is available to explore the resonance behaviors. First, Nur’s model is incorporated into the plate vibration model to quantify the porosity effects on the natural frequency of rock. Subsequently, considering the porous rock presented by the micro-CT slice image, the crack propagation resulting from the increasing penetration depth of the cutting tool is visualized by the discrete element method (DEM). The effects of rock porosity and the extent of crack propagation evaluated by porosity on the vibration characteristics of plate-structured rock are explored by employing Nur’s model, and the analytical solutions of natural frequency demonstrate agreement with the finite element method (FEM) simulation results. Next, a forced vibration plate model is used to obtain the amplitude–frequency responses and the distributions of the maximum principal stress under the normal-direction uniform excitations. Finally, the resonance effects of multiple distributions of vibration excitation on the plate model are explored by the FEM. The results indicate that the crack propagation induced by shallow penetration depths exerted a limited influence on the natural frequencies, thereby confirming the engineering applicability of the plate vibration model. Based on the model validation, an idealized solid plate is employed to investigate the resonance behaviors under multi-directional excitations with diverse spatial distributions. The vibration model of the plate demonstrates its extensive applicability and potential in optimizing rock-breaking efficiency in engineering practices.