Theoretical Study on the Dynamic Behavior of a Plate-Like Micro-Cantilever with Multiple Particles Attached

In this study, the dynamic characteristics of a plate-like micro-cantilever beam attached with multiple concentrated masses are studied. The vibration modes of the cantilever plate are represented by combinations of beam functions. Using classical mechanics (the effect of size is not considered) and the corrected Cosserat’s theorem (the effect of size is considered), we employ the Lagrange equations to establish a dynamic model of the plate-like micro-cantilever beam attached with multiple concentrated masses. The accuracy of the model proposed in this paper is verified by comparing with the results of published literature. Then, the natural frequencies of the cantilever plates are calculated with self-compiled algorithms, and the results of the plates with 1–5 masses are displayed. The results are in high accordance with the exact solution, and all errors are within 0.5%. The analysis shows that the proposed model and analysis method converges quickly and is highly efficient. In addition, the effects of characteristic lengths, Poisson's ratios and plate thickness on the micro-cantilever plate’s resonant frequency for the first five modes are analyzed.