Theoretical and experimental investigations on the resonance frequency shift characteristic of a ferromagnetic plate

•An analytical model is proposed for the field-dependent resonance frequency of a ferromagnetic plate.•A magnetic traction on the interface between a ferromagnetic material and air is derived.•Model predictions show good agreements with experimental data.•There is a critical angle to divide the positive and negative magnetic stiffness effect.•The critical angle is sensitive to the length-to-thick ratio of the plate.

The theoretical as well as experimental investigations on the resonance frequency shift characteristic of a ferromagnetic plate in an inclined magnetic field are presented. A magnetic traction on the interface between a ferromagnetic material and the air is derived. An analytical model with the nonlinear law of magnetization is proposed for the field-dependent resonance frequency of a ferromagnetic plate. Model predictions show good correlation with the experimental data at different inclined angles. Both the theoretical and experimental investigations show that there exists a critical angle of the inclined field, below which the resonance frequency of the ferromagnetic plate will increase with the magnetic field, and above which the frequency will decrease with increasing the field. The critical angle predicted by the model, which is 86°, is exactly in the range revealed by experiments. Furthermore, the predictions show that the critical angle is sensitive to the length-to-thick ratio of the plate.

Graphical abstractComparisons of the predictions and the experimentally determined resonance frequencies of a F82H plate in an in-plane field.Figure optionsDownload full-size imageDownload as PowerPoint slide