An analytical approach for free vibration and modal reordering response of sandwich beams/panels under in-plane compression

This study systematically investigates the free vibration characteristics of sandwich beams/panels subjected to initial in-plane compressive loads, revealing a novel phenomenon of modal reordering. A new analytical model is developed to accurately characterize the dynamic behavior of sandwich structures under in-plane compressive loading and to determine their natural frequencies. Through dimensional analysis, the study identifies key dimensionless parameters governing the free vibration response, including the thickness ratio, stiffness ratio, and the ratio of compressive load to critical buckling load. The complex interplay among these parameters and their impact on the vibration behavior is subsequently explored in depth. A key finding of this study lies in uncovering the underlying mechanism of modal reordering. The results demonstrate that sandwich beams/panels with larger thickness ratios are more susceptible to mode transitions under compressive loading, while the stiffness ratio dictates the characteristics of higher-order modes prone to transition. As the compressive load increases, the frequency curves of these initially high-order modes progressively approach and eventually intersect with those of lower-order modes, leading to a reordering of the modal sequence, wherein originally high-order modes shift to lower frequencies. However, this phenomenon has largely been overlooked in prior research, primarily due to limitations in experimental studies, where the selection of sandwich structures did not encompass the parameter range necessary to observe modal reordering. Finally, a comparative analysis with experimental data and finite element simulations further validates confirms the accuracy of the theoretical predictions and the existence of the modal reordering phenomenon.