Transient behavior of a cantilever plate subjected to impact loading: Theoretical analysis and experimental measurement

This study employed theoretical analysis and experimental measurements in an exploration of the transient behavior of a cantilever plate subjected to a dynamic impact force. The solution of transient displacement is established as a product of the time function and mode shapes for the cantilever plate. The superposition method was used to obtain the mode shapes and resonant frequencies for free vibrations, and the orthogonality of the mode shapes was used to determine the time function. We demonstrate that the results of transient behaviors including transient displacement, strain, velocity and acceleration of the cantilever plate can be explicitly presented in closed forms. In the experiment, the dynamic external force was produced by the impact of a steel ball on the cantilever plate, and a pair of Polyvinylidene fluoride (PVDF) sensors are used to measure the force history of the impact loading. Fotonic sensor (FS) was also used to obtain the time signals of transient displacement, and PVDF film sensors were used to determine transient strain in the cantilever plate. Our results obtained in the theoretical analysis are highly consistent with experimental measurement and FEM simulations in the time domain. This is a clear demonstration of the effectiveness of pairing theoretical analysis with impact loading histories measured using PVDF sensors in the representation of transient wave propagation behavior in a cantilever plate. Based on the proposed theoretical solution, we established the relationship between transient behaviors and vibrational characteristics that allow us to get more information of the physical phenomenon of the transient response. In transient signal, the contribution of each mode is related to the position of impact point and observation point. The position of exciting force and observation near the nodal lines of particular mode shapes can reduce the contribution of those modes in the transient waveform. We also investigated the influence on the transient response of a cantilever plate subjected to various impact loading duration, and indicate that the amplitude of transient displacement after the release of external force is depended on the impact force duration. Setting the force released at the time of period for specific mode, which provide the maximum contribution, can suppress the amplitude of oscillation in subsequent transient displacement.