Transverse Vibration Response and Time-Varying Analysis of Axially Moving Beams Based on Choi–Williams Distribution

Cantilever beams with axial extension and contraction functions as time-varying parameter systems have attracted extensive research due to their prevalence in engineering structures. In this paper, the dynamic characteristics of the flat-push bridge mechanism are investigated from the theoretical aspect, firstly, it is simplified into a cantilever beam model with axial motion, and the transverse vibration equations of the cantilever beam are established based on the Euler–Bernoulli beam theory and D’Alembert’s principle, and the transverse displacements of the beam are discretized using the Galerkin truncation method and solved numerically by using the Newmark-[Formula: see text] method for the second-order vibration differential equations with variable coefficients; second-order vibration differential equations were solved numerically by the Newmark-[Formula: see text] method; then the structural examples in the existing literature are verified numerically, and the calculation results are consistent with the literature results, indicating that the transverse vibration equations derived in this paper are solved effectively; then a parametric analysis of the speed of the cantilever beam during axial extension/contraction was done, which showed that the faster the speed of axial motion, the faster the rate of change of the dynamic characteristics of the beam and the more pronounced the vibration; finally, the power signal is decomposed in the time-frequency domain by using the Choi–Williams Distribution (CWD), and the time-frequency characteristics of the system under different speeds are analyzed, and the results show that the use of CWD technique can accurately reflect the system’s transient vibration frequency and vibration energy with the change rule of time and speed, and the axial motion speed of ±0.05[Formula: see text]m/s, the transient frequency of the theoretical prediction and the average relative deviation between the finite element modal frequencies are kept within 5% and the recognition accuracy is high. This analysis provides flexible technical guidance for vibration control in engineering structures.