Dynamic Modeling and Analysis of a Temperature-Dependent Axially Translating Functionally Graded Cantilever Beam

In this paper, the dynamics of an axially translating functionally graded cantilever beam (FGCB) with time-varying length are studied under environmental temperature variations. Firstly, the governing partial differential equation for the FGCB under different temperatures is established based on the Euler-Bernoulli beam theory. Secondly, the Galerkin discretization and the assumed mode method (AMM) are employed to derive the vibration equations for each mode. Then, the coupling effects of the axial translation motion and the bending deformation on the vibration response of the FGCB are analyzed through numerical simulation. The results showed that different initial lengths, velocities and accelerations can influence the dynamic response greatly. Moreover, the increase in temperature will increase the response amplitude and decrease the frequency of FGCB, but the increase in functionally gradient parameter will decrease both the amplitude and the frequency of the FGCB. Finally, the wavelet transform (WT) is utilized to perform a time-frequency analysis. It is found that the time-dependent frequency obtained by using WT is consistent with the first-order static frequency obtained theoretically. The variation of frequency with time can be obtained quickly and accurately by using WT. The results of this research are of great significance for the application of composite axially translating beams in practical engineering.