Transverse Modes and Frequencies of Beams Translating between Fixed end Supports

The effects of longitudinal steady translational motion on the vibration frequencies and modes of simple Euler beams are outlined. An example shows that the natural frequencies decrease monotonically with increasing translation velocity, while the mode shapes are complex, indicating significant phase disparities from point to point across the span. Divergence is shown to occur when the translation velocity is greater than the fundamental flexural wave propagation velocity.

More general equations of motion, governing the translating Timoshenko beam under axial loading, are derived in Appendix 1.