Transverse Modes and Frequencies of Beams Translating between Fixed end Supports

Abstract

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.

Static instability analysis for travelling membranes and plates interacting with axially moving ideal fluid

“…See e.g. Archibald and Emslie (1958), Miranker (1960), Swope and Ames (1963), Simpson (1973), Chonan (1986), Wickert and Mote (1990), Shen et al (1995), Wang (2003), Shin et al (2005), Sygulski (2007), and Kulachenko et al (2007a,b).…”

Analysis of the thermo-elastic vibration for axially moving Euler beam

“…Mote [1] studied the band saw vibrations by regarding it as an axially moving beam and the frequency curves were obtained. Simpson [2] analyzed the natural frequencies and mode curves of the axially moving beam with clamped boundary, his calculated results show that modes distorted violently as the moving speed increases. Moreover, Wickert [3] brought forth that axially moving beam belongs to gyroscopic system and researched the forced vibration of axially moving beam by modal analysis and Green's function method.…”

Vibrations of a continuous web on elastic supports

“…The effects of axial motion of the material on its frequency spectrum and eigenfunctions were investigated for strings by (2) and for beams by (33). It was shown that the natural frequency of each mode decreases when the transport speed increases, and that the travelling string and beam both experience divergence instability at a sufficiently high speed.…”