Coupled Axial and Transverse Vibration in Two Dimensions

Abstract

For a vibrating beam, bending and rigid body motion are the primary components of the overall behavior. Therefore, it may be sufficient to use a single degree of freedom model or a linear transverse model such as the Euler-Bernoulli, Rayleigh, shear, or Timoshenko model. A discussion of linear transverse models can be found in Chapter 3. The linear transverse models assume that the coupling between the transverse and the axial motion is negligible. However, the coupling becomes more significant with increasing slenderness ratio (the ratio of length to the radius of gyration of the cross-sectional area). Therefore, the nonlinear coupling effect in long slender members of compliant towers may be important in the overall response. It has also been observed that there are significant high frequency nonlinear effects that appear to be caused by extensional or longitudinal vibration in some cases in an ocean environment. Therefore, it is necessary to investigate the couple transverse and longitudinal response of a beam under realistic environmental forces.