Free vibration and stability of a cantilever beam attached to an axially moving base immersed in fluid

• Modeling of cantilever beam attached to an axially moving base in fluid is given.
• Coordinate transformation is introduced to fix the boundaries.
• Vibration and stability of the cantilever beam are studied by Galerkin method.
• Stability boundaries are obtained by numerical analysis.

Free vibration and stability are investigated for a cantilever beam attached to an axially moving base in fluid. The equations of motion of the slender cantilever beam affiliated to an axially moving base at a known rate while immersed in an incompressible fluid are derived first. An “axially added mass coefficient” is taken into account in the obtained equations. Then, a coordinate transformation is introduced to fix the boundaries. Based on the Galerkin approach, the natural frequencies of the beam system are numerically analyzed. The effects of moving speed of the base and several other system parameters on the dynamics and stability of the beam are discussed in detail. It is found that when the moving speed exceeds a certain value the beam becomes unstable and the instability type is sensitive to the system parameters. When the values of system parameters, such as mass ratio and axially added mass coefficient, are big enough, however, no instabilities are detected. The variations of the lowest unstable critical moving speed with respect to several key parameters are also investigated.