Modeling energy transport in a cantilevered Euler–Bernoulli beam actively vibrating in Newtonian fluid

• Simple analytical fluid–structure interaction (FSI) model of an Euler–Bernoulli beam immersed in Newtonian fluid is derived.
• Experimental verification that fluid effects on beam mode shape are negligible.
• The decrease of the coupled natural frequency (added mass effect) is analytically derived and experimentally confirmed.
• Increase in structural damping is experimentally observed while the analytical model proposed incorporates a damping increment due to the fluid.

When a mechanical and/or structural component is immersed in a fluid and it vibrates, the reasonable assumption is that part of the energy is transmitted to the adjacent media. For some engineering applications the energy transport between these two domains, i.e., structure and fluid, plays a central role. The work presented in this paper is focused on discussing the energy transport in beam-like structures as they can be used to represent flexible swimmers (fish-like pulsating mechanisms) in their simplest form. In order to expose the role of each of the fluid and beam properties effecting the energy transfer process, a simplified analytical fluid–structure interaction (FSI) model is derived. After analysis of the resulting coupled-systems' damping coefficient, a new energy transport component is added to the initial Euler–Bernoulli beam equation; a term associated with diffusion (fluid viscosity). In addition our modeling results in an added mass term, a characteristic consistent with previous literature. While deriving the model, an important assumption is made: beam mode shapes are not significantly affected by the domains' interaction. This hypothesis is experimentally tested in two different fluid media and confirmed to be reasonable for the first three vibration mode shapes.