Edge clearance effects on the added mass and damping of beams submerged in viscous fluids

Investigating the Influence of Fluid-Structure Interactions on Nonlinear System Identification

“…The solution of the damped Euler-Bernoulli equation can be represented by an infinite series of separation variables involving space and time functions, ( , ) = ∑ ( ) ( ) ∞ =1 (13) where ( ) represent the generalized modal coordinate or the modal displacement of the beam in the -th mode and ( ) is the normal mode-shape in the -th mode corresponding to undamped free vibration. The corresponding mode shape can be determined from the boundary conditions in which the clamped-free boundary conditions give [26], (0, ) = 0, ′ (0, ) = 0, ′′ ( , ) = 0, ′′′ ( , ) = 0 (14)…”

“…This method is somehow mathematically convenient and extremely useful in modelling techniques without loss of generality. Thus, the modal coordinate can be determined by substituting Equation (13) to Equation (12), multiplying the result by an arbitrary mode shape, W m (x), and integrating from 0 to L based on the orthogonality condition to give…”

“…The correct representation of this problem requires a coupling algorithm capable of representing the mutual forces between fluid and solid whilst preserving the continuity conditions in terms of displacements across the fluid-structure interface [9]. Due to the complex nature of these problems, experiments [5,6,10] and numerical modelling [11][12][13] are the preferred approach, leaving little space for analytical models. Consequently, the optimisation of systems designed around FSI principles is complex and expensive, both in terms of computational resources and time.…”

“…Numerous factors contribute to the generation of damping-e.g., aspect ratio [22,23] and fluid properties [13,24,25]-therefore estimating the exact damping values can be quite challenging. Nonetheless erroneous damping estimations result in considerable errors in the prediction of the dynamic responses, therefore this has been the topic of several research works.…”

“…Nonetheless erroneous damping estimations result in considerable errors in the prediction of the dynamic responses, therefore this has been the topic of several research works. The most common technique for calculating the damping is the quadrature peak picking method [26] (or the half-power point method in [27]) which is largely used in FSI characterisations [13,22,23,25,28]. Some low excited modes can create a distorted peak in the frequency response function which leads to an error in the quadrature peak picking method.…”