Aero-/hydro-elastic stability of flexible panels: Prediction and control using localised spring support

Abstract

We study the effect of adding localised stiffness, via a spring support, on the stability of flexible panels subjected to axial uniform incompressible flow. Applications are considered that range from the hydro-elasticity of hull panels of high-speed ships to the aero-elasticity of glass panels in the curtain walls of high-rise building in very strong winds. A two-dimensional linear analysis is conducted using a hybrid of theoretical and computational methods that calculates the system eigen-states but can also be used to capture the transient behaviour that precedes these. We show that localised stiffening is a very effective means to increase the divergence-onset flow speed in both hydro-and aero-elastic applications. It is most effective when located at the mid-chord of the panel and there exists an optimum value of added stiffness beyond which further increases to the divergence-onset flow speed do not occur. For aero-elastic applications, localised stiffening can be used to replace the more destructive flutter instability that follows divergence at higher flow speeds by an extended range of divergence. The difference in eigen-solution morphology between aero-and hydro-elastic applications is highlighted, showing that for the former coalescence of two non-oscillatory divergence modes is the mechanism for flutter onset. This variation in solution morphology is mapped out in terms of a non-dimensional mass ratio. Finally, we present a short discussion of the applicability of the stabilisation strategy in a full three-dimensional system.

Stability of a flexible insert in one wall of an inviscid channel flow

“…For the results at H/L = 2 the eigenvalue solution agrees with that presented in Pitman and Lucey (2009) for the open-flow system which was validated against a Galerkin analysis. The present divergence-onset prediction at Λ F = 40 also agrees with the findings of, for example, Weaver and Unny (1970), Garrad (1982), and Tan et al (2013) thereby validating the present computational modelling and its implementation.…”

“…4 (b). This different sequence of instability transitions has been presented and its physical causes explained in Tan et al (2013) for the corresponding open-flow configuration. What can be concluded from the new results of the present paper is that reducing the channel height does not modify the special solution morphology that applies at very low mass ratios.…”

Dynamic Pressure Analysis of Hemispherical Shell Vibrating in Unbounded Compressible Fluid

“…The velocity of fluid boundary vibration is, u = u s (t). Here, it assumes that |u s | = c. Therefore, the boundary conditions can be rewritten as Equation (6), where, the first term shows that the boundary of fluid is just the position of the shell, and both the second and third terms present that on the boundary of the far field, the velocity and pressure are approximate to the initial condition 0, p 0 , respectively.…”

“…From Equation (10), it is found that the pressure comes from two parts: the local acceleration, which is the velocity changes with respect to time, and the convective acceleration, which is the change in velocity with respect to space. It should be noted that there is only one boundary condition with respect to the pressure as prescribed in Equation (6). Therefore, the pressure at the position of r is an unknown value.…”

“…Such phenomenon is called fluid-structure interaction (FSI) effect. There are some publications in the literature devoted to the interaction of fluid and shell by theoretical approaches [5,6]. In the way of potential flow theory, Minami [7] derived the added mass ratio for a rectangular plate under the assumption that the vibration mode is simple harmonic.…”