On the couple dynamics of wall-mounted flexible plates in tandem

Abstract

The dynamics of two rectangular, flexible plates of low aspect ratio $h/b$ (height/width = 4) was experimentally investigated in tandem arrangements under uniform flows at various Cauchy numbers $Ca=\unicode[STIX]{x1D70C}_{f}bU_{0}^{2}h^{3}/(EI)\in [15,77]$ (where $\unicode[STIX]{x1D70C}_{f}$ is the fluid density, $U_{0}$ is the incoming flow velocity, $E$ is the Young’s modulus and $I$ is the second moment of the area) and spacings $s_{x}=\unicode[STIX]{x0394}x/h=0.5$, 1 and 2. Planar particle image velocimetry (PIV) and particle tracking velocimetry (PTV) were used to characterize the surrounding flow field and oscillations of the wall-mounted structures. Results show that the oscillations of the upstream plate were dominated by its natural frequency. However, the motions of the downstream plate were significantly modulated by the induced flow and coherent motions shed from the upstream structure. Such modulation led to highly correlated motions between the plates with similar amplitude in the case $s_{x}=0.5$, to comparatively larger oscillation amplitude of the downstream plate in the intermediate separation $s_{x}=1$, and roughly decoupled interaction for $s_{x}=2$. Despite that the intensity of the oscillations of the upstream plate increased monotonically with $Ca$, this was not the case for the downstream plate at $s_{x}=1$ and 2 due to flow fluctuations, vortex shedding and large structure deformation; as a result, it exhibited a local minimum. Supported with measurements, a mathematical model was derived to quantitatively explain this behaviour.