A cylinder of mass \(m\) is mounted in a water tunnel as shown in Figure 2.79 with the cylinder axis transverse to the flow direction. When there is no flow, a vertical force of \(F_{\text {static }}\) on the cylinder results in a deflection of \(x\). With flow in the tunnel, shedding vortices impart alternating forces on the cylinder. The velocity of the water is \(v\) in the \(x\) direction, the distance between vortices is \(d\), and the magnitude of the lateral forces is \(F_{v}\). The lateral forces can be modeled by the harmonic function \(F(t)=F_{v} \sin \omega t\). Find the amplitude of lateral steady-state response of the cylinder.

Transcribed Image Text:

m Figure 2.79: Cross section of an elastically mounted cylinder in fluid flow, excited by shedding vortices.