1Dof spring mass damper system by Michael Alletto

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Introduction

Fluid structure interaction is associated with a multitude of physical phenomena: the stability and response of aircraft wings, the flow through arteries, the vibration of heat exchanger, the vibration of compressor and turbine blades and many more [1]. In order to capture this phenomena accurately, it is important to sorrowfully validate both fluid and structure solvers first separately and after that both together. In this spirit, in this small tutorial we show a small validation case of the six degree of freedom solver of OpenFOAM. This solver is responsible to advance the location of a rigid body subject to fluid forces and restrains like springs and damper in time.

Set up

The next figure shows the setup of the simulation: We have a closed square with a fluid initially at rest. Actually the fluid part does not play a role in this tutorial since we are interested only in the movement of the one degree of freedom spring-mass-damper system. In order to exclude any influence of the fluid force on the movement of the circular cylinder we set the density $\rho$ and the viscosity $\nu$ to zero (actually to a very small value to avoid possible divisions by zero). In this way the pressure force which acts normal to the solid body surface and the shear stress which acts parallel to it do not influence the motion of the cylinder.


The mass m is set to m = 0.03575 kg, the spring constant k of the linear spring is set to k = 69.48 N/m. Two different damping cases are considered. The first one is an undamped system. In the second case the damping constant d is set to d = 0.0039 Ns/m which corresponds to a weakly damped system. For undamped and weakly damped systems the oscillation induced by the fluid on the structure can have potentially disastrous effects. The spring has an initial extension of z0 = 0.0016 m which corresponds to the diameter of the cylinder.

For this configuration we have an analytical solution which we can use to verify our solver:


References

[1] Earl H Dowell and Kenneth C Hall. Modeling of fluid-structure interac- tion. Annual review of fluid mechanics, 33(1):445–490, 2001.