  We present simulations of a circular cylinder undergoing vortex-induced
vibration in-line with a free stream in conjunction with a theory for the fluid
dynamics. Initially, it is shown that increasing the Reynolds number from 100
to 250 results in a 12-fold increase of the peak response amplitude at a fixed
mass ratio of $m^*=5$. Subsequently, $m^*$ is varied from 2 up to 20 at a fixed
Reynolds number of 180. The response amplitude as a function of the reduced
velocity $U^*$ displays a single excitation region with peak amplitudes of
approximately 1\% of the cylinder diameter, irrespectively of the $m^*$ value.
The vibration is always excited by the alternating shedding of single vortices.
We develop a new model for the in-line fluid force, which comprises an inviscid
inertial force, a quasi-steady drag, and a wake drag induced by vortex
shedding. Our analysis shows that the wake drag appropriately captures a
gradual shift in the timing of vortex shedding in its phase variation as a
function of $U^*$ while the magnitude of the wake drag displays a resonant
amplification within the excitation region. We use the theory to illustrate why
peak amplitudes, which occur when the vibration frequency is equal to the
structural frequency in still fluid, do not depend on $m^*$, in agreement with
our simulations as well as previous experiments at Reynolds numbers higher than
considered here. This new theory provides physical insight which could not be
attained heretofore by employing semi-empirical approaches in the literature.

Fluid Dynamics