  The heat capacity $C_{p}$ of an array of independent aluminum rings has been
measured under an external magnetic field $\vec{H}$ using highly sensitive
ac-calorimetry based on a silicon membrane sensor. Each superconducting vortex
entrance induces a phase transition and a heat capacity jump and hence $C_{p}$
oscillates with $\vec{H}$. This oscillatory and non-stationary behaviour
measured versus the magnetic field has been studied using the Wigner-Ville
distribution (a time-frequency representation). It is found that the
periodicity of the heat capacity oscillations varies significantly with the
magnetic field; the evolution of the period also depends on the sweeping
direction of the field. This can be attributed to a different behavior between
expulsion and penetration of vortices into the rings. A variation of more than
15% of the periodicity of the heat capacity jumps is observed as the magnetic
field is varied. A description of this phenomenon is given using an analytical
solution of the Ginzburg-Landau equations of superconductivity.
