  We investigate the nature of transverse kink oscillations of loops expanding
through the solar corona and how can oscillations be used to diagnose the
plasma parameters and the magnetic field. In particular, we aim to analyse how
the temporal dependence of the loop length (here modelling the expansion) will
affect the P1 /P2 period ratio of transverse loop oscillations.
  Due to the uncertainty of the loop's shape through its expansion, we discuss
separately the case of the loop that maintains its initial semi-circular shape
and the case of the loop that from a semi-circular shape evolve into an
elliptical shape loop. The equations that describe the oscillations in
expanding flux tube are complicated due to the spatial and temporal dependence
of coefficients. Using the WKB approximation we find approximative values for
periods and their evolution, as well as the period ratio. For small values of
time (near the start of the expansion) we can employ a regular perturbation
method to find approximative relations for eigenfunctions and eigenfrequencies.
  Using simple analytical and numerical methods we show that the period of
oscillations are affected by the rising of the coronal loop. The change in the
period due to the increase in the loop's length is more pronounced for those
loops that expand into a more structured (or cooler corona). The deviation of
periods will have significant implications in determining the degree of
stratification in the solar corona. The effect of expansion on the periods of
oscillations is considerable only in the process of expansion of the loop but
not when it reached its final stage.
