  Recent precise measurements of cosmic ray (CR) spectra show that the energy
distribution of protons is softer than those of heavier nuclei, and there are
spectral hardenings for all nuclear compositions above $\sim$200 GV. Models
proposed for these anomalies generally assume steady-state solutions of the
particle acceleration process. We show that, if the diffusion coefficient has a
weak dependence on the particle rigidity near shock fronts of supernova
remnants (SNRs), time-dependent solutions of the linear diffusive shock
acceleration at two stages of SNR evolution can naturally account for these
anomalies. The high-energy component of CRs is dominated by acceleration in the
free expansion and adiabatic phases with enriched heavy elements and a high
shock speed. The low energy component may be attributed to acceleration by slow
shocks propagating in dense molecular clouds with low metallicity in the
radiative phase. Instead of a single power-law distribution, the spectra of
time-dependent solutions soften gradually with the increase of energy, which
may beresponsible for the "knee" of CRs.
