  The cluster decays $^{228}$Th $\rightarrow \, ^{208}$Pb + $^{20}$O, $^{232}$U
$\rightarrow \, ^{208}$Pb + $^{24}$Ne, $^{236}$Pu $\rightarrow \, ^{208}$Pb +
$^{28}$Mg, $^{242}$Cm $\rightarrow \, ^{208}$Pb + $^{34}$Si are considered in
the framework of the multidimensional cluster preformation model. The
macroscopic potential energy surface related to the interaction between the
cluster and the residue nucleus is evaluated in the framework of the nonlocal
$\hbar^4$ extended Thomas-Fermi approach with Skyrme and Coulomb forces. The
shell-correction to the macroscopic potential energy is also taken into
account. The dynamical surface deformations of both the cluster and the residue
nucleus are taken into consideration at the barrier penetration path. The
heights of saddle points related to deformed nuclear shapes are lower than the
barrier height between the spherical cluster and residue nuclei; therefore the
dynamical deformations of nuclei increase the barrier penetrability and reduce
the half-life of cluster decay. The shell correction contribution into the
potential energy between cluster and residue nucleus is important for both the
potential landscape and the half-life evaluation. The experimental values of
cluster decay half-lives are well reproduced in the model.
