We investigate giant resonances of spherical nuclei on the basis of the Argonne V18 potential after unitary transformation within the Similarity Renormalization Group or the Unitary Correlation Operator Method supplemented by a phenomenological three-body contact interaction. Such Hamiltonians can provide a good description of ground-state energies and radii within Hartree-Fock plus low-order many-body perturbation theory. The standard Random Phase Approximation is applied here to calculate the isoscalar monopole, isovector dipole, and isoscalar quadrupole excitation modes of the 40Ca, 90Zr, and 208Pb nuclei. Thanks to the inclusion of the three-nucleon interaction and despite the minimal optimization effort, a reasonable agreement with experimental centroid energies of all three modes has been achieved.