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The systematic study of isoscalar (IS) and isovector (IV) giant quadrupoleresponses (GQR) in normal and superfluid nuclei presented in [G. Scamps and D.Lacroix, Phys. Rev. 88, 044310 (2013)] is extended to the case of axiallydeformed and triaxial nuclei. The static and dynamical energy densityfunctional based on Skyrme effective interaction are used to study staticproperties and dynamical response functions over the whole nuclear chart. Amongthe 749 nuclei that are considered, 301 and 65 are respectively found to beprolate and oblate while 54 do not present any symmetry axis. For these nuclei,the IS- and IV-GQR response functions are systematically obtained. In thesenuclei, different aspects related to the interplay between deformation andcollective motion are studied. We show that some aspects like the fragmentationof the response induced by deformation effects in axially symmetric andtriaxial nuclei can be rather well understood using simple arguments. Besidesthis simplicity, more complex effects show up like the appearance ofnon-trivial deformation effects on the collective motion damping or theinfluence of hexadecapole or higher-orders effects. A specific study is made onthe triaxial nuclei where the absence of symmetry axis adds further complexityto the nuclear response. The relative importance of geometric deformationeffects and coupling to other vibrational modes are discussed.

Systematic of isovector and isoscalar giant quadrupole resonances in normal and superfluid deformed nuclei