Due to great importance to define performance, reliability and safety requirements for advanced viscoelastic adhesives, polymers and foams a considerable effort has been devoted to the study of their mechanical material properties and a lot of different identification methods based on vibration tests have been developed in the last three decades. However most of them do not give the possibility to characterise the viscoelastic material properties, when storage and loss moduli are frequency and temperature dependent values. For this reason, a new inverse technique based on simple vibration vibration is developed to characterise the nonlinear mechanical properties of various viscoelastic materials. The present approach allows to preserve the frequency dependence of the storage and loss moduli of viscoelastic materials in a wide range of frequencies and to analyse structures using high damping tests. The computational effort has been substantially reduced by using an optimisation based on the planning of the experiments and the response surface technique in order to minimize the error functional. In the present investigation a universality of the developed technique was demonstrated characterising the viscoelastic material properties of a 3M damping polymer (ISD-112) used as a core material in sandwich panels with different dimensions and boundary conditions. Identification results show that no special geometrical requirements are necessary for tested samples and even some structural components can be used for the unknown viscoelastic material properties characterisation. It is important to note that our current approach, like any other inverse approach based on vibration tests, has a non-destructive character and does not require special specimens for testing. The identified material properties of a sandwich core generally reflect all the features of the technological processes used for the production of the sandwich structures. The inverse technique presented in this work can be applied not only to characterise nonlinear viscoelastic material properties of sandwich layers, but also to identify isotropic, orthotropic, elastic or viscoelastic material properties of various composites and structures due to its universality.