Classical governing equations of a three-layered sandwich beam are generalized with the aim to avoid the necessity of identical arrangement of both face layers at the end of the beam. In this way more shear deformations in the core are allowed for. This may significantly contribute to the increased dissipation of vibratory energy. Estimation of the response of the damped sandwich beam and the loss factor are based on truncated integral modal transformation in which the base functions are the modal data from the associated undamped system. Simple formula expressing the modal loss factor in terms of the portion of strain energy due to shear deformations in the core is developed. Presented approach is in fact a reinterpretation of the concept of damped normal modes in such a way that numerical computations are to be carried out only in the real domain while the previous formulation required numerical treatment in the complex domain.