  This paper addresses the dynamics of locally-resonant sandwich beams, where
multi-degree-of-freedom viscously-damped resonators are periodically
distributed within the core matrix. Using an equivalent single-layer Timoshenko
beam model coupled with mass-spring-dashpot subsystems representing the
resonators, two solution methods are presented. The first is a direct
integration method providing the exact frequency response under arbitrary
loads. The second is a complex modal analysis approach obtaining exact modal
impulse and frequency response functions, upon deriving appropriate
orthogonality conditions for the complex modes. The challenging issue of
calculating all eigenvalues, without missing anyone, is solved applying a
recently-introduced contour-integral algorithm to a characteristic equation
built as determinant of an exact frequency-response matrix, whose size is $4
\times 4$ regardless of the number of resonators. Numerical applications prove
exactness and robustness of the proposed solutions.
