Free and forced vibrations of damped locally-resonant sandwich beams

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