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This paper first employs and develops an exact wave-based vibration analysis approach to investigate a finite Timoshenko beam carrying periodic two-degree-of-freedom (2-DOF) uncoupled force-moment type resonators. In the approach, vibrations are described as structural waves that propagate along uniform structural elements and reflected and transmitted at structural discontinuities. Each uncoupled force-moment type resonator is considered as a cell which injects waves into the distributed beamdoi:10.3390/cryst10121132 fatcat:piqmvbvrdjbs5dx4vvtiqwm7t4