For narrow band vibration control applications, the alternating stop band characteristics of periodic structures have been widely used. The objective of the present work is to extend this idea for broadband excitations. We seek to synthesize a torsional periodic structure having the largest fraction of the frequencies falling in the attenuation bands of the structure. The unit cell of such a periodic structure is comprised of two distinct regions having different inertial and stiffness properties. Guidelines are derived for suitable selection of inertial and stiffness properties of the two regions in the unit cell, such that the maximal frequency region corresponds to attenuation bands of the periodic structure. It is found that higher the impedance mismatch between the neighbouring regions of the unit cell leads to maximal attenuating frequencies. It is found that more than 98% of the frequencies are blocked in the extreme case. For torsional excitations, it is shown that large, finite periodic structures corresponding to the optimal unit cell derived using the infinite periodic structure theory has significant vibration isolation benefits in comparison to a homogeneous structure or an arbitrarily chosen periodic structure. The periodic structure synthesized has potential applications in marine engines, where long rods are required for power transmission. © INTER-NOISE 2019 MADRID - 48th International Congress and Exhibition on Noise Control Engineering. All Rights Reserved.