Harmonic and transient torsional responses of a laminated circular disc (or a laminated circular cylinder), caused by torques applied on both ends of the disc, is investigated with use of a continuous analysis. By the analysis, the difficulty brought about by multitudinous reflections and transmissions, taking place at the interfaces of the laminated medium, can be bypassed. The continuous analysis is based on the recognition that stresses at periodic locations in a periodic structure must vary smoothly; therefore these discrete values as a whole approximately form a continuous function, which can be treated analytically. Via the analysis, it is concluded that the real, heterogeneous laminated disc can be modelled into a homogeneous, effective one. The corresponding effective solution provides accurate or exact values of displacements and stresses at the periodic locations of the laminated disc. The density of the effective disc is not a geometric-material constant; it depends on, among others, the frequency and other vibration parameters in the problem. Numerical results are given to validate the analysis.

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