Abstract <p>A mathematical two-level model of functioning of an innovative disc piezoelectric fiber FibrCD actuator in the form of a thin ring coil with a large number of turns of a flexible piezoelectric “signal” cable of small diameter with electrode outputs for connecting a control voltage has been developed. The piezoelectric layer of the cable has radial polarisation and is located between the core and the shielding electrode. Multiple cable turns are interconnected by polymer binder to form monolithic FibrCD actuator with composite fibrous structure. The elementary volume of the fibrous structure of the FibrCD actuator is characterized by a hexagonal cell of periodicity: a composite fiber piezoelectric cable in the center of a regular hexagonal prism. The finite element method calculated inhomogeneous electric and deformation fields in the periodicity cell and numerical values of all independent effective transversal-isotropic characteristics of elastic and piezoelectric properties of the composite fibre structure of the FibrCD actuator based on solutions of boundary value problems of electroelasticity for a representative fragment of the periodic structure in various simple cases of its electromechanical macroload. The found effective characteristics of the composite were used in setting at the “macro level” and exact analytical solution of the boundary value problem of the thermoelasticity theory for deformation fields of an extremely thin homogeneous disc (ring) of a FibrCD actuator with cylindrical anisotropy of transversal-isotropic effective properties, when the curvilinear axis of symmetry of these properties is directed along the circular coordinate within the thermoanalogy approach. Calculation and numerical analysis of deformation fields and operating characteristics of the circular FibrCD actuator were performed at various values of the ratio of its inner and outer radii. It was revealed that the presence of cylindrical anisotropy of the effective properties of the circular FibrCD actuator causes not only piezoelectric deformations at its “macro level,” but also a self-balanced stress state, even in the absence of fixing the outer circular contours of the circular FibrCD actuator when the control voltage is connected to the outputs of its electrodes. Dependences of operating characteristics: displacements and blocking stresses, respectively, on free or fixed contours of circular FibrCD-actuator from values of ratio of its internal and external radii are obtained. The reliability of the obtained analytical solutions is confirmed by comparing the radial displacement field of the extremely thin circular FibrCD actuator with the diagram of the displacement field according to the finite element method for the case of its free circular contours under the action of the control voltage.</p>