Extremal Hysteretic Energy Dissipation in a Dry-Friction Vibration Isolator with a Longitudinally Slit Cylindrical Shell and Deformable Filler

Vibration isolators based on a slit cylindrical shell with an elastic filler are proposed for the needs of the mining, oil and gas, and construction industries; in these devices, energy dissipation is provided by the effects of distributed positional dry friction between the contacting elements. Such vibration isolators are intended to operate under considerable loads and severe dimensional constraints, which requires a combination of high load-bearing capacity, sufficient compliance, and efficient energy dissipation. The aim of this work is an analytical study of hysteretic energy dissipation in the nonconservative contact system “slit cylindrical shell–deformable filler” with dry friction at the contact interface, and the determination of the conditions of maximum energy dissipation. A quasi-static model is developed in which the bending compliance of the slit shell is reproduced by an energetically equivalent orthotropic shell, while the filler is assumed to be elastic and incompressible. An analytical description of the hysteresis loop and an explicit expression for the energy dissipated per cycle are obtained. A nonmonotonic influence of the friction coefficient on energy dissipation is established: as friction increases, the dissipation first grows, reaches a maximum, and then decreases. The extremum is caused by the competition between the growth of the work of the friction forces and the reduction of the region of relative slip. An optimal level of compliance of the contact system is also established. As the depth of the loading cycle decreases, this optimum shifts toward larger values, while the maximum attainable dissipation is reduced. Joint variation of friction and compliance does not produce an isolated interior maximum, but forms an extended region of enhanced energy dissipation. Within a prescribed domain of admissible parameters, the global maximum is attained on its outer boundary. The relationships obtained provide a physically justified analytical basis for the rational design of shell-type vibration isolators, for the construction of numerical models, and for the planning of experimental tests.