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In this paper, the effects of high-static low-dynamic stiffness (HSLDS) isolators on the supports of a continuous rotating shaft for vibration control of a rotary system under mass eccentricity force are investigated. The rotating shaft is modeled using the Euler–Bernoulli beam theory. HSLDS isolators have a linear damping and linear and nonlinear (cubic) equivalent stiffness. Isolators are positioned on the supports of the rotating shaft, so that their forces are applied in radial directions. Equations of motion are extracted using the extended Hamilton principle and they are analyzed using the multiple scale method; then, the steady-state solutions and stability are studied. The effects of variations in linear and nonlinear parameters of the isolators on the static load bearing, resonant peak, frequency band of isolation and hardening nonlinearity are considered, in order to design an appropriate HSLDS isolator and to set its parameters in an optimal way. Investigating the effects of the cubic stiffness and damping values on bifurcations of the system, one may observe that inappropriate setting of these parameters causes strong or weak nonlinearity in the system and, consequently, HSLDS isolators perform less effectively than a linear one does. Then, the results are verified through analyzing the time history of the rotary system under study.

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