Random Response of Nonlinear System with Inerter-based Dynamic Vibration Absorber

Inerter-based dynamic vibration absorber (IDVA) has been widely used to reduce the responses of vibration systems. Its application to the nonlinear system is underexamined and will be explored. In the present investigation, an IDVA is applied to a randomly excited nonlinear system which is of concern. The random response of the nonlinear system is analyzed by introducing a generalized harmonic transformation and establishing the relationships between the responses of the nonlinear main system and the IDVA secondary system. Numerical results are given to illustrate the applicability and effectiveness of the proposed method. The influences of the parameters of the IDVA, the main nonlinear system, and the excitation on the mean-square displacement response of the nonlinear system are investigated. Furthermore, the suppression effectiveness of the IDVA is discussed in detail. Comparison of the approximate analytical results and simulation results shows that the proposed method is accurate and effective in quite large parameter ranges. Moreover, it is found that the response suppression effectiveness of the IDVA is robust to the main system nonlinearity and to the intensity of the random excitation.