Vibration control of a pre-twisted rotating beam with nonlinear bi-stable attachments

The influence of the nonlinear bi -stable attachment on the vibration suppression of a pre-twisted rotating cantilever beam is investigated in this study. The kinetic and potential energies of the system, comprising a pre-twisted rotating Euler-Bernoulli beam and the nonlinear bi -stable attachments, are obtained, and the equations of motion are derived using the Rayleigh-Ritz method. The natural frequencies and mode shapes of the beam (without the attachments) obtained using the present formulation are validated with the results obtained from Ansys. Subsequently, the flapwise vibration control of the pre-twisted rotating beam subjected to a base excitation is studied. A parametric study is performed for various amplitudes of base excitation, rotational speeds, and the number and position of the bi -stable attachments. Results show significant vibration suppression capabilities of the nonlinear attachments, and hence the proposed system could potentially be used for rotating beam-type structures such as wind turbine blades.