Tuned nonlinear spring-inerter-damper vibration absorber for beam vibration reduction based on the exact nonlinear dynamics model

Abstract

Nonlinear vibration absorbers have been extensively investigated for passive vibration control, motion isolation, and synchronous energy harvesting. This paper studies the exact nonlinear dynamics of a simply-supported beam carrying a nonlinear spring-inerter-damper energy absorber for primary resonance vibration reduction. The nonlinear governing equations of the system are derived from the energy method by considering the midplane stretching, structural discontinuity, and nonlinear boundary conditions at the spring-inerter-damper location of the beam and directly solved using the method of multiple scales. The nonlinear frequency correction factor, frequency response function, peak nonlinear frequency response, and bifurcation frequency are obtained and investigated for various system parameters. The influence of the location, spring stiffness, inertial mass, and damping of the nonlinear vibration absorber on the beam dynamics, including natural frequency, mode shape, and nonlinear frequency response, are studied. The stiffness and mass of the nonlinear vibration absorber are optimally tuned to minimize the peak nonlinear frequency response of the beam. The results show that ignoring the nonlinear boundary conditions at the spring-inerter-damper location could lead to serious underestimation of the nonlinear frequency responses. The nonlinear stiffness of the vibration absorber enhances the system nonlinearity but has no contribution to the peak nonlinear frequency response of the beam. Increasing the damping of the vibration absorber could effectively mitigate the beam vibration. When the nominal frequency of the absorber is tuned to be close to the natural frequency of the beam, the beam vibration is mostly reduced.