Application of the Harmonic Balance Method to Centrifugal Pendulum Vibration Absorbers

The harmonic balance method (HBM) is a powerful analysis tool for nonlinear vibrating systems, provided that the forms of the nonlinearities of the system result in a manageable algebraic system of equations. The authors of Cochelin and Vergez (J Sound Vib 324(1):243-262, 2009) created a framework that modifies the structure of the equations of motion involving a wide variety of nonlinearities into a quadratic form, which then can be approximated with HBM with as many assumed harmonics the problem needs for a satisfactory accuracy. In this work, we employ this framework for the analysis of centrifugal pendulum vibration absorbers (CPVA). The crucial step of this framework is the recasting of the variables into the required form. It has been shown that the dimensionless equations of motion for point mass CPVAs with general paths fitted to a rigid rotor can be put into the quadratic polynomial form. Two benchmark problems with known dynamical characteristics are investigated and the results show that this approach provides a powerful tool for investigating steady-state responses of these absorber systems. This will be very beneficial for design evaluations of CPVA systems where parameter values do not allow for the application of perturbation methods and/or make direct simulations very time consuming.