Prediction of resonant response of blades having 3D nonlinear shroud constraint using multi-harmonic balance method

A 3D shroud contact model is employed for the prediction of the resonant response of blades having 3D shroud constraint. In this study, the bladed system is assumed to be tuned and the assumed blade motion has three components, namely axial, tangential, and radial components. When subjected to cyclic excitation, the constrained force at the shroud contact is often a periodic function and can be considered as a feedback force that influences the response of the shrouded blade. Based on the 3D shroud contact model, an impedance model is developed to evaluate the resulting constrained force. By using the Multi-Harmonic Balance Method along with Fast Fourier Transform, the constrained force can be integrated with the receptance of the tuned blade system so as to calculate the forced response of the system. It results in a set of nonlinear algebraic equations that can be solved iteratively to yield the relative motion at the shroud contact and the associated constrained force. This study shows that due to the variation of contact normal load, both even and odd harmonic components of the constrained force exist. In addition, the internal resonance and the jump phenomenon can be accurately predicted by using the Multi-Harmonic Balance Method.