Nonlinear Vibration Analysis of a Two-Blade System with Shroud-to-Shroud Contact by Using Response-Dependent Nonlinear Normal Modes

Periodic forced response analysis of nonlinear real systems is a computationally demanding task. In order to reduce the computational burden, different approaches are proposed in the literature. The reduced computational effort required for the response-dependent nonlinear normal modes (RDNMs) developed recently, making them suitable for the computation of the steady-state harmonic response of nonlinear systems by employing modal superposition method (MSM). RDNMs are obtained by representing the nonlinear internal forces as a nonlinearity matrix multiplied by the displacement vector using describing function method (DFM). The nonlinearity matrix is considered as a structural modification to the linear system, and RDNMs are calculated by solving the eigenvalue problem of this modified system. However, the solution of a large eigenvalue problem is computationally demanding. Therefore, a further reduction is made by applying the dual modal space method. A detailed study is conducted on the finite element model of a two-blade system having a shroud-to-shroud contact in order to investigate the performance of utilizing RDNMs in MSM. The finite element model of the system is obtained in commercial finite element software, and one-dimensional friction elements with normal load variation are used at the contact interface. Harmonic balance method (HBM) is used to obtain the nonlinear algebraic equations representing the steady-state response of the system which are solved by Newton’s method. Several case studies are performed, and the effect of using different number of RDNMs is studied.