# Nonlinear Vibration Analysis of a Two-Blade System with Shroud-To-Shroud Contact by using Response Dependent Nonlinear Normal Modes

2024-1
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, make 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 are studied.
42nd IMAC, A Conference and Exposition on Structural Dynamics, 2024
Citation Formats
T. Ahi, E. Ciğeroğlu, and H. N. Özgüven, “Nonlinear Vibration Analysis of a Two-Blade System with Shroud-To-Shroud Contact by using Response Dependent Nonlinear Normal Modes,” presented at the 42nd IMAC, A Conference and Exposition on Structural Dynamics, 2024, Orlando, USA, 2024, Accessed: 00, 2024. [Online]. Available: https://hdl.handle.net/11511/108705.