Node Sampling for Nonlinear Vibration Analysis of Structures with Intermittent Contact

Bilinear amplitude approximation for piecewise-linear oscillators

“…In this section, the vibration amplitude of a full bladed disk system with piecewise-linear nonlinearity is first calculated using in-house code based on a hybrid frequency/time (HFT) domain solver [25][26][27][28]. Engine order excitation 0 with force amplitude of 1 kN was applied at specified frequencies to obtain forced responses.…”

“…The goal of BAA is to find the steady-state amplitude of vibration of the system when excited by harmonic forcing under the following assumptions: (a) state (3) (partially open) lasts a much shorter time interval than states (1) and (2), (b) the motion of the structure is periodic, (c) during each vibration cycle there is only one time interval when the system is in state (1) and only one time interval when the system is in state (2); thus, one entire vibration cycle is approximated by states (1) and (2), and (d) the motion in state (1) is dominated by one mode of the structure with fully open contact, and the motion in state (2) is dominated by one mode of the structure with fully sliding at the contact surfaces. Assumption (a) is in fact exactly satisfied when the gap at the contacting surfaces is zero for the structure with zero internal stresses [24,27].…”

“…For example, mistuned bladed disks with cracks have piecewise-linear nonlinearity due to the intermittent contact at the crack surfaces. Therefore, to obtain the amplitude of vibration at the resonant frequencies, nonlinear forced responses need to be calculated using more efficient numerical methods (e.g., hybrid frequency/time domain methods) [25][26][27][28].…”

Dynamic Modeling and Projection-Based Reduction Methods for Bladed Disks With Nonlinear Frictional and Intermittent Contact Interfaces

“…For contact modeling in blisks, it is desirable to strike a balance between accurately capturing dominant effects of contact interactions, which are pertinent to blisk dynamics and maintaining feasible simulation times. The modeling method currently preferred for nonlinear blisk simulations [11,46,50,52,61,80,124,[140][141][142][143][144][145][146][147][148] is a penalty-based method, which involves using arrays of local contacts on every surface and approximating the contact effects on small regions around each location. For convenience, the local contact may be described between nodes at the contact surfaces of FE models, as it is easier to obtain the responses of these nodes during calculations.…”

Measurement point selection and modal damping identification for bladed disks

“…An example of such a case is the forcing calibrated by using the procedure proposed by Holland et al 2 Griffin et al 17 found that slightly mistuned system modes can be well represented as a linear combination of tuned system modes. This relationship has been used in studying the effects of crack propagation, [18][19][20] and multi-stage phenomena. 21 Therefore, the optimal measurement locations for a set of tuned system modes of a blisk (in a frequency range of interest) are also the best locations for the slightly mistuned blisk.…”