A Modified Nonlinear Modal Synthesis Scheme for Mistuned Blisks with Synchronized Switch Damping

Abstract

In the authors' previous work (MSSP 2017), we show that the synchronized switch damping based on negative capacitor (SSDNC) is a good candidate for vibration suppression of tuned blisks. In this paper, we consider the mistuned case and propose an efficient numerical approach to accelerate the required statistical analysis. Although SSDNC is a type of nonlinear piezoelectric damping, through an in-depth nonlinear modal analysis, we show that the modal information of the system remains unchanged with respect to the nonlinear modal amplitude. Based on this, an accelerated nonlinear component modal synthesis (NCMS) method is proposed to predict and further analyse the dynamic characteristics of the nonlinear system. The precision and efficiency of the proposed method is compared with that of the multiharmonic balance method. The stochastic characteristics of the blisk are studied with two sources of mistuning. The first one is random stiffness mistuning and the second one is capacitance mistuning. The investigation is carried out with different mistuning levels and under different engine-order excitations. The results show that the NCMS method can accurately predict the forced response of the mistuned blisk with SSDNC, and the calculation cost can be considerably reduced. Two advantages of the SSDNC technique applied to the mistuned blisk have been revealed in the statistical view. The first one is that the SSDNC can suppress the amplified vibration induced by the mistuning of the blisk significantly. The second one is that the vibration-suppression performance of SSDNC is insensitive to the mistuning of the blisk and that of the electrical circuits.

Dual-Connected Synchronized Switch Damping for Vibration Control of Bladed Disks in Aero-Engines

“…To solve this nonlinear structural dynamic problem, we employ the multi-harmonic balance method with a few numerical treatments to enhance the convergence. We have developed an in-house code which passes several test cases and has already been applied to analyze local SSDI [28], SSDNC [29] and dry friction dampers [37]. This method is much faster than the numerical integral method such as the Runge-Kutta method or the Newmark method to calculate the steady-state response.…”

“…It basically shares the same frequency band of the local SSDI. As proved in the literature [24][25][26][27][28][29][30][31][32] that the SSDI can work in a relatively wide frequency band thus provides multi-modal damping.…”

Vibration Reduction of Mistuned Bladed Disks Via Piezoelectric-Based Resonance Frequency Detuning

“…Maximizing this voltage inversion then requires choosing a negative capacitance with a magnitude slightly larger than the piezoelectric capacitance; however, as the negative capacitance is an active element, the system becomes unstable if the negative capacitance has a magnitude equal to or less than the piezoelectric capacitance. Citing the performance benefits of the SSDNC approach, Liu et al applied the approach to reduce vibration in tuned and mistuned blisks modeled using lumped-parameter elements [60,61].…”

“…[60] As the switching circuit is nonlinear, they also applied a nonlinear component mode synthesis approach to decrease the computation time required to obtain the steady-state response magnitude. [61] This solution approach enabled a performance analysis of a mistuned blisk via Monte Carlo simulations that showed that SSDNC offered excellent vibration-reduction potential over all engine-order excitations and mistuning strengths tested. 12.…”

A Linearised Analysis for Structures With Synchronized Switch Damping

“…For implementations to complex structures (such as bladed disk in aero-engines), it is much more difficult to carry out experiments. There are also seldom numerical studies [18], [19], because nonlinear dynamic analyses are generally less efficient than the linear ones. The most commonly used numerical tool for steady-state response analysis is Multi-Harmonic Balance Method (MHBM) [20].…”