Vibration of Nearly Periodic Structures and Mistuned Bladed Rotors

Abstract

This is the first comprehensive volume on nearly periodic structures and mistuned blade vibration. Alok Sinha presents fundamental concepts and state-of-the-art techniques in the analysis of free and forced response of a nearly periodic structure, weaving together his own work (covering thirty-five years of research in this field) with works by other researchers. He also discusses similarities between tools used in bladed rotor analysis and condensed matter physics. Specific subjects covered include the reasons behind mode localization, the reasons behind amplitude amplification of steady-state response, state-of-the-art computational techniques for mistuned bladed rotors including multistage rotors, identification of mistuning from measured response, vibration localization in linear atomic chains, and analysis of two-dimensional periodic structures.

Key Features of the Transient Amplification of Mistuned Systems

“…Under the cyclic symmetry condition, the vibration modes have harmonic shape, i.e. their j th components are in the form [7] GTP-20-1517 4 Carassale where r is called harmonic index and floor(•) is the rounding towards -. For the cases r=0 and r=N/2 (if N is even), the eigenvector r (s) does not exist.…”

“…Let us assume that the blade motion is entirely described by the mode pair with harmonic index r, i.e. : (7) where the extraction of the real part is required due to the choice of using a complex-valued force in Eq. (4), thus xj and yj are complex valued as well.…”

“…Blade mistuning produces the increment of the dynamic response of some blades when the disk is excited with a resonant or quasi-resonant force. On this matter the literature is vast, and a wide list of references can be found for example in [6] and in the recent monography [7]. Analytical formulations developed in the quasi-steady regime, i.e.…”

Vibration of carbon nanotubes with defects: order reduction methods

“…The two methods of order reduction considered here are MDA and MMDA. While both have been described in detail elsewhere [12][13][14], their application to almost-periodic atomic systems is novel.…”

Nonlinear mode interaction effects in the vibration of bladed-disks

“…For this, a mass-spring model with 3 DOF per sector is used to study the nonlinear modal. This type of models has been successfully used in previous works because of their low computational requirements (Sinha, 2017). The model parameters (elastic, aerodynamic, and friction) are calibrated using actual experimental data from a low-pressure turbine from the FUTURE European project.…”